Momentum and Impulse Calculator

What is momentum?

Momentum is the product of an object's mass and velocity: p = m × v. Its unit is kg·m/s. It has direction: momentum points the same way as velocity. Momentum measures how hard it is to stop something heavy and fast.

What is impulse?

Impulse is a force multiplied by the time it acts: J = F × Δt. Its unit is N·s, which is the same as kg·m/s. Impulse equals the change in the object's momentum:

F × Δt = m × (v₂ − v₁)

This is Newton's second law written another way.

Why time matters

The same change in momentum needs a large force if it happens quickly and a small one if it takes longer. That is why airbags, helmets, seat belts and bending your knees on landing all work: they stretch the stopping time and cut the force.

Example

A 0.45 kg ball at rest is kicked and leaves at 20 m/s, with the foot in contact for 0.01 seconds. The change in momentum is 0.45 × 20 = 9 kg·m/s and the average force is 9 / 0.01 = 900 N.

For a 0.2 kg ball that hits a wall at 10 m/s and comes back at 8 m/s the direction reverses, so the velocities have opposite signs: Δp = 0.2 × (8 − (−10)) = 3.6 kg·m/s. The change in momentum is larger than if the ball had simply stopped.

Limits

The calculation is one dimensional and the force is an average. In a real impact the force rises and then falls, and its peak is above the average. For the velocities of two objects after they collide, use the collision calculator.