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Physics and motion questions, answered
Force, energy, work and power, velocity and acceleration, momentum, torque, projectiles, waves and optics.
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Acceleration Calculator
What is the formula for acceleration?
Acceleration equals the change in velocity divided by time: a = (v - u) / t, where u is initial velocity, v is final velocity, and t is the time interval. Rearranging gives v = u + at to find final velocity, u = v - at to find initial velocity, and t = (v - u) / a to find time.
What are the units of acceleration?
The SI unit of acceleration is metres per second squared, written m/s2. This means for every second that passes, velocity changes by that many metres per second. Gravitational acceleration on Earth is approximately 9.81 m/s2.
Can acceleration be negative?
Yes. Negative acceleration, sometimes called deceleration, means the object is slowing down. If a car goes from 30 m/s to 0 m/s in 10 seconds, the acceleration is (0 - 30) / 10 = -3 m/s2. The negative sign indicates the velocity decreased over the time interval.
Acceleration Due to Gravity Calculator
What is the acceleration due to gravity on Earth?
The standard acceleration due to gravity on Earth is 9.807 m/s² (often rounded to 9.8 m/s² or 9.81 m/s²). This is the rate at which any object accelerates toward Earth's surface in free fall, ignoring air resistance. It varies slightly by location: it is slightly weaker at the equator (9.780 m/s²) due to Earth's rotation and equatorial bulge, and slightly stronger at the poles (9.832 m/s²). The value 9.807 m/s² is the internationally defined standard gravity.
How do you calculate acceleration due to gravity from mass and radius?
Gravitational acceleration is calculated using Newton's law of gravitation: g = GM/r², where G is the gravitational constant (6.674 x 10^-11 N m²/kg²), M is the mass of the planetary body in kilograms, and r is the radius of the body in metres. For Earth, this gives g = (6.674 x 10^-11 x 5.972 x 10^24) / (6.371 x 10^6)² = 9.82 m/s² (very close to the standard 9.807 m/s²; the small difference is because standard gravity also accounts for Earth's rotation). The same formula applies to any body, so you can calculate the surface gravity of the Moon, Mars, or any planet.
How far does an object fall in free fall?
The distance an object falls from rest under gravity is given by d = ½gt², where g is gravitational acceleration and t is the time in seconds. This calculator uses the pure Newtonian value g = GM/r² of approximately 9.820 m/s² for Earth, so after 1 second an object falls 4.91 m, after 2 seconds 19.64 m, and after 3 seconds 44.19 m. The velocity at any point is v = gt, so after 3 seconds on Earth the velocity is 29.46 m/s (106.1 km/h). These equations assume no air resistance.
Air Force PT Calculator (USAF PFA Score)
How is the USAF PFA composite score calculated?
The US Air Force Physical Fitness Assessment (PFA) composite score is a weighted average of three components: the 1.5-mile run (60% weighting), push-ups (20% weighting), and sit-ups (20% weighting). Each component is first scored on a 0 to 100 scale against age- and gender-specific tables. The composite is then computed as: composite = (run score x 0.6) + (push-up score x 0.2) + (sit-up score x 0.2). A composite of 90 or above is Excellent, 75 to 89.9 is Satisfactory, and below 75 is Unsatisfactory.
What is a passing score on the Air Force PT test?
To pass the USAF Physical Fitness Assessment you need a composite score of 75 or above and you must achieve at least the minimum score in each component (a component minimum failure results in an overall Unsatisfactory regardless of composite total). Scores of 75 to 89.9 are rated Satisfactory, and scores of 90 or above are rated Excellent. Airmen who score Unsatisfactory are required to retest and may face administrative action.
How often do Air Force members take the PT test?
Active duty US Air Force members are required to take the Physical Fitness Assessment once every 12 months if they score Excellent or Satisfactory (above 90 or 75 to 89.9), or every 6 months if they have previously received an Unsatisfactory. Reserve and National Guard members typically test once per year. Members on certain medical waivers or profiles may have components omitted or replaced with alternative assessments.
Allele Frequency Calculator
How do you calculate allele frequency from genotype counts?
To find the frequency of allele A (called p), count all the A alleles in the population and divide by the total number of alleles. Each AA individual contributes 2 A alleles, each Aa individual contributes 1 A allele, and each aa individual contributes 0 A alleles. The formula is: p = (2 x count_AA + count_Aa) / (2 x total individuals). The frequency of allele a (called q) is simply q = 1 - p, because all allele frequencies in a two-allele system must sum to 1.
What is Hardy-Weinberg equilibrium and when does it apply?
Hardy-Weinberg equilibrium (HWE) describes a theoretical state in which allele and genotype frequencies remain constant from generation to generation. It applies when five conditions are met: the population is very large (no genetic drift), mating is random (panmixia), there is no mutation, there is no migration into or out of the population, and there is no natural selection. Under these conditions, genotype frequencies are predicted by p squared (AA), 2pq (Aa), and q squared (aa). Real populations rarely satisfy all conditions perfectly, so departures from HWE can reveal evolutionary forces at work.
What does a significant chi-square result for Hardy-Weinberg equilibrium mean?
A significant chi-square result (p-value below 0.05, or chi-square above 3.84 with 1 degree of freedom) means the observed genotype counts differ from what Hardy-Weinberg equilibrium predicts more than would be expected by chance alone. This suggests the population may not be in HWE, which can indicate non-random mating (inbreeding or assortative mating), natural selection acting on the locus, recent migration, or a founder effect or population bottleneck. It can also result from genotyping error. The chi-square test requires expected counts of at least 5 per genotype class for reliable results.
Angular Acceleration Calculator
What is angular acceleration?
Angular acceleration is the rate at which an object's angular velocity changes over time. It is denoted by the Greek letter alpha (α) and measured in radians per second squared (rad/s²). A positive value means the object is spinning faster; a negative value (deceleration) means it is slowing down. The formula is α = Δω / t, where Δω is the change in angular velocity in rad/s and t is the elapsed time in seconds.
How do you calculate angular acceleration from torque?
Angular acceleration can also be found using Newton's second law for rotation: α = τ / I, where τ (tau) is the net torque applied in newton-metres (N·m) and I is the moment of inertia of the object in kilogram-metres squared (kg·m²). This is the rotational equivalent of the linear formula a = F / m. For example, a net torque of 50 N·m applied to a flywheel with a moment of inertia of 10 kg·m² produces an angular acceleration of 5 rad/s².
What is the difference between angular velocity and angular acceleration?
Angular velocity (ω) describes how fast an object is rotating at a given instant, measured in radians per second (rad/s) or revolutions per minute (rpm). Angular acceleration (α) describes how quickly that rotation rate is changing, measured in rad/s². A constant angular velocity means zero angular acceleration, just as a constant linear speed means zero linear acceleration. When a motor spins up from rest to full speed, angular acceleration is positive during that spin-up period and returns to zero once the target speed is reached.
Angular Frequency Calculator (omega = 2πf)
What is the formula for angular frequency?
Angular frequency (omega, measured in radians per second) is calculated using the formula omega = 2 * pi * f, where f is the ordinary frequency in hertz (cycles per second). It can also be expressed as omega = 2 * pi / T, where T is the period in seconds. For example, a signal oscillating at 1 Hz has an angular frequency of 2 * pi = 6.2832 rad/s. A 50 Hz mains power supply has an angular frequency of 2 * pi * 50 = 314.16 rad/s.
What is the difference between angular frequency and ordinary frequency?
Ordinary frequency (f) counts the number of complete cycles per second, measured in hertz (Hz). Angular frequency (omega) measures the rate of rotation or oscillation in radians per second. Since one full cycle covers 2 * pi radians, angular frequency is always 2 * pi times larger than ordinary frequency. Angular frequency is especially useful in physics and engineering because the mathematics of oscillating systems, wave equations, and rotating vectors simplifies when expressed in radians rather than cycles.
How do I convert angular frequency to period?
The period T (in seconds) is the reciprocal of ordinary frequency, so T = 1 / f = 2 * pi / omega. For example, if a motor shaft rotates at an angular frequency of 100 rad/s, its period is 2 * pi / 100 = 0.06283 seconds per revolution, and its ordinary frequency is 100 / (2 * pi) = 15.92 Hz. This calculator converts between all three quantities simultaneously.
Angular Momentum Calculator
What is angular momentum?
The rotational analogue of momentum, equal to the moment of inertia times the angular velocity.
Why is it conserved?
With no external torque, angular momentum stays constant, so reducing the moment of inertia increases the spin rate.
What units is it in?
Kilogram metres squared per second in SI.
Angular Velocity Calculator
What is the formula for angular velocity from frequency?
Angular velocity omega equals 2 pi times frequency f: omega = 2pi f. Since one revolution is 2pi radians and frequency counts revolutions per second, multiplying by 2pi converts revolutions per second to radians per second. For RPM, divide by 60 first to get revolutions per second.
How do you convert RPM to radians per second?
Multiply RPM by 2pi and divide by 60. So 3000 RPM becomes 3000 times 2pi / 60 = 314.16 rad/s. The factor of 2pi converts revolutions to radians and the factor of 60 converts minutes to seconds.
How is angular velocity related to linear speed?
Linear speed v at radius r equals angular velocity omega times radius: v = omega times r. A point further from the axis moves faster even though it completes one revolution in the same time. This is why the rim of a spinning disc travels faster than a point near the centre.
API Gravity Calculator
What is API gravity and how is it calculated?
API gravity is a measure of how heavy or light petroleum is relative to water, expressed in degrees (°API). It is defined by the American Petroleum Institute using the formula: API Gravity = (141.5 / SG) - 131.5, where SG is the specific gravity of the liquid measured at 60°F (15.6°C) relative to water at the same temperature. A liquid with an API gravity greater than 10 is lighter than water and will float; a liquid with an API gravity less than 10 is heavier than water and will sink. Most crude oils range from about 10 to 70 degrees API.
What do the API gravity classification grades mean?
The petroleum industry classifies crude oil by API gravity into four grades. Light crude oil has an API gravity above 31.1 degrees and flows easily, commands a higher price, and yields more petrol and diesel during refining. Medium crude oil falls between 22.3 and 31.1 degrees API. Heavy crude oil is between 10.0 and 22.3 degrees and requires more energy-intensive refining. Extra heavy crude (below 10 degrees API) is denser than water and includes bitumen and tar sands. Light crudes are generally more valuable because they require less processing to produce high-value products.
How do I convert API gravity back to specific gravity?
To convert API gravity back to specific gravity, rearrange the API formula: Specific Gravity = 141.5 / (API + 131.5). For example, an oil with 35 degrees API has a specific gravity of 141.5 / (35 + 131.5) = 141.5 / 166.5 = 0.8499, meaning it is about 85% the density of water at 60°F. Both measurements reference 60°F (15.6°C), which is the standard temperature for petroleum density measurements.
Average Velocity Calculator
What is the difference between average velocity and average speed?
Average speed is the total distance travelled divided by time, while average velocity is the total displacement divided by time. Displacement is a vector: it measures how far you are from your starting point in a straight line. If you travel 10 m east and then 10 m west, your displacement is zero and your average velocity is zero, but your average speed is the full 20 m divided by the time taken.
How do you calculate average velocity from multiple segments?
Add all the individual displacements (remembering that displacements in opposite directions cancel) to get the total displacement, then add all the individual times to get the total time. Average velocity equals total displacement divided by total time.
What are the units of average velocity?
The SI unit is metres per second (m/s). This calculator also converts the result to kilometres per hour (km/h) by multiplying m/s by 3.6. For reference, 15 m/s equals 54 km/h.
Beat Frequency Calculator
What is beat frequency?
Beat frequency is the rate at which the combined amplitude of two overlapping sound waves rises and falls. When two waves of slightly different frequencies play simultaneously, they alternately reinforce and cancel each other, producing a pulsing or throbbing sound. The beat frequency equals the absolute difference between the two individual frequencies: f_beat = |f1 - f2|. For example, if one tuning fork vibrates at 440 Hz and another at 444 Hz, the beat frequency is 4 Hz, meaning 4 pulses per second are heard.
How is beat frequency used in music tuning?
Musicians use beats to tune instruments. When two instruments (or an instrument and a reference pitch) are slightly out of tune, beats are clearly audible. As the player adjusts the instrument's pitch to match the reference, the beat frequency decreases. When the beats disappear entirely, the two frequencies are identical and the instrument is in tune. Piano tuners traditionally use this technique with tuning forks to set each string to the correct pitch.
What is the beat period and how does it relate to beat frequency?
The beat period is the time between successive amplitude peaks (the interval between each audible pulse). It is the reciprocal of the beat frequency: T_beat = 1 / f_beat. For example, a beat frequency of 4 Hz means the amplitude peaks every 0.25 seconds. A very low beat frequency (such as 1 Hz) produces one slow pulse per second, while a high beat frequency (above about 20 Hz) begins to sound like a separate low-pitched tone rather than individual beats.
Bolt Torque Calculator
What is the nut factor K?
K is a single dimensionless number that bundles together the friction in the threads and under the bolt head or nut. Typical values are about 0.2 for lightly lubricated steel, 0.3 for dry fasteners and 0.1 to 0.15 with good lubrication. It strongly affects the torque needed for a given preload.
How much preload should I target?
A common target is around 70 to 75 percent of the bolt proof load, which keeps the joint tight while leaving a margin below yield. The exact figure depends on the bolt grade, the joint and any design standard. Always check the manufacturer or engineering specification.
Why is torque only an estimate of clamp force?
Most of the applied torque is lost to friction, so the actual preload depends heavily on surface finish, lubrication and condition. The same torque can produce quite different clamping force on different bolts. For critical joints, angle control or direct tension measurement is more reliable.
Bolt Torque Calculator NZ
How does torque create bolt tension?
Tightening torque stretches the bolt slightly, and that stretch produces the tension that clamps the joint. The torque-tension relationship gives the resulting preload as the torque divided by the nut factor times the bolt diameter, accounting for friction losses.
What is the nut factor K?
The nut factor bundles together the friction in the threads and under the bolt head into a single number. About 0.2 is typical for plain steel bolts as received. Lubrication lowers it, producing more tension per unit torque, while dry or corroded threads raise it.
Why does lubrication matter so much?
Most of the applied torque is consumed overcoming friction, with only a small fraction stretching the bolt. Lubricating the threads cuts that friction, lowering the nut factor, so the same torque produces noticeably more clamping tension. This is why torque specs assume a particular friction condition.
Bullet Energy Calculator
How is bullet energy calculated?
Kinetic energy in foot-pounds equals the bullet weight in grains multiplied by the velocity in feet per second squared, divided by the industry constant 450,240. For example, a 150 grain bullet at 2,820 fps carries (150 x 2,820 squared) / 450,240, which is about 2,649 foot-pounds or 3,592 joules.
What is the difference between foot-pounds and joules?
They are both units of energy. One foot-pound equals about 1.3558 joules, so to convert foot-pounds to joules you multiply by 1.3558. Ammunition sold in New Zealand is often labelled in joules, while American data usually uses foot-pounds.
How much energy do I need for hunting?
Energy alone does not decide a clean kill: bullet construction, expansion and shot placement matter as much or more. As a rough guide, figures around 1,500 to 2,000 foot-pounds are often quoted for deer sized game, but check the rules and ethical guidance for the species and area you are hunting.
Buoyant Force Calculator (Archimedes' Principle)
What is the formula for buoyant force?
The buoyant force is calculated using Archimedes' principle: F = rho x V x g, where rho is the density of the fluid (kg/m3), V is the volume of fluid displaced by the object (m3), and g is the acceleration due to gravity (9.81 m/s2 on Earth). The result is in newtons (N). An object floats when its weight is less than or equal to the maximum buoyant force available (i.e. when it displaces its own weight of fluid).
What is the difference between buoyant force and weight?
Weight (W) is the downward gravitational force on an object: W = m x g, where m is the object's mass. Buoyant force (F_b) is the upward force exerted by the fluid: F_b = rho_fluid x V_displaced x g. An object sinks if its weight exceeds the maximum buoyant force (i.e. if the object is denser than the fluid). It floats if its weight is less than the buoyant force at full submersion. It is neutrally buoyant when weight equals buoyant force exactly.
How do I find the volume of an irregularly shaped object for buoyancy calculations?
The most practical method for irregular shapes is water displacement: submerge the object fully in a measuring container and note the rise in water level. The displaced volume equals the volume of the object. For regular shapes (spheres, cylinders, cuboids), you can calculate the volume from their dimensions using standard geometric formulas. Alternatively, if you know the object's mass and density, volume equals mass divided by density (V = m / rho_object).
Centrifugal Force Calculator
What is the formula for centrifugal force?
The centrifugal force formula is F = mv²/r, where m is the mass in kilograms, v is the linear (tangential) speed in metres per second, and r is the radius of circular motion in metres. An equivalent form using angular velocity is F = mω²r, where ω (omega) is in radians per second. Both formulas give the same result; the choice depends on whether you know linear speed or angular velocity. The force is expressed in newtons (N).
What is the difference between centrifugal force and centripetal force?
Centripetal force is the real inward force that keeps an object moving in a circle, directed towards the centre of rotation. Centrifugal force is the apparent outward force felt by an object in a rotating reference frame; it is a pseudo-force (fictitious force) that arises because the rotating frame is non-inertial. In everyday terms, the sensation of being pushed outward on a roundabout or in a turning car is what people call centrifugal force. The magnitudes of centripetal and centrifugal force are equal: F = mv²/r.
How do I convert RPM to angular velocity for the centrifugal force formula?
To convert RPM (revolutions per minute) to angular velocity in radians per second, use the formula: ω = RPM × 2π / 60. For example, 300 RPM gives ω = 300 × 2π / 60 = 31.42 rad/s. Once you have ω, the centrifugal force is F = mω²r. This calculator accepts RPM directly and performs the conversion automatically.
Centripetal Acceleration Calculator
What is centripetal acceleration?
The inward acceleration of an object moving in a circle, equal to v squared over r, caused by the constant change in direction.
Why is there acceleration at constant speed?
Because velocity includes direction. Going around a circle the direction changes constantly, which is an acceleration.
How do I get the centripetal force?
Multiply by the mass: F = m times v squared over r. See the centripetal force calculator.
Centripetal Force Calculator
What is centripetal force?
Centripetal force is the net inward force that keeps an object moving in a circle. It is not a new type of force but whatever real force provides the inward pull: tension in a string, friction between tyres and road, or gravity in an orbit. The formula is F = mv squared divided by r, where m is mass, v is speed, and r is the radius.
Why does speed affect centripetal force so strongly?
Because the formula has speed squared in it. Doubling the speed quadruples the centripetal force needed to hold the same radius. This is why cornering at twice the speed demands four times the grip, and why high-speed bends on roads require much tighter engineering tolerances.
What is centripetal acceleration?
Centripetal acceleration is the rate of change of velocity direction for an object in circular motion. It equals speed squared divided by radius (a = v²/r) and always points toward the centre of the circle. It is the acceleration that must be provided by the centripetal force.
Conservation of Momentum Calculator
What is the law of conservation of momentum?
The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In a collision between two objects, the total momentum before the collision equals the total momentum after: m1*v1i + m2*v2i = m1*v1f + m2*v2f. Momentum is a vector quantity (it has both magnitude and direction), so signs matter: velocities to the right are positive and velocities to the left are negative by convention.
What is the difference between an elastic and an inelastic collision?
In an elastic collision, both momentum and kinetic energy are conserved. The objects bounce off each other without any energy being converted to heat, sound, or deformation. In a perfectly inelastic collision, momentum is conserved but kinetic energy is not: the objects stick together after impact and move as one combined mass. The maximum kinetic energy is lost in a perfectly inelastic collision. Real-world collisions fall somewhere between these two extremes.
How do you find final velocities in an elastic collision?
For an elastic collision between two objects, you solve the simultaneous equations for conservation of momentum and conservation of kinetic energy. The standard result is: v1f = ((m1 - m2) * v1i + 2 * m2 * v2i) / (m1 + m2) and v2f = ((m2 - m1) * v2i + 2 * m1 * v1i) / (m1 + m2). For a perfectly inelastic collision where the objects stick together, the combined final velocity is: vf = (m1 * v1i + m2 * v2i) / (m1 + m2).
Contact Lens Vertex Distance Calculator
What is vertex distance and why does it matter for contact lenses?
Vertex distance is the gap between the back surface of a spectacle lens and the front of the cornea, typically 12 to 14 mm. Because spectacle lenses sit away from the eye while contact lenses rest directly on the cornea (vertex distance zero), the same physical lens power produces a different effective correction at the eye plane. For prescriptions stronger than approximately +/- 4.00 dioptres this difference becomes clinically significant, and the contact lens power must be adjusted using the vertex distance formula: F_contact = F_spectacle / (1 - d x F_spectacle), where d is the vertex distance in metres.
Do I need a vertex distance correction for low prescriptions?
For prescriptions below +/- 4.00 dioptres the vertex correction is generally less than 0.25 D, which falls within the standard rounding step used for contact lens powers. Optometrists typically apply vertex correction for prescriptions of +/- 4.00 D or stronger. For lower powers, the spectacle sphere and cylinder values are usually carried across directly to the contact lens prescription. Always confirm with your optometrist, as individual fitting factors also apply.
Is this calculator a substitute for an optometrist fitting?
No. This calculator demonstrates the vertex distance formula used in optical theory and can help you understand how your spectacle prescription relates to a contact lens prescription. Contact lens fitting involves many additional factors including corneal curvature (base curve), lens diameter, tear film, and lens material. A registered optometrist must perform a contact lens fitting and issue a valid contact lens prescription before you purchase or wear contact lenses.
Electric Potential Energy Calculator NZ
What is electric potential energy?
It is the energy stored in the electrostatic interaction of two charges, equal to the work done to bring them together from far apart. For two point charges it is Coulomb's constant times the product of the charges over their separation.
Why can it be negative?
The charges keep their signs in the formula. Opposite charges attract, so energy is released as they come together, giving a negative potential energy. Like charges repel, so work must be done to push them together, giving a positive potential energy.
How does it relate to Coulomb's force?
The force law has distance squared in the denominator, while the potential energy has distance to the first power. In fact the potential energy equals the force times the distance for this inverse relationship, linking the two closely.
Cutoff Frequency Calculator
What is cutoff frequency?
Cutoff frequency is the point where a filter's output has dropped to about 70.7% of its input amplitude (a 3 decibel drop in power). It marks the boundary between the passband, where signals pass through with little attenuation, and the stopband, where they are increasingly reduced. For a simple RC filter it equals 1 divided by 2 pi times resistance times capacitance.
How do you calculate the cutoff frequency of an RC filter?
The cutoff frequency of an RC filter is fc = 1 / (2 pi R C), where R is resistance in ohms and C is capacitance in farads. This formula applies to both RC low-pass and RC high-pass filters, since the cutoff point depends only on the resistor and capacitor values, not on which way the filter is arranged.
Is cutoff frequency the same for RL and RLC filters?
No. An RL filter's cutoff is fc = R / (2 pi L). A series RLC filter has a resonant frequency of f0 = 1 / (2 pi sqrt(L C)), and its cutoff (bandwidth) frequencies sit above and below resonance, spaced according to the circuit's quality factor Q = (1/R) sqrt(L/C). Each filter type has its own formula because the component arrangement changes how impedance varies with frequency.
De Broglie Wavelength Calculator
What is the de Broglie wavelength formula?
The de Broglie wavelength is given by lambda = h / p, where h is Planck's constant (6.62607015 x 10^-34 J s) and p is the momentum of the particle (p = m x v for non-relativistic speeds). A smaller wavelength means a more wave-like particle is harder to observe; larger, faster objects have wavelengths far too small to detect, which is why everyday objects do not show observable wave behaviour.
Why do electrons have a measurable de Broglie wavelength but a thrown ball does not?
Wavelength is inversely proportional to momentum (mass times velocity). An electron has an extremely small mass (about 9.109 x 10^-31 kg), so even at everyday laboratory speeds its momentum is tiny and its wavelength (typically sub-nanometre) is large enough to cause observable diffraction, as seen in electron microscopy and electron diffraction experiments. A thrown ball has a mass around a million trillion trillion times larger, so its momentum is enormous and its de Broglie wavelength works out to roughly 10^-34 metres, far too small to ever detect.
Does the de Broglie wavelength formula work for photons?
The relationship lambda = h / p applies to photons too, but photon momentum is calculated differently since photons have zero rest mass. For photons, momentum is p = E / c (energy divided by the speed of light), which combined with E = hc / lambda gives the same lambda = h / p result. This calculator uses p = m x v, which is the standard non-relativistic form for particles with mass such as electrons, protons and neutrons. For a light-specific calculation, use a dedicated photon energy calculator.
Displacement Calculator
What is the formula for displacement?
The most common SUVAT formula is s = ut + 0.5at², where s is displacement, u is initial velocity, a is acceleration, and t is time. When you know initial and final velocities and acceleration instead, use s = (v² - u²) divided by 2a. Both give the same result when the motion is under constant acceleration.
What is the difference between displacement and distance?
Distance is the total length of path travelled, regardless of direction. Displacement is the straight-line change in position from start to finish, including direction. If you walk 5 m east and then 5 m west, the distance is 10 m but the displacement is zero.
How far does an object fall in 3 seconds?
Using s = ut + 0.5at² with initial velocity u = 0 and acceleration a = 9.81 m/s² (gravity): s = 0 + 0.5 times 9.81 times 9, which equals 44.15 metres. This is the distance fallen from rest under gravity alone, ignoring air resistance.
Doppler Effect Calculator
What is the Doppler effect?
The Doppler effect is the change in observed frequency of a wave when the source and the observer are moving relative to each other. When a sound source approaches you, the waves are compressed and you hear a higher pitch. When it recedes, the waves are stretched and the pitch drops. This is why an ambulance siren sounds higher pitched as it approaches and lower pitched as it passes and moves away. The same effect applies to light, radio waves, and other wave phenomena.
What is the Doppler effect formula?
The Doppler formula for sound is f_obs = f0 times (v plus v_observer) divided by (v minus v_source), where f0 is the emitted frequency, v is the wave speed in the medium, v_observer is the speed of the observer (positive when moving towards the source), and v_source is the speed of the source (positive when moving towards the observer). The signs change for recession: use minus for v_observer when moving away, and plus for v_source when moving away.
How is the Doppler effect used in everyday technology?
The Doppler effect is used in radar speed guns (police and traffic monitoring), weather radar (to track storm movement), medical ultrasound (to measure blood flow velocity), sonar, and radio astronomy (to measure the velocity of stars and galaxies via redshift). GPS satellites also need to correct for Doppler shifts in their signal frequencies.
Drag Force Calculator NZ
What is the drag equation?
The drag force equals one half of the fluid density, times the speed squared, times the drag coefficient, times the frontal area. It is the standard way to estimate aerodynamic or hydrodynamic resistance, capturing the effects of fluid, speed, shape and size.
Why does drag matter more at high speed?
Because drag rises with the square of the speed, and the power needed to overcome it rises with the cube. So at high speed, drag dominates the resistance and consumes most of the energy, which is why streamlining matters most for fast vehicles and why fuel use climbs on the motorway.
What is a typical drag coefficient?
A sleek modern car is around 0.25 to 0.30, an SUV higher, a cyclist sitting upright around 1.0, and a flat plate facing the flow over 1.0. A lower drag coefficient means a more streamlined shape that slips through the air with less resistance.
Engine Displacement Calculator
How do you calculate engine displacement?
Displacement is pi over 4 times the bore squared times the stroke, times the number of cylinders. With bore and stroke in millimetres the result is in cubic millimetres, which you divide by 1,000 for cubic centimetres and by a million for litres.
What are bore and stroke?
The bore is the diameter of each cylinder, and the stroke is the distance the piston travels from the bottom to the top of the cylinder. Together with the number of cylinders they set the engine's total swept volume, its displacement.
Why is displacement quoted in litres?
Engine size is commonly rounded to litres, like a 2.0 litre or 3.5 litre engine, as a simple headline figure. The exact cubic centimetre value is the precise total swept volume of all the cylinders combined.
Escape Velocity Calculator
What is escape velocity?
Escape velocity is the minimum speed an object must have at the surface of a body (planet, moon, or other massive object) to escape its gravitational pull without any additional thrust. It is derived by equating kinetic energy to gravitational potential energy: 0.5 times m times v squared equals G times M times m divided by r. Solving for v gives ve = square root of (2GM/r), where G is the gravitational constant (6.674e-11 N m2 per kg2), M is the mass of the body, and r is its radius.
What is the escape velocity of Earth?
The escape velocity at Earth's surface is approximately 11.18 km/s (about 40,250 km/h or 25,000 mph). This is the minimum speed needed to launch an object from Earth's surface on a trajectory that will take it infinitely far away (ignoring atmospheric drag and Earth's rotation). Rockets do not actually need to reach this speed all at once; continuous thrust allows escape at lower instantaneous speeds.
Why does the Moon have a lower escape velocity than Earth?
The Moon has both a smaller mass and a smaller radius than Earth. The escape velocity formula ve = sqrt(2GM/r) means that a lower mass reduces escape velocity directly, while a smaller radius (which means you are closer to the centre of gravity at the surface) increases it. For the Moon, the mass effect dominates: the Moon's mass is about 1/81 of Earth's, and its radius is about 1/3.67 of Earth's, giving an escape velocity of about 2.38 km/s, roughly 21% of Earth's.
Final Velocity Calculator
What is the formula v = u + at?
The first SUVAT equation: final velocity equals initial velocity plus acceleration times time, for constant acceleration.
Can I solve for time or acceleration?
Yes. Choose the unknown in the dropdown and enter the other three values; the calculator rearranges for you.
Does it assume constant acceleration?
Yes. The SUVAT equations only hold when acceleration is constant over the interval.
Force Calculator (F = ma)
What is Newton's Second Law of Motion?
Newton's Second Law of Motion states that the net force acting on an object equals the product of its mass and its acceleration: F = ma. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s²). One newton is defined as the force required to accelerate a one-kilogram mass at one metre per second squared. The law also means you can rearrange the formula to find mass (m = F/a) or acceleration (a = F/m) if the other two values are known.
How do I convert newtons to kilonewtons or pound-force?
One kilonewton (kN) equals 1,000 newtons (N). To convert newtons to kilonewtons, divide by 1,000. For example, 5,000 N = 5 kN. To convert newtons to pound-force (lbf), multiply by approximately 0.2248. For example, 100 N = 22.48 lbf. These conversions are useful in engineering contexts where forces are large (kN) or where imperial units are used (lbf).
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms (kg). It does not change with location. Weight is the gravitational force acting on that mass, measured in newtons (N). Weight is calculated using F = ma, where a is the acceleration due to gravity (approximately 9.81 m/s² on Earth's surface). A 10 kg object has a weight of about 98.1 N on Earth, but only about 16.3 N on the Moon (gravity is roughly 1.63 m/s² there) while its mass remains 10 kg in both places.
Force Calculator
What is Newton's Second Law?
Newton's Second Law states that the net force acting on an object equals its mass multiplied by its acceleration: F = ma. Force is measured in Newtons (N), mass in kilograms (kg), and acceleration in metres per second squared (m/s2). A force of 1 Newton accelerates a mass of 1 kg at 1 m/s2.
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms, and does not change with location. Weight is the gravitational force acting on that mass, measured in Newtons: W = mg, where g is gravitational acceleration (9.81 m/s2 on Earth). A 10 kg object has a weight of 98.1 N on Earth but only about 16.2 N on the Moon.
How many Newtons are in a kilogram-force?
One kilogram-force (kgf) equals 9.80665 Newtons, which is the weight of one kilogram of mass under standard gravity. Kilogram-force is a deprecated unit still used in some engineering and everyday contexts, such as cable tension and hydraulic pressure ratings.
Free Fall Calculator with Initial Velocity NZ
How do I calculate free fall with an initial velocity?
Use the equations of motion: the distance is the initial velocity times time plus one half of gravity times time squared, and the final velocity is the initial velocity plus gravity times time. This calculator applies both for an object already moving downward.
Does this include air resistance?
No, it assumes constant gravitational acceleration with no air resistance. This is accurate for dense, compact objects over modest distances and times. For light objects or long falls, air resistance matters and the object approaches a terminal velocity instead.
What if the object is just dropped?
Set the initial velocity to zero. The distance then reduces to one half of gravity times time squared, and the final velocity to gravity times time, the familiar equations for an object dropped from rest. The calculator handles both cases.
Frequency Calculator
What is the relationship between frequency and period?
Frequency and period are reciprocals of each other. Frequency equals 1 divided by the period, and the period equals 1 divided by the frequency. A period of 0.02 seconds means 50 complete cycles every second, so the frequency is 50 Hz, which is New Zealand mains frequency.
What is angular frequency?
Angular frequency, written as omega, is the rate of change of a wave's phase in radians per second. It equals 2 times pi times the frequency in hertz. For a 50 Hz signal, omega equals 2 x pi x 50, which is about 314.16 rad/s. Angular frequency is especially useful in electronics, mechanics, and signal processing.
How do I find frequency from a wave's speed and wavelength?
Frequency equals wave speed divided by wavelength. For example, a sound wave in air (343 m/s) with a wavelength of 0.686 m has a frequency of 343 divided by 0.686, which is 500 Hz.
Friction Calculator
What is the formula for friction force?
Friction force equals the coefficient of friction multiplied by the normal force: F = mu times N. On a flat surface the normal force equals the object's weight (mass times gravity), so friction equals the coefficient times mass times 9.81. A higher coefficient or heavier object gives a larger friction force.
What is the difference between static and kinetic friction?
Static friction acts before an object starts to move and has a maximum value that must be overcome to start sliding. Kinetic friction acts while the object is already sliding and is usually slightly lower. This is why it takes more force to start something moving than to keep it moving at constant speed.
What are typical values for the coefficient of friction?
Coefficients vary widely depending on the surface pair. Rubber on dry concrete is around 0.6 to 0.8 (static). Steel on steel is about 0.15 to 0.3. Ice on ice or ice on steel can be as low as 0.03. A coefficient above 1 is possible for very grippy combinations like rubber on rubber.
G-Force Calculator NZ
What is g-force?
G-force expresses an acceleration as a multiple of normal gravity, where one g is the acceleration we feel standing on Earth. In circular motion it is the centripetal acceleration divided by gravity, describing how strongly you are pushed as you turn.
How is g-force calculated for a turn?
Find the centripetal acceleration, the speed squared divided by the radius, then divide by 9.81. The result is the g-force. A faster speed or tighter radius gives a higher g-force, and because of the square, doubling speed quadruples it.
How much g-force can a person take?
Brief moderate g-forces are fine, but sustained forces above about five g become hard to tolerate, and high g can cause loss of consciousness as blood is pulled from the brain. Pilots and racing drivers train and use equipment to withstand higher g-forces.
Gibbs Free Energy Calculator NZ
What does Gibbs free energy tell you?
Its sign tells you whether a reaction is spontaneous. A negative change means the reaction can proceed on its own, a positive change means it needs energy to be driven, and zero means the system is at equilibrium. It combines enthalpy and entropy into one decisive number.
What is the formula for Gibbs free energy?
The change in Gibbs free energy equals the change in enthalpy minus the temperature times the change in entropy. Temperature must be in kelvin. Because entropy is usually given in joules and enthalpy in kilojoules, the entropy term is converted so the units match.
How does temperature affect spontaneity?
Because the entropy term is multiplied by temperature, raising the temperature increases its influence. A reaction that is non-spontaneous when cold can become spontaneous when hot, or the reverse, depending on the signs of enthalpy and entropy. The switch happens at the temperature where free energy is zero.
Gravitational Force Calculator
What is Newton's law of universal gravitation?
It states that every mass attracts every other mass with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centres. The formula is F = G times m1 times m2 divided by r squared, where G = 6.674 x 10 to the -11 N m2/kg2.
Why is gravity so weak between everyday objects?
Because the gravitational constant G is extremely small, about 6.674 times 10 to the -11. The attractive force only becomes significant when at least one mass is enormous, like a planet. Between two people or household objects the force is far too tiny to notice or measure without precision instruments.
How is this calculator related to weight?
Weight is simply the gravitational force the Earth exerts on an object. Entering the Earth's mass (5.97e24 kg), a person's mass (70 kg), and the Earth's radius (6.37e6 m) returns approximately 687 newtons, which is a 70 kg person's weight, confirming g is approximately 9.82 m/s2 at the surface.
Gravitational Potential Energy Calculator
What is gravitational potential energy?
It is the energy an object has because of its height above a chosen reference level. If the object falls, that energy converts into kinetic energy of motion. It equals mass times gravity times height.
Why does the reference level matter?
Potential energy is always measured relative to a chosen zero height, usually the ground or floor. Changing where you call zero changes the value. Only the difference in height between two points has physical meaning for energy released.
What units should I use?
Use kilograms for mass and metres for height, with gravity in metres per second squared, and the answer comes out in joules. Convert grams to kilograms by dividing by 1000. Mixing units is the most common error.
Hydraulic Force Calculator
How do I convert pressure units?
One megapascal equals 1,000,000 pascals and is the same as 10 bar, while 1 bar is roughly 14.5 psi. Enter pressure in pascals here, so 10 MPa becomes 10,000,000. Getting the units right is the most common source of error.
Is the retract force the same as the extend force?
No. On extension the full piston area is pressurised, but on retraction the rod takes up part of that area, so the effective area and the resulting force are smaller. This calculator gives the full-bore extend force.
Does this account for friction and losses?
No, it gives the theoretical force from pressure and area only. Real cylinders lose some force to seal friction and pressure drop, so the usable output is a little lower. Allow a sensible margin when sizing a cylinder.
Kinetic Energy Calculator
What is the kinetic energy formula?
Kinetic energy is calculated using KE = 0.5 x m x v squared, where m is mass in kilograms and v is velocity in metres per second. The result is in Joules. Doubling the speed quadruples the kinetic energy because velocity appears as a squared term in the formula.
Why does speed have a bigger effect on kinetic energy than mass?
Because velocity is squared in the formula while mass is linear. Doubling the mass doubles the kinetic energy, but doubling the speed multiplies it by four. This is why vehicle crash severity increases dramatically at higher speeds.
What is the unit of kinetic energy?
The SI unit of kinetic energy is the Joule (J), which equals one kilogram times metre squared per second squared (kg m2 s-2). For larger amounts, energy is commonly expressed in kilojoules (kJ, 1000 J) or kilowatt-hours (kWh, 3,600,000 J).
LC Resonant Frequency Calculator NZ
What is resonant frequency?
It is the frequency at which an LC circuit naturally oscillates, with energy passing back and forth between the inductor and capacitor. At this frequency the circuit responds most strongly, which is what lets radios and other devices tune to one frequency and reject others.
What is an LC circuit used for?
LC circuits, also called tank circuits, are used to tune radios and televisions, to build oscillators that generate signals, in RF and wireless systems to select frequencies, and in filters. Their resonant frequency sets which frequency they pick out.
How do I change the resonant frequency?
Reduce the inductance or capacitance to raise the frequency, or increase them to lower it. Because the frequency depends on the inverse square root of their product, halving the frequency needs four times the product, which is why radios use a variable capacitor to tune across a band.
Lead Velocity Rate Calculator
What is a good lead velocity rate?
There is no single right number because it depends on your stage and market. Fast growing companies often target double digit monthly growth, while a steady single digit positive rate can be healthy for an established business. The key is a consistent upward trend rather than one strong month.
Why use LVR instead of revenue?
Revenue lags by the length of your sales cycle, so it tells you about deals that started weeks or months ago. Lead velocity reacts almost immediately to your marketing, so it warns you of changes in demand much sooner. That makes it a better steering metric for the month ahead.
What counts as a qualified lead?
A qualified lead is one that meets your agreed criteria for being a genuine sales prospect, such as fitting your target customer and showing real intent. The exact definition is yours, but it must stay the same each month. Changing it mid stream makes the growth figure meaningless.
Lorentz Force Calculator
What is the Lorentz force?
The Lorentz force is the force a magnetic field exerts on a moving electric charge. Its size is the charge times the speed times the field strength times the sine of the angle between the velocity and the field, and it always acts at right angles to the motion.
How do you calculate the magnetic force on a charge?
Multiply the charge, the speed, the magnetic field and the sine of the angle between the velocity and the field. The force is greatest when the charge moves at right angles to the field, where the sine is one, and zero when it moves along the field.
Why does the Lorentz force do no work?
Because the magnetic force is always perpendicular to the velocity, it changes the direction of motion but not the speed, so it does no work on the charge. This is why charged particles move in circles or spirals in a magnetic field.
Momentum Calculator
What is the formula for momentum?
Momentum p equals mass m times velocity v, written p = mv. Mass is in kilograms and velocity in metres per second, giving momentum in kilogram metres per second (kg m/s). It measures how much motion an object has and how hard it is to stop.
What is impulse and how does it relate to momentum?
Impulse J is the product of force and the time over which it acts: J = F times t. The impulse-momentum theorem states that impulse equals the change in momentum. So to stop a moving object, applying a larger force for a shorter time or a smaller force for a longer time both work, as long as the product equals the object's momentum.
Why do crumple zones reduce injury in crashes?
By extending the time over which the car decelerates, crumple zones reduce the average force on occupants. Since impulse equals change in momentum, the total change in momentum (the crash) is fixed, but spreading it over more time means a smaller force, which is what causes injury.
Momentum and Impulse Calculator
What is the difference between momentum and impulse?
Momentum is the quantity of motion an object has, equal to mass times velocity. Impulse is the change in that momentum, equal to force multiplied by the time it acts. Impulse and the change in momentum are always equal for a single object.
Why are the units kg m/s and N s the same?
A newton is one kilogram metre per second squared. Multiplying that by seconds cancels one second, leaving kilogram metres per second. So newton seconds and kilogram metres per second describe the same physical quantity.
Does direction matter for momentum?
Yes. Momentum is a vector, so it has both size and direction. When objects move in opposite directions you must assign signs, treating one direction as positive and the other as negative before adding.
Orbital Period Calculator NZ
What is Kepler's third law?
It relates an orbit's period to its size and the central mass: the period is two pi times the square root of the semi-major axis cubed divided by the gravitational constant times the mass. Larger orbits take longer, and more massive central bodies shorten the period.
What is the semi-major axis?
It is half the longest diameter of an elliptical orbit, and for a circular orbit it is simply the radius from the centre of the central body. It is the measure of orbit size used in Kepler's third law, entered here in metres.
Why is a low-Earth orbit about 90 minutes?
Because at a few hundred kilometres altitude, the orbital radius and the Earth's mass give a period of roughly 90 minutes through Kepler's law. This calculator returns about 92 minutes for a 400-kilometre orbit, which matches the International Space Station and similar satellites.
Pay Frequency Converter NZ
How do I convert weekly pay to monthly?
Multiply weekly pay by 52 to get the annual figure, then divide by 12 for monthly. There are not exactly four weeks in a month, so multiplying weekly by four understates monthly pay. This calculator does the conversion correctly.
Does this show take-home pay?
Yes. It applies PAYE income tax, the ACC earners levy, and optional KiwiSaver and student loan deductions to show your net pay at each frequency, not just the gross.
Why compare pay at different frequencies?
Job offers are quoted on different cycles, and bills fall on their own schedule. Seeing your pay at every frequency helps you compare offers fairly and line up your budget with your actual pay rhythm.
Photon Energy Calculator
What is the formula for photon energy?
Photon energy can be calculated from wavelength using E = hc divided by lambda, or from frequency using E = hf, where h is Planck's constant (6.626 times 10 to the power of negative 34 joule seconds), c is the speed of light (2.998 times 10 to the power of 8 metres per second), lambda is the wavelength in metres and f is the frequency in hertz.
What is the energy of a 500 nm photon?
A photon with a wavelength of 500 nanometres (green visible light) has an energy of approximately 3.97 times 10 to the power of negative 19 joules, or about 2.48 electronvolts. The electronvolt unit is more convenient at the atomic scale because it avoids the small exponents that appear in joules.
Why is shorter wavelength light more energetic?
Because photon energy is inversely proportional to wavelength (E = hc/lambda), halving the wavelength doubles the energy. Ultraviolet and X-ray photons have much shorter wavelengths than visible light and therefore carry more energy per photon, which is why they can cause more biological damage.
Potential Energy Calculator
What is the formula for gravitational potential energy?
Gravitational potential energy is PE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s2 on Earth), and h is height in metres above a reference point. The result is in Joules. When an object falls, this potential energy converts to kinetic energy.
What reference point should I use for height?
Height h is always measured relative to a chosen reference point, which you define as zero. Commonly this is the ground, the floor of a room, or sea level, depending on the problem. The actual choice does not matter as long as you are consistent, because only differences in potential energy have physical significance.
Is potential energy converted to kinetic energy during free fall?
Yes. In the absence of air resistance, the total mechanical energy (potential plus kinetic) is conserved. As an object falls, it loses potential energy (PE = mgh decreases as h decreases) and gains kinetic energy (KE = half mv squared increases). At the moment of impact, all the initial potential energy has converted to kinetic energy, giving v = sqrt(2gh).
Projectile Motion with Air Drag Calculator NZ
Why does air drag reduce the range?
Drag is a force that always opposes motion, so it continuously saps the projectile's speed throughout the flight. This shortens the horizontal distance, lowers the peak height, and steepens the descent. The faster and lighter the projectile, the more drag matters relative to gravity.
What is the drag factor?
It is a single number combining the air density, the drag coefficient (which depends on shape) and the cross-sectional area. A larger or less streamlined object has a higher drag factor and so loses more range. Dividing it by mass gives the deceleration drag produces per unit of speed squared.
Why simulate instead of using a formula?
Because drag depends on the square of the speed, the equations of motion have no simple closed-form solution. The calculator therefore steps the motion forward in tiny time slices, applying gravity and drag at each step, which gives an accurate numerical answer for the range, height and flight time.
Projectile Motion Calculator
What angle gives maximum range in projectile motion?
When launched from level ground with no air resistance, a projectile achieves its maximum range at a launch angle of 45 degrees. At angles above or below 45 degrees the range is shorter. When the launch point is above the landing point, the optimal angle is slightly less than 45 degrees.
What is the formula for projectile range?
For a projectile launched from ground level at velocity v0 and angle theta, the horizontal range is R = v0 squared times sin(2 theta) divided by g, where g is 9.81 m/s2. When the initial height is not zero, you must solve the quadratic equation for time of flight first, then multiply horizontal velocity by that time.
Does air resistance affect projectile motion?
Yes. Real projectiles experience drag that reduces range and maximum height compared to the ideal values this calculator produces. The results here assume a vacuum (no air resistance) and a flat Earth, which gives good estimates for short-range, low-speed problems such as sports science and school physics experiments.
Projectile Range Calculator
Which angle gives the greatest range?
On level ground and ignoring air resistance, a launch angle of 45 degrees gives the greatest horizontal range for a given speed. Angles either side of 45 degrees give shorter ranges. Real conditions with drag can shift the best angle slightly lower.
Does this account for air resistance?
No. The calculator uses the ideal projectile motion equations that ignore drag and assume level ground. Real ranges are usually shorter than the ideal, especially for light objects or high speeds. Treat the result as an upper estimate.
What value of gravity should I use?
For most work on Earth, 9.81 metres per second squared is accurate enough. It varies a little with latitude and altitude, so use a local value if you need precision. The Moon and other bodies have very different values.
RLC Resonant Frequency Calculator
What is the resonant frequency of an RLC circuit?
The resonant frequency of an RLC circuit is the frequency at which the inductive reactance and capacitive reactance are equal and cancel each other out, leaving only resistance in the circuit. At resonance, impedance is at its minimum (for a series RLC) or maximum (for a parallel RLC), and current is at its maximum or minimum. The formula is f0 = 1 / (2 x pi x square root of (L x C)), where L is inductance in henries and C is capacitance in farads.
What is the Q factor of an RLC circuit?
The Q factor (quality factor) measures how sharply peaked the resonant response is. A higher Q means the circuit responds to a narrower band of frequencies around resonance. For a series RLC circuit, Q = (1/R) x square root of (L/C). For a parallel RLC circuit, Q = R x square root of (C/L). A Q greater than 0.5 means the circuit is underdamped and will oscillate when disturbed.
What is angular frequency omega0?
Angular frequency omega0 is the resonant frequency expressed in radians per second rather than cycles per second (hertz). The relationship is omega0 = 2 x pi x f0. Angular frequency is convenient in circuit analysis because it removes the 2 x pi factors from the impedance formulas for inductors (Z_L = j x omega x L) and capacitors (Z_C = 1 / (j x omega x C)).
Sound Intensity Calculator
What is the inverse square law for sound?
The inverse square law states that sound intensity is inversely proportional to the square of the distance from the source. The formula is I = P divided by (4 pi r squared), where P is the acoustic power in watts and r is the distance in metres. Doubling the distance from a point source reduces the intensity to one quarter of its previous value, which is a drop of about 6 dB.
How do you convert sound intensity to decibels?
Sound intensity level in decibels is L = 10 times log base 10 of (I divided by I0), where I0 is the reference intensity of 1 times 10 to the power of negative 12 watts per square metre. For example, an intensity of 1 times 10 to the power of negative 3 W/m squared gives L = 10 times log10(1e-3 divided by 1e-12) = 10 times 9 = 90 dB.
What is a point source assumption for sound?
The inverse square law assumes a point source radiating uniformly in all directions into free space with no reflections. Real sources are not perfect points, and reflections from walls or surfaces can add to the measured intensity. The formula gives a useful first estimate of intensity outdoors away from boundaries.
Spring Potential Energy Calculator NZ
How is energy stored in a spring calculated?
The elastic potential energy is one half of the spring constant times the displacement squared. Because of the square, stretching or compressing a spring twice as far stores four times the energy. This calculator uses the effective constant of the combination.
How do springs combine in series and parallel?
Parallel springs, side by side, add their constants and are stiffer. Series springs, end to end, combine like parallel resistors: the effective constant is the reciprocal of the sum of the reciprocals, making them softer than either spring alone.
How do I use it for a single spring?
Read the energy from one spring by entering its constant; in series, set the second constant very high so it has little effect, or in parallel set it to zero. The energy for a single spring is simply one half of its constant times the displacement squared.
Standing Wave Calculator
What is a standing wave?
A standing wave forms when a wave reflects back on itself and the two waves combine, creating a pattern that appears to stay still, with fixed points called nodes and points of maximum movement called antinodes. A plucked guitar string is a standing wave.
How do you find the harmonics of a string?
For a string fixed at both ends, the nth harmonic frequency is n times the wave speed divided by twice the length. The wavelength of the nth harmonic is twice the length divided by n. The first harmonic is the fundamental, the lowest note.
What is the fundamental frequency?
The fundamental is the lowest frequency a string can vibrate at, the first harmonic, equal to the wave speed divided by twice the length. The higher harmonics are whole-number multiples of it, and together they give an instrument its tone.
SUVAT Calculator
What are the SUVAT equations?
SUVAT refers to the five variables in uniform-acceleration kinematics: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). The four equations linking them are: v = u + at; s = ut + 0.5at2; v2 = u2 + 2as; and s = 0.5(u + v)t. Knowing any three variables lets you solve for the other two.
When can I use SUVAT equations?
SUVAT equations only apply when acceleration is constant (uniform) throughout the motion. Common cases include free-fall under gravity, a car braking uniformly, and a ball thrown vertically. If acceleration varies with time, you need calculus-based kinematics instead.
What is displacement in SUVAT?
Displacement (s) is the net change in position from start to finish, measured in metres. It is a vector quantity, so it can be positive or negative depending on direction. It differs from total distance travelled if the object reverses direction during the motion.
Displacement Calculator
What does this equation give?
The displacement of an object under constant acceleration, from its initial velocity, the acceleration and the time.
How is time found?
By solving the quadratic in t. The calculator returns the first positive time that fits.
What if acceleration is zero?
Then s = ut, and time is simply s divided by u.
Terminal Velocity Calculator
What is terminal velocity?
Terminal velocity is the constant speed that a falling object reaches when the gravitational force pulling it down equals the aerodynamic drag force pushing up. At this speed, acceleration becomes zero and the object falls at a steady rate. The formula is vt = square root of (2mg divided by rho times Cd times A), where m is mass, g is gravitational acceleration, rho is fluid (air) density, Cd is the drag coefficient, and A is the cross-sectional area presented to the flow.
What is the terminal velocity of a skydiver?
A skydiver in a stable, belly-to-earth position typically reaches a terminal velocity of about 53 to 60 m/s (190 to 215 km/h or 120 to 135 mph). In a head-down dive position, where the cross-sectional area is much smaller, speeds of over 90 m/s (325 km/h) are possible. The spread-eagle belly position presents the largest area (roughly 0.6 to 0.9 square metres) and has a drag coefficient of around 1.0, which limits speed.
How does weight affect terminal velocity?
Heavier objects (higher mass) reach a higher terminal velocity, assuming the same drag coefficient and cross-sectional area. This is because gravity pulls harder on a heavier object, requiring more drag force (and therefore more speed) to balance it. This is why a lead ball reaches the ground before a feather in air: the lead ball has a much higher weight-to-drag ratio. In a vacuum, both would fall at the same rate.
Torque Calculator
What is torque and how is it calculated?
Torque is the turning or twisting effect of a force around a pivot point. It is calculated as tau = F times r times sin(theta), where F is the force in newtons, r is the lever arm length in metres, and theta is the angle between the force vector and the lever arm. At 90 degrees (force perpendicular to arm) torque is maximised; at 0 degrees it is zero.
Why does a longer spanner make it easier to loosen a bolt?
Because torque equals force times lever arm length. A longer spanner (greater r) produces more torque for the same applied force, making it easier to overcome the thread friction. This is why breaker bars, extension tubes, and long-handled wrenches are used for stubborn fasteners.
How do you calculate power from torque?
Power P equals torque tau times angular velocity omega: P = tau x omega. Angular velocity in radians per second from RPM is RPM x 2pi / 60. So a motor producing 50 N·m at 3000 RPM (314.16 rad/s) delivers 50 x 314.16 = 15,708 watts, or about 15.7 kW.
Torque to Horsepower Calculator
What is the formula for horsepower from foot-pounds and RPM?
Horsepower equals torque in foot-pounds times RPM divided by 5252. The constant 5252 comes from converting the rotational power formula: P = tau * omega, with omega in rad/s and the unit conversions between feet, pounds, and watts folded in. For example, 100 ft-lb at 3000 RPM gives 100 times 3000 divided by 5252, which is 57.12 hp.
What is the difference between torque and horsepower?
Torque is a rotational force, measured in foot-pounds or Newton-metres. Horsepower is a rate of doing work, a power unit. They are related by speed: a high-torque engine that spins slowly may produce less horsepower than a lower-torque engine that spins much faster. On a dyno chart, horsepower and torque curves always cross at 5252 RPM when torque is in ft-lb.
How do you convert foot-pounds to Newton-metres?
One foot-pound equals 1.35582 Newton-metres. To convert, multiply foot-pounds by 1.35582. For example, 100 ft-lb equals 100 times 1.35582, which is 135.58 N-m.
Velocity Calculator
What is the formula for velocity?
Velocity equals distance divided by time: v = d / t. To find distance, rearrange to d = v x t. To find time, use t = d / v. This formula gives average velocity, assuming constant speed over the entire journey.
What is the difference between speed and velocity?
Speed is a scalar quantity describing how fast an object moves, with no direction. Velocity is a vector quantity that includes both magnitude and direction. In everyday calculations like this one, the two terms are often used interchangeably when direction is not being tracked.
How do you convert m/s to km/h?
Multiply metres per second by 3.6 to get kilometres per hour. For example, 10.44 m/s multiplied by 3.6 equals 37.58 km/h. To convert m/s to mph, multiply by 2.23694.
Velocity Squared Calculator
When should I use v squared = u squared + 2as?
When you know displacement and acceleration but not time, and want a velocity, or vice versa.
Why are velocities positive?
The square root gives a magnitude. Assign a direction based on the physical setup if needed.
Is this a SUVAT equation?
Yes, the third of the four equations of motion for constant acceleration.
Wave Power Calculator NZ
How is wave power calculated?
For deep-water waves, the power per metre of wavefront is the density of seawater times gravity squared, over sixty-four pi, times the wave height squared times the period. Taller waves and longer periods carry much more power, with height having a squared effect.
Why does wave height matter so much?
Because power depends on the square of the significant wave height. Doubling the wave height quadruples the power carried. The period also matters, raising power in direct proportion, so long-period swells from distant storms are especially energetic.
Does this apply in shallow water?
No, the formula is for deep water, where the depth exceeds about half the wavelength. In shallow water, waves interact with the seabed and the relationship changes, so the deep-water formula overestimates the power. Most wave-energy resource assessment uses the deep-water case.
Wavelength Calculator
What is the wave equation?
The wave equation is v = f x lambda, where v is the wave speed in metres per second, f is the frequency in hertz, and lambda is the wavelength in metres. Rearranged, wavelength = speed divided by frequency, and frequency = speed divided by wavelength.
What wave speed should I use for light?
Light and all electromagnetic waves travel at about 3 x 10 to the 8 metres per second (299,792,458 m/s exactly) in a vacuum. For sound in air at room temperature use about 343 m/s. The speed changes in different media, such as glass or water.
What electromagnetic spectrum region is 600 nm light in?
Light with a wavelength of about 600 nm falls in the visible orange-red region of the electromagnetic spectrum. The visible spectrum runs from about 380 nm (violet) to 700 nm (deep red). Shorter wavelengths are ultraviolet; longer are infrared.
Work Done Calculator
What is work in physics?
The energy transferred when a force moves an object through a distance: W = Fd when the force is along the motion.
What unit is work in?
The joule, equal to one newton metre, the same unit as energy.
What if the force is at an angle?
Multiply by the cosine of the angle between the force and the direction of motion: W = Fd cos(theta).
Answers are gathered from the calculators and guides listed above and are general information, not advice. Last reviewed 2026-09-06. See also the finance glossary, the guides and the reference data.