Mechanics

Momentum Calculator (p = mv)

Calculate momentum from mass and velocity (p = mv). Understand collisions, impulse and why heavy, fast things are hard to stop.

p = m × v
Momentum
37,500kg·m/s

How it works

Momentum is 'quantity of motion': mass times velocity. It measures how hard something is to stop. A slow lorry and a fast bicycle can carry similar momentum — and require a similar impulse to bring to rest.

Momentum is conserved in every collision, explosion and push-off in the universe. When two objects interact, the total momentum before equals the total momentum after. That single rule lets physicists reconstruct car crashes, particle collisions and billiard shots alike.

To change momentum you apply a force over time (impulse = force × time). Doubling the time available to stop halves the average force — the core insight behind airbags, helmets and bending your knees when you land.

Use it in real life

Road safety: a 1,500 kg car at 25 m/s (90 km/h) carries 37,500 kg·m/s of momentum. Airbags extend the stopping time so the force on your chest drops dramatically.

Sports: a heavier bat swung at the same speed transfers more momentum to the ball — but only if you can maintain the swing speed. Physics sets the trade-off.

Rocketry: rockets work purely on momentum conservation — throwing exhaust mass backwards at high velocity pushes the rocket forwards.

Frequently asked questions

What's the difference between momentum and kinetic energy?

Momentum (mv) is about how hard something is to stop and is always conserved in collisions. Kinetic energy (½mv²) is about how much damage or work motion can do, and can convert to heat and deformation. A crash conserves momentum but destroys kinetic energy into crumpled metal.

Why do airbags reduce injury?

Your momentum change in a crash is fixed — you go from moving to stopped. Airbags stretch that change over more time, and since force = momentum change ÷ time, more time means less force on your body.

Is momentum a vector?

Yes — it has direction. Two identical cars heading toward each other at equal speed have a combined momentum of zero, which is why head-on collisions are so destructive: all that motion has to become deformation.