Electrical questions, answered

Volts Amps Watts Ohms Calculator

What is Ohm's Law?

Ohm's Law states that voltage equals current multiplied by resistance: V = I x R. It describes the relationship between these three fundamental electrical quantities in a linear (ohmic) conductor. If you know any two of voltage, current and resistance you can calculate the third.

What is the formula for electrical power?

Electrical power in watts equals voltage in volts multiplied by current in amperes: P = V x I. Combined with Ohm's Law this gives three equivalent power formulas: P = V x I, P = I squared x R, and P = V squared divided by R. Knowing any two of V, I, R or P lets you find all four quantities.

What is the difference between watts and volt-amps?

Watts measure real (active) power, which is the rate at which energy is actually consumed. Volt-amps (VA) measure apparent power in AC circuits and equals voltage multiplied by current without accounting for the phase angle between them. In DC circuits watts and volt-amps are equal. In AC circuits watts equal volt-amps multiplied by the power factor.

How many watts does 12 volts at 2 amps produce?

12 volts at 2 amperes produces 24 watts (P = V x I = 12 x 2 = 24 W). The resistance of the load is 6 ohms (R = V / I = 12 / 2 = 6 ohms).

100 Amp Wire Size Calculator NZ

What size wire do I need for a 100 amp circuit in NZ?

For a 100A single-phase circuit using copper cable installed in free air, a minimum of 35 mm² (rated at approximately 119A in free air per AS/NZS 3008.1.1) is typically required. If the cable is run in conduit or enclosed, you may need 50 mm² because the current rating drops with reduced ventilation. The exact size also depends on run length: longer runs increase voltage drop, which may require a larger cable to keep the drop within 5% of the supply voltage (about 11.5V for a 230V circuit). Always have a licensed electrician confirm sizing before installation.

How is voltage drop calculated for a cable run?

For a single-phase AC circuit, voltage drop is calculated as: V_drop = (2 × L × I × R) / 1000, where L is the one-way cable length in metres, I is the current in amps, and R is the conductor resistance in milliohms per metre (mΩ/m). The factor of 2 accounts for the active and neutral conductors. For three-phase circuits, V_drop = (√3 × L × I × R) / 1000. AS/NZS 3000 (the Wiring Rules) recommends keeping voltage drop to no more than 5% from the point of supply to the point of use.

Can I use aluminium cable for a 100 amp circuit?

Yes, aluminium cable can be used for 100A circuits, but it requires a larger cross-section than copper for the same current because aluminium has higher resistivity. An aluminium cable roughly one to two sizes larger than copper is needed to achieve the same current rating and voltage drop. For a 100A circuit where 35 mm² copper would suffice, approximately 50 to 70 mm² aluminium may be needed. Aluminium cables also require approved connectors to prevent corrosion at terminations. Consult your licensed electrician and check AS/NZS 3008.1.1 for the appropriate aluminium rating.

12 Volt Wire Size Calculator

What voltage drop should I allow in a 12V circuit?

For most 12V applications, a voltage drop of 3% (0.36V) is the accepted standard. This leaves at least 11.64V at the load, which is sufficient for most automotive and marine devices. For sensitive electronics, lighting, and audio equipment, a tighter 2% drop (0.24V) is recommended. For basic non-critical loads such as heaters or winches, up to 5% (0.60V) is sometimes acceptable. The voltage drop limit you choose directly affects the required wire size: a tighter limit requires thicker wire.

Why do 12V systems need thicker wire than 240V systems?

Wire size is determined by current (amps), not voltage. At 12V, delivering the same power (watts) requires far higher current than at 240V. For example, a 120W load draws 10A at 12V but only 0.5A at 240V. Higher current causes more voltage drop across a given wire resistance and more heat generation, so thicker wire is needed. This is why 12V wiring in caravans, boats, and solar systems uses noticeably heavier cable than household wiring for the same power level.

Should I use AWG or mm² wire sizes in New Zealand?

New Zealand uses metric wire sizing (mm²) for most electrical work under AS/NZS 3000 (the Wiring Rules). However, AWG (American Wire Gauge) is commonly used for automotive, marine, and imported solar components. Both measurements describe the copper conductor cross-section area, just in different systems. This calculator shows both so you can match the specification of whichever standard applies to your components. Always verify conductor ratings with your supplier, as insulation type and temperature rating also affect the maximum current capacity.

220 Volt Wire Size Calculator

What wire size do I need for a 20 amp 220 volt circuit?

A 20 amp 220 volt circuit typically requires 12 AWG (approximately 4 mm²) copper wire, which is rated for 20 A and keeps voltage drop under 3% on runs up to about 30 metres. For runs beyond roughly 30 metres, step up to 10 AWG (6 mm²) to stay within a 3% voltage drop. Always check local electrical codes and consult a licensed electrician for any fixed wiring installation.

How is wire size calculated for a 220V circuit?

Wire size for a 220V circuit is calculated using the voltage drop formula: Voltage Drop = (2 x Length x Current x Resistivity) / Cross-sectional Area. In practice, you select the smallest wire gauge whose resistance produces a voltage drop at or below your threshold (typically 3% to 5% of the supply voltage, or 6.6V to 11V for a 220V circuit). For copper wire, resistivity is approximately 0.0172 ohm·mm² per metre. Increasing wire size (larger mm² or lower AWG number) reduces resistance and therefore voltage drop.

Can I use AWG wire sizes for 220V circuits in New Zealand?

New Zealand uses the metric mm² cross-sectional area system rather than American Wire Gauge (AWG). Standard NZ cable sizes are 1.5 mm², 2.5 mm², 4 mm², 6 mm², 10 mm², 16 mm², and 25 mm². AWG sizes are common in North America and some imported equipment. This calculator shows both AWG and the nearest mm² equivalent so you can cross-reference. For NZ installations, always specify cable by mm² and have work done by a licensed electrician in compliance with AS/NZS 3000 (the Wiring Rules).

AC Wattage Calculator

How many watts does a 12,000 BTU air conditioner use?

Divide the BTU per hour rating by the EER. A 12,000 BTU per hour unit with an EER of 10 draws about 1,200 watts while the compressor is running. The same unit with an EER of 8 would draw about 1,500 watts, so efficiency makes a real difference to the electrical load.

What is EER and how is it different from COP?

EER is the cooling output in BTU per hour divided by the electrical input in watts. COP is the same ratio expressed in consistent units, watts of cooling per watt of input. EER equals COP multiplied by 3.412, so a heat pump with a cooling COP of 3 has an EER of about 10.2.

How much does it cost to run an air conditioner?

Multiply the running wattage by the hours used, divide by 1,000 to get kilowatt hours, then multiply by your electricity price. A 1,200 watt unit running 6 hours a day at 32 cents per kilowatt hour costs about $2.30 a day, or about $69 over 30 days. Because the compressor cycles on and off, real consumption is usually a little lower than the running draw suggests.

Amp Hour Battery Life Calculator

How do I calculate battery life from amp-hours?

Battery life in hours equals the amp-hour (Ah) capacity divided by the load current in amperes: runtime = Ah / I. For example, a 100 Ah battery running a 5 A load will last 100 / 5 = 20 hours. This assumes 100% discharge efficiency and a constant discharge rate. In practice, lead-acid batteries typically derate to 50% usable capacity to extend cycle life, so a 100 Ah lead-acid battery effectively delivers 50 Ah.

What is the difference between amp-hours and watt-hours?

Amp-hours (Ah) measure charge, which is the product of current and time. Watt-hours (Wh) measure energy, which is the product of power and time. To convert amp-hours to watt-hours, multiply by the battery voltage: Wh = Ah x V. A 100 Ah, 12 V battery stores 1,200 Wh or 1.2 kWh of energy. Watt-hours are useful when comparing batteries of different voltages or sizing a solar or backup power system.

What is the C-rate of a battery?

The C-rate describes the rate of discharge relative to the battery's total capacity. A C-rate of 1C means the battery is discharged in one hour. A C-rate of 0.5C (or C/2) means it is discharged in two hours. High C-rates reduce the effective capacity of many battery types, especially lead-acid, due to internal resistance effects. Lithium batteries generally tolerate higher C-rates without significant capacity loss.

Cable Size Calculator NZ

What wire size do I need for 20 amps in NZ?

For a 20 A circuit in NZ (230 V single-phase), a 2.5 mm² copper conductor is the standard minimum for most fixed wiring runs up to around 20 metres. For longer runs or where voltage drop must stay within 3%, you may need 4 mm². Always confirm with a licensed electrician, as installation method, insulation type, grouping, and ambient temperature all affect the permitted current-carrying capacity under AS/NZS 3000.

How is minimum wire size calculated?

Wire size is determined by two independent checks. First, the conductor must have sufficient current-carrying capacity (ampacity) to carry the load continuously without overheating. This depends on the conductor cross-section, insulation rating, installation method, and grouping factor. Second, the voltage drop along the cable run must not exceed the permitted limit (typically 3% for final sub-circuits under AS/NZS 3000). The voltage drop formula for a single-phase AC circuit is: V_drop = (2 x L x rho x I) / A, where L is the one-way cable length in metres, rho is the resistivity of copper (approximately 0.0175 ohm.mm²/m at 20°C), I is the current in amps, and A is the conductor cross-section in mm². The larger of the two minimum sizes governs.

Do I need a licensed electrician to install wiring in NZ?

Yes. In New Zealand, all fixed electrical wiring work must be carried out by, or under the direct supervision of, a registered electrician licensed under the Electricity Act 1992. This includes replacing cable, adding circuits, and connecting to the switchboard. Using the wrong wire size or carrying out unlicensed electrical work is dangerous and may void your home insurance. This calculator is a planning and learning tool, not a substitute for professional advice.

Amps to Watts Calculator

How do I convert amps to watts?

For DC circuits multiply current by voltage: P = V times I. For single-phase AC circuits also multiply by the power factor: P = V times I times PF. A 10 A load on a 240 V AC circuit with PF = 1.0 uses 2,400 W.

What is the difference between watts and volt-amps?

Watts (W) measure real power, which is the energy actually converted to heat, light, or mechanical work. Volt-amps (VA) measure apparent power, which is the total current draw on the circuit. They are equal only when the power factor is 1.0. For inductive or capacitive loads the VA rating is higher than the watt rating.

How many watts is 10 amps at 240 volts?

At unity power factor (PF = 1.0), 10 A on a 240 V supply equals 10 times 240 = 2,400 W or 2.40 kW. If the power factor is 0.9, the real power is 10 times 240 times 0.9 = 2,160 W.

Auckland Congestion Charge Calculator NZ

How much will Auckland congestion charging cost?

Auckland's time-of-use (congestion) scheme is not yet finalised, but the charge being proposed is between $3.50 and $5.00 per trip at peak times only, capped at a maximum of two charged trips per day. At the top proposed rate of $5.00 per trip, a commuter who is charged once each way on a typical workday (2 trips per day) would pay about $10 per day. Over 5 days a week and 48 weeks a year that is roughly $2,400 per year. Someone charged once a day at $5.00 over the same pattern would pay about $1,200 a year. The exact rate, charged hours, boundary and any exemptions or discounts have not been confirmed.

When does Auckland congestion charging start?

The enabling law, the Land Transport Management (Time of Use Charging) Amendment Act 2025, came into force in November 2026. That allows a scheme to be set up, but it does not switch charging on. Auckland Transport, Auckland Council and the Government still have to design the scheme, consult, and make a final decision, which is expected around 2028. No charging is in place yet and no firm start date for charges has been confirmed.

How often are you charged under Auckland congestion charging?

Under the proposal you are only charged when you cross the charged area during peak periods, and the charge is capped at a maximum of two charged trips per day. So even if you make several peak trips, you would pay at most two charges in a day (for example one charge in the morning peak and one in the afternoon peak). Travel outside the charged peak hours, or staying within the charged zone without crossing the boundary, would not attract a charge. The precise rules are still being worked through.

Battery Capacity Calculator

How do I work out battery runtime?

Divide the capacity in amp-hours by the load current in amps. A 100 Ah battery at 5 A lasts about 20 hours.

How much energy does a battery store?

Multiply the amp-hours by the voltage to get watt-hours.

Why is real runtime shorter?

High discharge currents, temperature and ageing reduce usable capacity, an effect captured by Peukert’s law. Allow a margin.

Battery Charge Time Calculator

How do I calculate battery charge time?

Divide the amp hours you need to replace by the charger current, then divide by the charging efficiency. For a 100 Ah battery charged 80 percent at 10 A and 85 percent efficiency, that is 80 divided by (10 times 0.85), which is about 9.4 hours.

Why does the last part of charging take longer?

Most chargers taper the current as the battery fills, the absorption stage for lead acid or constant voltage for lithium, so the final 10 to 20 percent charges more slowly than a simple estimate suggests. Real time to full is usually a bit longer than the calculation.

What efficiency should I use?

Lead acid batteries are roughly 80 percent efficient when charging, so use about 80. Lithium batteries are more efficient, around 90 to 95 percent, so use a higher figure. Lower efficiency means more energy is lost as heat and charging takes longer.

Battery Size Calculator

How do I size a battery for my load?

Multiply the load in watts by the runtime in hours to get watt-hours, then divide by the system voltage, the usable depth of discharge and the system efficiency. For 600 W for 4 hours on a 12 V bank at 50 percent depth of discharge and 85 percent efficiency you need about 471 Ah, or a 5.65 kWh bank.

What depth of discharge should I use?

Lead-acid batteries last longest if you use only about 50 percent of their capacity, while lithium (LiFePO4) can safely use 80 to 90 percent. A lower depth of discharge means a bigger battery but a longer service life.

Why is the battery bigger than the energy I use?

Losses in the inverter and wiring, plus the limit on how deeply you can discharge, mean the nominal battery has to be larger than the energy you actually draw. Dividing by the depth of discharge and the efficiency accounts for that headroom.

Buffer Capacity Calculator

What is buffer capacity and what are its units?

Buffer capacity (beta) is a measure of how much strong acid or strong base a buffer solution can absorb before the pH changes by one unit. It is expressed in moles per litre per pH unit (mol/L/pH unit). A higher beta value means the buffer is more resistant to pH changes. A value of 0.1 mol/L/pH unit, for example, means that adding 0.1 mol of strong acid to one litre of the buffer would lower the pH by approximately one unit.

When is buffer capacity at its maximum?

Buffer capacity is at its maximum when the solution pH equals the pKa of the weak acid (i.e. when the ratio of conjugate base to acid is 1:1). At this point the Henderson-Hasselbalch equation gives pH = pKa and the Van Slyke equation gives a maximum beta of approximately 0.576 multiplied by the total buffer concentration. Moving the pH more than about one unit away from the pKa substantially reduces buffer capacity, which is why effective buffers are chosen so that the target pH is within one unit of the weak acid pKa.

What is the difference between buffer capacity and buffer range?

Buffer capacity (beta) is a quantitative value describing resistance to pH change at a specific pH, whereas buffer range is the practical pH interval over which a buffer works effectively. The generally accepted buffer range is pKa plus or minus one pH unit. Within this range, both the weak acid and its conjugate base are present in significant concentrations, so the buffer can resist additions of both acid and base. Outside this range, one component becomes too dilute to provide meaningful buffering.

Capacitance Calculator

What is the formula for capacitance of a parallel plate capacitor?

The capacitance of a parallel plate capacitor is C = epsilon_r x epsilon_0 x A / d, where epsilon_r is the relative permittivity (dielectric constant) of the material between the plates, epsilon_0 is the permittivity of free space (8.854 x 10 to the minus 12 F/m), A is the plate area in square metres, and d is the separation between the plates in metres. Increasing the plate area or dielectric constant, or decreasing the separation, all increase capacitance.

What is Q = CV?

Q = CV is the charge stored on a capacitor, where Q is charge in coulombs, C is capacitance in farads and V is the voltage across the capacitor. If you know the capacitance and the voltage applied to it you can find the charge stored. Rearranging gives V = Q/C and C = Q/V.

What are typical capacitance values in electronics?

Capacitance values in electronics span an enormous range. Small signal capacitors used in radio frequency circuits are typically in the picofarad (pF) range. General purpose decoupling and filter capacitors are in the nanofarad (nF) to microfarad (uF) range. Electrolytic capacitors used in power supplies range from tens to thousands of microfarads. Supercapacitors can reach farads or more.

Capacitive Reactance Calculator (Xc = 1 / 2πfC)

What is capacitive reactance and how is it calculated?

Capacitive reactance (Xc) is the opposition a capacitor offers to alternating current (AC). Unlike resistance, which is constant, reactance depends on both the capacitance value and the frequency of the AC signal. The formula is Xc = 1 / (2 x pi x f x C), where f is the frequency in hertz and C is the capacitance in farads. The result is in ohms. A larger capacitor or a higher frequency results in lower reactance, meaning the capacitor passes more current.

How does frequency affect capacitive reactance?

Capacitive reactance is inversely proportional to frequency. As frequency increases, reactance decreases. At very high frequencies a capacitor acts almost like a short circuit (very low opposition). At very low frequencies or DC (zero Hz), a capacitor blocks current entirely, giving theoretically infinite reactance. This behaviour makes capacitors useful as high-pass filters, coupling elements in audio circuits, and bypass capacitors in power supplies.

What is the difference between reactance and impedance?

Reactance (Xc) is the imaginary component of impedance that arises from the capacitor alone. Impedance (Z) is the total opposition to AC in a circuit and combines both resistance (R) and reactance (Xc or XL). In a circuit containing a resistor and a capacitor in series, the total impedance is Z = sqrt(R squared + Xc squared). Reactance is measured in ohms, as is impedance, but reactance involves a 90-degree phase shift between voltage and current whereas pure resistance has no phase shift.

Capacitor Charge Calculator NZ

How much charge does a capacitor store?

The charge equals the capacitance multiplied by the voltage across the capacitor, the relationship Q equals C times V. A larger capacitance or a higher voltage stores more charge. This calculator works it out, along with the stored energy and the time constant.

What is the RC time constant?

It is the resistance times the capacitance, and it sets how quickly a capacitor charges or discharges through that resistor. After one time constant the capacitor reaches about 63 percent of the final voltage, and after five it is considered effectively fully charged.

How much energy does a capacitor hold?

The stored energy is one half of the capacitance times the voltage squared. Because of the square, doubling the voltage quadruples the energy. This is the energy released when the capacitor discharges, which is how a camera flash delivers a sudden burst of power.

Capacitor Charge & Discharge Calculator NZ

How long does a capacitor take to charge?

It approaches the supply voltage along an exponential curve set by the time constant, the resistance times the capacitance. After one time constant it reaches about 63 percent, after three about 95 percent, and after five it is considered fully charged at over 99 percent.

What is the difference between charging and discharging?

Charging rises from zero toward the supply voltage, following one minus the exponential decay. Discharging falls from the supply voltage toward zero, following the exponential decay directly. Both are governed by the same time constant, so they take the same time to reach a given percentage.

What is the time constant?

It is the resistance multiplied by the capacitance, measured in seconds. It sets the pace of charging and discharging: the larger it is, the slower the capacitor responds. Expressing the elapsed time as a multiple of the time constant makes the curve easy to read.

Capacitor Charge Time Calculator

How long does it take a capacitor to fully charge?

A capacitor in an RC circuit never reaches exactly 100% charge mathematically, but it is considered fully charged after 5 time constants (5tau). At 5tau the capacitor holds 99.3% of the supply voltage. The time constant tau equals R times C (resistance in ohms multiplied by capacitance in farads). For example, a 10 kilohm resistor with a 100 microfarad capacitor has tau = 1 second, and is considered fully charged after 5 seconds.

What is the RC time constant formula?

The time constant tau (in seconds) equals resistance R (in ohms) multiplied by capacitance C (in farads): tau = R x C. After one time constant the capacitor reaches 63.2% of the supply voltage. After two time constants it reaches 86.5%, and after three it reaches 95.0%. The voltage at any time t is given by Vc(t) = Vs x (1 - e^(-t/tau)), where Vs is the supply voltage and e is Euler's number (approximately 2.718).

How do I calculate the time to reach a specific voltage?

To find the time needed to charge to a target voltage Vc from a supply voltage Vs, rearrange the charging equation: t = -tau x ln(1 - Vc/Vs), where ln is the natural logarithm. The target voltage must be less than the supply voltage. For example, to charge to 8 V from a 12 V supply with tau = 1 second: t = -1 x ln(1 - 8/12) = -1 x ln(0.333) = 1.099 seconds.

Capacitor Code Calculator

What does the capacitor code 104 mean?

On a 3-digit code the first two digits are the significant figures and the third is the number of zeros to add, giving a value in picofarads. So 104 is 10 followed by 4 zeros, which is 100,000 pF, equal to 100 nF or 0.1 uF.

How do I read a small capacitor code?

A 1 or 2 digit code is simply the value in picofarads, so 22 means 22 pF. A letter after the number is the tolerance, for example J is plus or minus 5%, K is plus or minus 10% and M is plus or minus 20%.

How do I convert pF, nF and uF?

There are 1,000 picofarads in a nanofarad and 1,000 nanofarads in a microfarad. So 100,000 pF is 100 nF, which is 0.1 uF. This calculator shows all three units at once so you can match whichever a circuit or part list uses.

Capacitor Energy Calculator

How do I calculate the energy stored in a capacitor?

The energy stored in a capacitor is E = 0.5 x C x V squared, where C is the capacitance in farads and V is the voltage across the capacitor in volts. The result is in joules. For example, a 1000 uF capacitor charged to 12 V stores E = 0.5 x 0.001 x 144 = 0.072 joules (72 millijoules).

What is Q = CV for a capacitor?

Q = CV is the charge stored on a capacitor, where Q is in coulombs, C is the capacitance in farads and V is the voltage across the capacitor. For a 1000 uF capacitor at 12 V, Q = 0.001 x 12 = 0.012 coulombs, or 12 millicoulmbs. The charge is the same on both plates in magnitude (one positive, one negative).

What is the discharge time constant of a capacitor?

When a charged capacitor discharges through a resistor R, the voltage follows an exponential decay. The time constant is tau = R x C in seconds. After one time constant, the voltage has fallen to about 36.8% of its initial value (1/e). After five time constants the capacitor is considered fully discharged for practical purposes.

Capacitor Size Calculator

How do I calculate the capacitor size for power factor correction?

To find the capacitor size for power factor correction, you need the real power (W), the existing power factor, and the target power factor. First, calculate the reactive power currently consumed: Q_initial = P x tan(arccos(PF_initial)). Then find the target reactive power: Q_final = P x tan(arccos(PF_target)). The reactive power the capacitor must supply is Q_c = Q_initial - Q_final (in VAr). Finally, the required capacitance is C = Q_c / (2 x pi x f x V^2), where f is the supply frequency in Hz and V is the supply voltage in volts. The result in farads is usually converted to microfarads (1 F = 1,000,000 µF).

What capacitor size do I need for a 50 Hz RC filter?

For an RC low-pass filter at a given cutoff frequency, the capacitor size is C = 1 / (2 x pi x f_c x R), where f_c is the desired cutoff frequency in Hz and R is the resistance in ohms. For example, to set a cutoff at 1,000 Hz with a 10,000 ohm resistor: C = 1 / (2 x pi x 1000 x 10000) = 15.9 nF. The cutoff frequency is the point at which the output signal is attenuated to 70.7% of its input level (the -3 dB point).

What is the difference between µF, nF, and pF for capacitors?

Capacitance is measured in farads (F). Because a farad is a very large unit, capacitors are commonly rated in microfarads (µF, 1/1,000,000 of a farad), nanofarads (nF, 1/1,000,000,000 of a farad), and picofarads (pF, 1/1,000,000,000,000 of a farad). Power factor correction capacitors are typically in the range of 1 to 100 µF. Signal-filtering capacitors are often in the nF to pF range. The conversions are: 1 µF = 1,000 nF = 1,000,000 pF.

Carrying Capacity Calculator

What is carrying capacity?

Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely, given the available resources such as food, water, shelter, and space. In the logistic growth model, a population grows rapidly when small relative to K and slows as it approaches K. At K, births and deaths balance and net growth is zero. Carrying capacity is not fixed; it changes if resource availability, technology, or environmental conditions change.

How is carrying capacity calculated from population data?

The logistic growth equation is N(t) = K / (1 + ((K - N0) / N0) * exp(-r * t)), where N(t) is the population at time t, K is the carrying capacity, N0 is the initial population, r is the intrinsic growth rate, and t is time. If you know N0, r, and the population at two different times, you can solve numerically for K. Alternatively, if K and r are known, you can project the population at any future time. The inflection point, where growth is fastest, occurs at N = K / 2.

What is the difference between logistic and exponential growth?

Exponential growth (J-curve) occurs when resources are unlimited: N(t) = N0 * exp(r * t). The population grows faster and faster with no upper limit. Logistic growth (S-curve) adds a carrying capacity constraint. As the population approaches K, the growth rate slows and eventually reaches zero. Real populations typically follow logistic growth because resources are finite. The logistic model is described by dN/dt = r * N * (1 - N/K).

Congestion Charge vs Public Transport Calculator NZ

Is it cheaper to drive or take public transport once congestion charging applies?

It depends on your daily costs. Driving usually combines fuel, parking and (under congestion charging) a daily charge for entering the priced zone. Public transport is a single daily fare. Adding a congestion charge raises the cost of driving and often tips the balance towards public transport, especially where parking is expensive. As an example, driving at $8 fuel, $20 parking and a $5 congestion charge is $33 per day, while a $11 daily public transport fare is far cheaper. Over 220 commuting days that is $7,260 to drive versus $2,420 by public transport, a saving of $4,840 a year. Enter your own figures above to compare your situation.

What costs should I include when comparing driving with public transport?

For driving, include the obvious running costs you pay every commuting day: fuel (or charging) for the trip, parking at or near your destination, and any congestion charge for entering the priced zone. For a fuller picture you could also factor in tolls, vehicle wear and depreciation, insurance and road user charges, though those are harder to attribute to a single trip. For public transport, include the daily fare, allowing for any return trip, transfers, or off-peak and capped-fare discounts your operator offers. This calculator focuses on the direct daily out-of-pocket costs so the comparison is clear and easy to adjust.

Does this calculator account for travel time?

No. This calculator compares money only, not time. Driving and public transport can take very different amounts of time depending on traffic, the route and how often services run, and a congestion charge is partly designed to reduce traffic and speed up trips. Time has a value too, so if one option is much faster you may judge it worth a higher cost. Use this tool for the dollar comparison, then weigh the time difference and convenience separately against your own value of time.

Current Divider Calculator

What is the current divider formula?

For two resistors R1 and R2 connected in parallel with a total current I entering the parallel combination, the current through R1 is I1 = I x R2 / (R1 + R2), and the current through R2 is I2 = I x R1 / (R1 + R2). Notice each branch current depends on the OTHER resistor's value, so more current flows through the smaller resistance. The two branch currents always add back up to the total current I.

Why does more current flow through the smaller resistor?

Both resistors in a parallel branch share the same voltage across them, since they are connected between the same two nodes. Current through each resistor is that shared voltage divided by its resistance (Ohm's law: I = V / R). Since the resistors have the same V but different R, the smaller resistance permits proportionally more current. This is the opposite relationship to a voltage divider, where more voltage drops across the larger resistor.

What is the equivalent resistance of two parallel resistors?

The equivalent resistance of two resistors in parallel is Req = (R1 x R2) / (R1 + R2). This value is always smaller than the smallest individual resistor. It represents the single resistance that would draw the same total current I from the same total voltage V as the two resistors combined, and is used to find the voltage across the parallel combination as V = I x Req before applying the current divider rule.

Current Ratio Calculator

What is a good current ratio?

A ratio between about 1.5 and 3 is often seen as comfortable, meaning you hold enough short term assets to cover your short term debts. The ideal level varies by industry. A ratio below 1 suggests possible liquidity pressure.

What counts as a current asset or liability?

Current assets are items expected to become cash within twelve months, such as cash, receivables and inventory. Current liabilities are obligations due within twelve months, such as payables and short term loans. Both come straight from your balance sheet.

How is the current ratio different from the quick ratio?

The current ratio includes all current assets, including inventory. The quick ratio strips out inventory because it can be slow to sell. The quick ratio is therefore a stricter test of immediate liquidity.

Cycling Power Output Calculator

What is a good cycling power output in watts?

For recreational cyclists, 150 to 220 W sustained is typical. The W/kg ratio is more meaningful than raw watts: 2.5 to 3.5 W/kg is a trained recreational cyclist, while 4.5 W/kg and above is considered elite level.

How does gradient affect cycling power?

Every 1 percent increase in gradient adds roughly 10 to 15 W for a 75 kg rider at 20 km/h. On flat roads, aerodynamic drag is the main resistance. On steep climbs, gravity dominates and raw watts-per-kilogram becomes the key performance number.

What is FTP in cycling?

FTP stands for Functional Threshold Power, the highest average power a rider can sustain for approximately one hour. Most cycling training zones are defined as percentages of FTP. A typical untrained adult might have an FTP of 100 to 150 W, while trained cyclists often sit between 250 and 350 W.

dBm to Watts Calculator NZ

What is dBm?

dBm is a unit of power expressed as a logarithmic ratio referenced to 1 milliwatt (mW). It is calculated as dBm = 10 x log10(power in mW / 1 mW). Because it is logarithmic, dBm is convenient for describing very large ranges of power, such as signal strength in wifi networks, fibre optic links and radio frequency (RF) systems, where power can range from nanowatts to hundreds of watts.

How do you convert dBm to watts?

To convert dBm to watts, first convert to milliwatts using mW = 10^(dBm / 10), then divide by 1000 to get watts. For example, 30 dBm equals 10^(30/10) = 1000 mW, which is 1 watt. A common reference point is 0 dBm, which always equals exactly 1 mW or 0.001 W.

Why is 3 dB roughly double the power?

Because dBm is a base-10 logarithmic scale, adding 3 dB multiplies the power by 10^(3/10), which is approximately 2.0. Adding 10 dB multiplies power by exactly 10x. This is why a small change in dBm (such as going from -70 dBm to -67 dBm wifi signal strength) represents a doubling of actual signal power, even though the number only changed by 3.

Electric Field Calculator NZ

What is electric field strength?

It is the force per unit charge that a test charge would experience at a point, describing the electrical influence of a source charge on the surrounding space. It is measured in newtons per coulomb and points away from positive charges and toward negative ones.

How does the field change with distance?

It falls with the square of the distance from the charge, the inverse-square law. So moving twice as far reduces the field to a quarter, and three times as far to a ninth. This is why fields are very strong close to a charge and fade quickly away from it.

The force on any charge placed in the field is simply the field strength multiplied by that charge. So the field is the force per unit charge, and once you know it, you can find the force on any charge by multiplying, linking it directly to Coulomb's law.

Electrical Power Calculator (P = VI)

What does P = VI mean?

P = VI is the fundamental formula for electrical power. P stands for power measured in watts (W), V stands for voltage measured in volts (V), and I stands for current measured in amperes (A). The formula states that power equals voltage multiplied by current. For example, a 240 V appliance drawing 5 A of current consumes 1,200 W (1.2 kW) of power. The formula can be rearranged to find any unknown: V = P / I and I = P / V.

How do I convert watts to kilowatts?

Divide watts by 1,000 to get kilowatts. For example, 1,200 W equals 1.2 kW. Kilowatts are more commonly used for appliances and electricity billing. New Zealand power bills charge per kilowatt-hour (kWh), which is the energy consumed by a 1 kW device running for one hour. To find how much it costs to run an appliance, multiply its power in kW by the hours it runs and then by your electricity rate per kWh.

What is the difference between AC and DC power calculations?

For direct current (DC) circuits, P = VI is exact and straightforward. For alternating current (AC) circuits, the formula gives apparent power in volt-amperes (VA) when you use the peak or RMS values of voltage and current directly. True power in watts for AC circuits is P = VI x power factor (PF), where the power factor accounts for the phase difference between voltage and current caused by reactive loads (motors, transformers). For resistive loads such as heaters and incandescent lights, the power factor is 1, so P = VI applies directly. This calculator uses the simple P = VI relationship, which is suitable for DC circuits and resistive AC loads.

Electrical Power Calculator

What is the formula for electrical power?

Electrical power can be calculated three ways depending on which quantities you know: P = V times I (voltage times current), P = I squared times R (current squared times resistance), or P = V squared divided by R (voltage squared divided by resistance). All three formulas give the same result for a purely resistive circuit.

How do I convert watts to kilowatts?

Divide watts by 1,000 to get kilowatts. For example, 1,200 W equals 1.20 kW. Kilowatts are the standard unit used on electricity bills, and kilowatt-hours (kWh) measure the energy consumed over time.

How much does it cost to run a 1200 W appliance?

A 1,200 W appliance running for one hour uses 1.2 kWh. At a typical New Zealand residential electricity rate of around 35 cents per kWh, that is about 42 cents per hour or roughly $1.00 per day if run for 2.5 hours. Use the calculator to adjust for your actual rate and usage time.

Gas vs Electric Cooking Calculator NZ

Is gas or electric cooking cheaper to run?

For the energy alone, gas can be cheaper per unit of heat, but piped gas carries a daily fixed charge that often outweighs the saving if gas is only used for cooking. Electric, especially induction, is efficient and uses power you already pay for.

Does the gas fixed charge matter?

Yes, a lot. If you keep piped gas just for cooking, the daily fixed charge can add up to far more than the cooking energy itself, which is why many households find electric cooking cheaper overall once that charge is counted.

What about bottled gas?

Bottled LPG avoids a daily piped charge but costs more per unit of energy. You can enter your own gas price here to compare bottled or piped gas against electric for your situation.

Inductor Energy Calculator NZ

How is energy stored in an inductor?

In the magnetic field created by the current flowing through it. The energy equals one half of the inductance times the current squared. This is why the current through an inductor cannot change instantly, since that would require an instant change in stored energy.

Why does interrupting an inductor cause voltage spikes?

Because the stored magnetic energy cannot vanish instantly. When the current is suddenly cut, the inductor drives a large voltage to try to keep the current flowing, producing a spike. This is why flyback diodes are placed across relays and motors to absorb it safely.

What is flux linkage?

Flux linkage is the inductance times the current, the magnetic analogue of momentum. Its rate of change determines the voltage induced across the inductor, by Faraday's law. A larger flux linkage means more stored magnetic energy and a bigger spike if interrupted.

LED Array Calculator

How do I size an LED resistor?

Subtract the total LED forward voltage from the supply, then divide by the current: R = (Vs minus N times Vf) / I.

How many LEDs can I put in series?

As many as fit under the supply voltage with some headroom for the resistor. Their forward voltages add up.

What power rating should the resistor have?

At least the dissipation shown (leftover voltage times current), with margin, so a quarter or half watt part is often used.

LED Resistor Calculator

Why does an LED need a series resistor?

An LED is a diode and has an exponential current-voltage characteristic. Without a current-limiting resistor, even a small increase in voltage above the forward voltage can cause the current to rise sharply and destroy the LED. A series resistor absorbs the voltage difference between the supply and the LED forward voltage, limiting the current to the desired level.

What is the formula for an LED series resistor?

The required resistance is R = (Vsupply minus Vforward) / I, where Vsupply is the supply voltage, Vforward is the LED forward voltage, and I is the desired current in amperes. The power dissipated in the resistor is P = (Vsupply minus Vforward) x I, which must be less than the resistor's power rating.

What is a typical LED forward voltage?

Forward voltage depends on the LED colour. Red and yellow LEDs are typically 1.8 to 2.2 V. Green and blue LEDs are typically 2.8 to 3.5 V. White LEDs use a blue die with a phosphor coating and are usually 2.8 to 3.6 V. Infrared LEDs are typically around 1.2 to 1.5 V. Always check the datasheet for your specific LED.

Magnetic Force on a Current-Carrying Wire Calculator NZ

What is the force on a current-carrying wire?

It is the force a magnetic field exerts on a wire carrying current, equal to the field strength times the current times the length of wire times the sine of the angle between them. This force is what makes electric motors and loudspeakers work.

Why does the angle matter?

Only the component of the wire at right angles to the field contributes, captured by the sine of the angle. The force is greatest when the wire is perpendicular to the field, at ninety degrees, and zero when the wire lies parallel to the field.

How does this relate to electric motors?

A motor places current-carrying coils in a magnetic field. The force on the wires, given by this formula, pushes the coils, and with the right arrangement this produces continuous rotation. So this force is the fundamental principle that converts electrical energy into mechanical motion.

Ohm's Law Calculator

What is Ohm's Law?

Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, given by the formula V = I times R, where V is voltage in volts, I is current in amperes, and R is resistance in ohms. It is the foundational relationship in basic circuit analysis.

How do I use this calculator to find resistance?

Select Solve for Resistance from the dropdown, enter the voltage (V) and current (I), and the calculator returns R = V divided by I. For example, 12 V and 3 A gives 4 ohms.

Once you know voltage and current you can calculate power using P = V times I. You can also express power purely in terms of resistance: P = I squared times R, or P = V squared divided by R. This calculator shows the power result alongside the Ohm's Law solution.

Ohm's Law Power Wheel Calculator NZ

What is the Ohm's law power wheel?

It is a diagram combining Ohm's law and the power formula to show all twelve ways of finding voltage, current, resistance or power from any two of them. This calculator implements the whole wheel: enter two values and it returns the other two automatically.

How many values do I need to enter?

Exactly two. Ohm's law and the power law connect the four quantities so that any two determine the other two. Enter the two you know and leave the rest blank, and the calculator solves for the remaining values.

How does it work when I know power and resistance?

When you provide power and resistance, the current is the square root of power divided by resistance, and the voltage is the square root of power times resistance. The calculator handles these square-root forms automatically, along with every other combination.

Inverting Op-Amp Gain Calculator

What sets the gain of an inverting amplifier?

The ratio of the feedback resistor to the input resistor, with a minus sign: Av = minus Rf / Rin.

Why is the gain negative?

The configuration inverts the signal, so the output swings opposite to the input. The magnitude is Rf over Rin.

Does the op-amp itself affect the gain?

For an ideal op-amp with enough open-loop gain, only the resistors set the closed-loop gain.

Non-Inverting Op-Amp Gain Calculator

What is the gain of a non-inverting amplifier?

One plus the feedback resistor divided by the ground resistor: Av = 1 + Rf / Rin.

Can the gain be less than one?

No. A non-inverting amplifier has a minimum gain of one (a unity-gain buffer when Rf is zero).

Why use non-inverting instead of inverting?

It keeps the signal polarity and offers very high input impedance, good for sensors and buffering.

Parallel-Plate Capacitor Calculator NZ

What determines a capacitor's capacitance?

For a parallel-plate capacitor, the plate area, the gap between the plates, and the dielectric material between them. Capacitance grows with area and with the dielectric constant, and falls as the gap widens. This is the parallel-plate capacitance formula.

What is the dielectric constant?

It is the relative permittivity of the insulating material between the plates, a measure of how much it increases capacitance compared with a vacuum. It is one for a vacuum or air, and higher for materials like plastic, glass or ceramic, which is why they boost capacitance.

How do real capacitors get high capacitance?

By using a large plate area, a very thin gap, and a high-permittivity dielectric. Practical capacitors roll large thin plates together with a thin dielectric film between them, packing a large effective area and small gap into a tiny component for high capacitance.

Resistor Power Rating Calculator NZ

How do I calculate resistor power dissipation?

Multiply the current through the resistor squared by its resistance, which equals the voltage across it times the current. This gives the power it turns into heat. This calculator computes it and recommends a safe power rating to choose.

What power rating should I choose?

Pick a rating comfortably above the dissipated power. A common rule is to double it, so a resistor dissipating 1 watt should be rated at least 2 watts. Then round up to the next standard size, such as an eighth, quarter, half, one or two watts.

Why not run a resistor near its rating?

Running a resistor close to its maximum rating makes it hot, which can shift its value, shorten its life and risk failure or scorching. A safety margin keeps it cooler and more reliable, which is why doubling the dissipated power is a common design rule.

Time-of-Use Charge Calculator NZ

What is time-of-use charging?

Time-of-use charging is a form of road pricing where drivers pay a charge to use specific roads or to enter a defined area, with the price varying by the time of day. The aim is to manage demand: charges are highest during peak periods (such as morning and evening commutes) and lower or zero during off-peak times and overnight. By making peak travel more expensive, the scheme encourages some drivers to change their travel time, route, or mode (for example to public transport), which reduces congestion and improves journey reliability for everyone who still travels at peak. The revenue collected is typically reinvested in the transport network.

How is a time-of-use charge different from a toll?

A toll is a fixed fee charged to use a specific piece of infrastructure, such as a motorway, bridge, or tunnel, and it is usually the same amount no matter when you travel. Its purpose is mainly to recover the cost of building and maintaining that road. A time-of-use charge is different in two ways: the price varies by time of day to manage demand, and it applies to using a road or area during busy periods rather than to recover the cost of one structure. In short, a toll pays for the road, while a time-of-use charge is designed to reduce peak congestion by spreading demand across the day.

Which NZ cities are considering time-of-use charging?

Auckland is the most advanced, with central government and Auckland Council working on enabling legislation for a time-of-use charging scheme aimed at the most congested parts of the city. Other large urban centres, including Wellington, Christchurch, Tauranga, and Hamilton, have been identified as places where time-of-use charging could be considered in future as a congestion management tool. No scheme is yet operating in New Zealand, and the boundaries, charge levels, hours of operation, and exemptions are set per region and have not been finalised. Always check the latest Ministry of Transport and local council information before relying on any figure.

Tradie Charge-Out Rate Calculator NZ

How do I work out my charge-out rate?

Start from the take-home you want, gross it up for tax and ACC, add your overheads, and divide by the hours you can actually bill. The result is the rate you need to charge, which is well above an employee hourly wage.

Why is a charge-out rate higher than a wage?

A charge-out rate has to cover unbillable time like quoting and admin, overheads such as vehicle, tools, insurance and phone, plus your own tax and ACC. An employee wage is only the pay, with the employer carrying those costs.

What are billable hours?

Billable hours are the hours you can actually charge a client, which is far fewer than the hours you work, after quoting, travel, admin, leave and downtime. Using a realistic billable-hours figure is the key to setting the right rate.

Transformer Turns Ratio Calculator NZ

How does a transformer change voltage?

By the ratio of turns on its two coils. The secondary voltage equals the primary voltage times the secondary turns divided by the primary turns. More secondary turns step the voltage up; fewer step it down, in direct proportion to the turns ratio.

What is the difference between step-up and step-down?

A step-up transformer has more secondary turns than primary, so the turns ratio is above one and the voltage rises. A step-down transformer has fewer secondary turns, a ratio below one, and the voltage falls. The grid uses both: stepping up for transmission and down for use.

Why does current change the opposite way to voltage?

Because a transformer roughly conserves power, which is voltage times current. So if the voltage is stepped down, the current is stepped up by the same ratio, and vice versa. This is why a step-down transformer can deliver a higher current than its primary draws.

Voltage Divider Calculator

What is the voltage divider formula?

The output voltage of a voltage divider is Vout = Vin x R2 / (R1 + R2), where Vin is the input voltage, R1 is the top resistor connected between Vin and the output node, and R2 is the bottom resistor connected between the output node and ground. When R1 equals R2 the output is exactly half the input voltage.

When is a voltage divider not accurate?

A voltage divider is only accurate when the load connected to the output draws very little current compared with the divider current. If a low-impedance load is connected, it effectively appears in parallel with R2, lowering the output voltage. As a rule of thumb the load impedance should be at least ten times the combined R1 and R2 to keep the output within a few percent of the ideal value.

How do I choose R1 and R2 values for a voltage divider?

Start with the ratio you need: R2 / (R1 + R2) = Vout / Vin. Then choose absolute values that set the divider current to a practical level. High resistance values waste less power but make the divider more sensitive to load impedance. Low resistance values are more stable under load but draw more current and waste more power as heat.

Voltage Drop Calculator

What is voltage drop?

Voltage drop is the reduction in voltage caused by the resistance of a wire carrying current. Every wire has some resistance, and when current flows through that resistance, energy is lost as heat and the voltage at the far end of the run is lower than at the source. The drop is calculated as V = I x R, where I is the current in amperes and R is the total round-trip resistance of the wire in ohms.

What is an acceptable voltage drop for NZ wiring?

For fixed wiring in New Zealand buildings, a voltage drop of up to 5% of the supply voltage is generally acceptable under AS/NZS 3000:2018 for most circuits. Critical loads such as motor starting circuits may require a tighter limit. For low-voltage DC circuits such as solar or automotive wiring, 3% or less is a common design target.

How does wire gauge affect voltage drop?

A larger diameter wire has lower resistance per metre, so it produces less voltage drop at the same current and length. AWG numbers run backwards: a smaller AWG number means a thicker wire with lower resistance. For example, AWG 12 has a conductor diameter of 2.053 mm and a cross-sectional area of 3.31 mm squared, giving a resistance of about 5.21 milliohms per metre of copper.

LM317 Voltage Regulator Resistor Calculator

What is the LM317 output formula?

Vout = 1.25 times (1 + R2/R1). The 1.25 volt reference is scaled by the resistor ratio.

What value of R1 is recommended?

Commonly 240 ohms, which keeps the regulator’s minimum load current satisfied.

Does the adjust pin current matter?

It is small (about 50 microamps) and usually ignored, but it can add a few millivolts with large R2.

Watt Calculator

How do I calculate watts from amps and volts?

Multiply amps by volts: Watts = Amps x Volts (P = I x V). For example, a device drawing 5 amps at 230 V uses 1,150 watts (1.15 kW). This is the fundamental power formula and applies to both DC circuits and AC circuits (for resistive loads with a power factor of 1).

How many watts are in a kilowatt?

One kilowatt (kW) equals 1,000 watts. To convert watts to kilowatts, divide by 1,000. To convert kilowatts to watts, multiply by 1,000. For example, a 2.4 kW kettle uses 2,400 watts. New Zealand mains voltage is 230 V at 50 Hz, so a 10-amp circuit at 230 V can supply up to 2,300 watts (2.3 kW).

How do I convert watts to horsepower?

Divide watts by 745.7 to get mechanical horsepower (hp). So 1,000 W = 1.34 hp. To convert horsepower to watts, multiply by 745.7. For example, a 1.5 hp motor produces approximately 1,118 watts. This conversion uses the mechanical horsepower standard (1 hp = 745.699872 W), which is the most commonly used definition.

Watts to Amps Calculator

How do I convert watts to amps?

For a DC circuit, divide power in watts by voltage in volts: I = P divided by V. For a single-phase AC circuit, you also divide by the power factor: I = P divided by (V times PF). The power factor accounts for reactive loads such as motors and fluorescent lights, which draw more current than the real power alone would suggest.

What is a power factor and why does it matter?

Power factor (PF) is the ratio of real power (watts) to apparent power (volt-amps). A purely resistive load like an electric heater has PF = 1.0. Motors, transformers, and switch-mode power supplies typically have a PF between 0.7 and 0.95. A lower power factor means more current is drawn for the same useful power, which matters when sizing cables and circuit breakers.

How many amps does a 2400 W appliance draw on 240 V?

At unity power factor (PF = 1.0), a 2,400 W appliance on a 240 V circuit draws I = 2400 divided by (240 times 1.0) = 10.00 A. If the power factor is 0.9, the current rises to 2400 divided by (240 times 0.9) = 11.11 A.

Wire Gauge AWG Calculator

What does AWG stand for?

AWG stands for American Wire Gauge, a standardised system for specifying the diameter of round, solid, non-ferrous electrical wire. The AWG scale runs backwards: a higher AWG number means a thinner wire with higher resistance and lower current capacity. AWG 10 is thicker than AWG 14. AWG is widely used in the USA, Canada and in the electronics industry worldwide, including in New Zealand for speaker, automotive and low-voltage wiring.

How do I convert AWG to mm?

The diameter of an AWG wire in millimetres is given by the formula d = 0.127 x 92^((36-AWG)/39) mm. For example, AWG 12 gives d = 0.127 x 92^((36-12)/39) = 0.127 x 92^(24/39) = 2.053 mm. The cross-sectional area is A = pi/4 x d squared in mm squared.

What is the maximum current for AWG 12 wire?

AWG 12 copper wire has a conductor diameter of 2.053 mm. As a single core in free air it can carry roughly 41 A, which is the indicative free-air figure this calculator shows. For general building wiring enclosed in conduit or grouped in a multi-core cable the rating is much lower, typically around 20 A. In New Zealand, the AS/NZS 3008 standard specifies current-carrying capacity based on installation method, cable type and ambient temperature, and your licensed electrician should determine the correct sizing for fixed wiring.

How We Keep Data Current

How often is Calculate.co.nz updated?

Source data is reviewed on a twice-monthly cycle, and tools are updated whenever a rate, threshold or rule changes. Larger annual events such as the 1 April tax-year rollover and the May Budget trigger a fuller review.

Where does Calculate.co.nz get its rates?

From primary New Zealand sources, including Inland Revenue, the Reserve Bank of New Zealand, Stats NZ, MBIE, MSD and Waka Kotahi, plus the underlying legislation. Each rate is tracked back to the source it comes from.