What is Newton's second law?

Newton's second law states that force equals mass times acceleration, F equals m a. The bigger the mass or the acceleration, the bigger the force needed to produce it.

A newton is the force that gives a one kilogram mass an acceleration of one metre per second squared. The weight of a 1 kilogram object on Earth is about 9.81 newtons.

What units does this use?

Mass in kilograms and acceleration in metres per second squared give force in newtons. Keep these SI units for a correct result in newtons.

Force Calculator

This force calculator applies Newton's second law of motion, the famous equation F equals m a, and solves it for the force, the mass or the acceleration. The law is one of the most important statements in all of physics: it says the force acting on an object equals its mass multiplied by the acceleration that force produces, so a heavier object, or a faster change in motion, demands a larger force. You choose what to solve for, enter the other two values, and the calculator returns the answer, whether that is the force needed to accelerate a given mass, the mass that a known force and acceleration imply, or the acceleration a force will produce on a mass. The natural units are kilograms for mass and metres per second squared for acceleration, which give force in newtons, where one newton is the force that accelerates one kilogram at one metre per second squared. As a familiar reference, the downward weight of a one kilogram object on Earth is about 9.81 newtons, since gravity accelerates it at 9.81 metres per second squared. This is essential for mechanics problems, engineering and understanding everything from car performance to rocket thrust. Keep to SI units for an answer in newtons. Enter your two known values to see the result straight away.

Solve for

Mass (kg)

Acceleration (m/s²)

Force (N)

4,500 N

force

Mass in kilograms and acceleration in m/s² give force in newtons. Estimate only.

How it works

The calculator uses F equals m a. To find force it multiplies mass by acceleration, to find mass it divides force by acceleration, and to find acceleration it divides force by mass. The quantity you are solving for is hidden, so you only enter the two you know.

Worked example

To accelerate a 1500 kilogram car at 3 metres per second squared takes a force of 1500 times 3, which is 4500 newtons. The same 4500 newtons on a lighter car would produce a larger acceleration.

Related calculators

Acceleration Calculator: change in velocity.
Kinetic Energy Calculator: energy of motion.
Velocity Calculator: speed and distance.
Kinematic Equations Calculator: SUVAT motion.

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