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 (F = ma)

Solve Newton's Second Law of Motion for force, mass, or acceleration. Enter any two known values and the calculator instantly finds the third. Results are shown in newtons (N), kilonewtons (kN), and pound-force (lbf).

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Standard physics formula Newton's Second Law of Motion. SI units (kg, m/s², N).

F = m × a

1. Solve For

I want to calculate

Enter mass and acceleration below to calculate force.

2. Enter Known Values

Force (F) newtons

Mass (m) kilograms

Acceleration (a) m/s²

m/s²

Please enter valid positive numbers for both known values.

Result

Result
-
-

In kilonewtons

In pound-force

lbf

Calculation Breakdown

Formula used-

Solving for-

Known: Mass (m)-

Known: Acceleration (a)-

Force (F)-

Unit Conversions

Newtons (N)-

Kilonewtons (kN)-

Pound-force (lbf)-

Dyne (CGS)-

Kilogram-force (kgf)-

Worked example: -

Newton's Second Law: F = ma Explained

Newton's Second Law of Motion is one of the most fundamental relationships in classical physics. It states that the net force acting on an object is directly proportional to its mass and its acceleration. In equation form: F = m × a, where F is force in newtons (N), m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²).

The law can be rearranged to solve for any of the three variables:

F = m × a - find force when mass and acceleration are known
m = F / a - find mass when force and acceleration are known
a = F / m - find acceleration when force and mass are known

What Is a Newton?

One newton (N) is the SI unit of force. It is defined as the force required to accelerate a mass of one kilogram at one metre per second squared. This means: 1 N = 1 kg × 1 m/s². Named after Sir Isaac Newton, who published his laws of motion in 1687 in his work Principia Mathematica, this unit is the standard throughout science and engineering.

Common Acceleration Values

Context	Acceleration (m/s²)	Notes
Earth's surface gravity (g)	9.81	Standard gravity; used to calculate weight
Moon's surface gravity	1.62	About 1/6 of Earth's
Mars surface gravity	3.72	About 38% of Earth's
Free fall (Earth)	9.81	Ignoring air resistance
Typical car braking	7 to 9	Emergency braking on dry road
Sports car 0-100 km/h	5 to 8	Depends on vehicle

Worked Example

A car of mass 1,500 kg accelerates at 3 m/s². What is the net force required?

F = m × a = 1,500 kg × 3 m/s² = 4,500 N (or 4.5 kN)

This is the net force, meaning the total forward thrust minus any friction or drag. In practice, the engine must produce more than 4,500 N of force to overcome resistance and still achieve this acceleration.

Weight vs Force

Weight is a common application of F = ma. Your weight in newtons is your mass in kilograms multiplied by the acceleration due to gravity (9.81 m/s² on Earth). For example, a person of mass 70 kg weighs 70 × 9.81 = 686.7 N. When you stand on bathroom scales, they measure this gravitational force and display it as kilograms for convenience. In physics, however, weight is always a force in newtons, while mass is always in kilograms.

Related Calculators

Science and Engineering Calculators - hub for all physics and engineering tools
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Kinematic Equations (SUVAT) Solver - solve all five equations of motion
Electrical Power Calculator (P = VI) - Ohm's law equivalent for electrical circuits
Angular Velocity Calculator - rotational motion and centripetal force

Method: Formula applied: F = m × a (Newton's Second Law of Motion). Unit conversions: 1 kN = 1,000 N; 1 lbf = 4.44822 N; 1 dyne = 0.00001 N; 1 kgf = 9.80665 N. Reference: Newton, I. (1687). Philosophiae Naturalis Principia Mathematica. NIST SI Units (physics.nist.gov).

This calculator applies Newton's Second Law and assumes all values are in SI units (kg, m/s², N). It calculates net force only. Real-world forces include friction, drag, and other resistances which must be accounted for separately in engineering applications.

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