Momentum Calculator
Calculate momentum from mass and velocity, or solve for either.
About the Momentum Calculator
Momentum measures how hard it is to stop a moving object: mass times velocity. A 1,500 kg car at 20 m/s (72 km/h) carries 30,000 kg·m/s, the same as a 15,000 kg truck at just 2 m/s.
In a collision with no outside force, the total momentum before equals the total after. That rule lets you predict speeds after a crash or a recoil, and the impulse (force × time) needed to stop an object always equals its momentum.
The formula
p = m v
- p
- momentum, in kilogram metres per second (kg·m/s)
- m
- mass, in kilograms (kg)
- v
- velocity, in metres per second (m/s); negative for the opposite direction
Worked example
Two carts stick together after a collision
- Cart A: 1,000 kg at 10 m/s, so p = 10,000 kg·m/s. Cart B: 1,500 kg at rest, p = 0
- Total momentum stays 10,000 kg·m/s
- Combined mass 2,500 kg, so v = 10,000 ÷ 2,500 = 4 m/s
Things to keep in mind
- Momentum is a vector: give velocities in one direction a positive sign and the opposite direction a negative sign.
- Classical formula; at speeds near light, relativistic momentum is larger.
Questions people ask
Is momentum conserved in all collisions?
Yes, as long as no external force acts on the objects. Kinetic energy is conserved only in elastic collisions; in a crash some becomes heat, sound and bent metal.
What's impulse?
Force multiplied by the time it acts, equal to the change in momentum. Stopping a 0.145 kg ball moving at 40 m/s (5.8 kg·m/s) in 0.1 s needs an average force of 58 N.
Why do airbags and crumple zones help?
They stretch the stopping time. The same change in momentum over a longer time means a smaller force on the passenger.