WorldCalcs

Force Calculator

Solve Newton's second law F = m × a for force, mass, or acceleration.

Reviewed by the WorldCalcs team · Methodology · Last reviewed: July 2026

Force

98.1 N

F = m × a

What is force?

Force is a push or a pull that can change an object's motion. Newton's second law of motion sums it up in three symbols: F = m × a — force equals mass times acceleration. Push the same shopping trolley harder and it speeds up faster; load it with more mass and the same push produces less acceleration. Force is measured in newtons (N), where one newton is the force that gives a one-kilogram mass an acceleration of one metre per second squared.

The formula

Newton's second law rearranges three ways, so any two knowns give the third:

  • Force: F = m × a
  • Mass: m = F / a
  • Acceleration: a = F / m

The units are newtons (N) for force, kilograms (kg) for mass, and metres per second squared (m/s²) for acceleration. Written out, 1 N = 1 kg·m/s².

Worked example

A 10 kg object accelerates at 9.81 m/s². Multiply mass by acceleration: 10 × 9.81 = 98.1 N. If you instead know a 100 N force acts on a 20 kg mass, the acceleration is 100 ÷ 20 = 5 m/s².

Force vs. weight

Weight is just a specific force: the pull of gravity on a mass. On Earth's surface, acceleration due to gravity is about g = 9.80665 m/s², so weight = mass × g. A 70 kg person weighs 70 × 9.80665 ≈ 686.4655 N. That's why the calculator offers a one-tap "Earth gravity" button — set acceleration to g and the force you get out is weight in newtons. Mass stays the same everywhere; weight changes with gravity, which is why you'd weigh less on the Moon.

Related: Ohm's Law Calculator, Science Calculators.

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Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer

How to use

Pick what you want to find, enter the two known values, and the calculator applies F = m × a (or a rearrangement) to solve for the third. Use SI units — newtons (N), kilograms (kg) and metres per second squared (m/s²).

Weight is just force from gravity, so the "Use Earth gravity" button sets acceleration to g = 9.80665 m/s² for quick weight-in-newtons calculations.

Frequently asked questions

What is the formula for force?+

Newton's second law gives force as mass times acceleration: F = m × a. Rearranged, mass is F ÷ a and acceleration is F ÷ m.

What is a newton?+

A newton (N) is the SI unit of force. One newton is the force needed to accelerate a 1 kg mass at 1 m/s², so 1 N = 1 kg·m/s².

How do I calculate mass from force and acceleration?+

Divide force by acceleration: mass = F ÷ a. A 50 N force producing 10 m/s² of acceleration acts on 50 ÷ 10 = 5 kg.

How do I find acceleration from force and mass?+

Divide force by mass: acceleration = F ÷ m. A 100 N force on a 20 kg object gives 100 ÷ 20 = 5 m/s².

What is the difference between mass and weight?+

Mass is the amount of matter in an object and stays constant. Weight is the force of gravity on that mass, weight = mass × g, so it changes with gravity.

How much does 1 kg weigh in newtons?+

On Earth, about 9.80665 N, using standard gravity g = 9.80665 m/s². So a 1 kg mass weighs roughly 9.81 N.

What is Newton's second law?+

It states that the net force on an object equals its mass times its acceleration (F = m × a). A bigger force means more acceleration; more mass means less acceleration for the same force.

How do I convert force to kilograms-force?+

Divide newtons by 9.80665. One kilogram-force (kgf) equals 9.80665 N, so 98.1 N is about 10 kgf.

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