Momentum Calculator (p = mv)

Momentum

Momentum is mass in motion — the product of how much there is and how fast it's going. It's what makes a slow-moving lorry harder to stop than a fast bicycle, and it's measured in kilogram-metres per second.

p = m × v  ·  impulse = Δp = F × t

Momentum vs kinetic energy

Both describe motion, but differently. Momentum scales with velocity, whilekinetic energy scales with velocitysquared. Double the speed and momentum doubles but energy quadruples. Momentum is what's conserved in a collision; energy is what does the damage.

Impulse — why crumple zones work

To change momentum you need a force acting over a time, and that product is called impulse. Since Δp = F × t, the same change in momentum can come from a big force over a short time or a small force over a long one. Crumple zones, airbags, and crash mats all work by stretching out the stopping time so the force stays survivable. Enter a stopping time above and the calculator shows the average force it implies.

Worked example

A 1000 kg car at 20 m/s has momentum 1000 × 20 = 20 000 kg·m/s. Stopping it in 5 seconds needs an average force of 20 000 / 5 = 4000 N. Stop it in 0.1 seconds — a crash rather than a brake — and the force becomes 200 000 N, fifty times higher. Same momentum, wildly different outcome.

Direction matters, and this treats one axis

Momentum is a vector, and this page works along a single line — which is correct for a head-on collision and wrong for anything at an angle. In two dimensions the components must be conserved separately. The impulse figure also assumes the force is constant over the stopping time, which real impacts are not; a measured peak force is typically several times the average this implies.