Momentum Calculator
Momentum, impulse, and the principle behind crumple zones.
Work out Momentum. Momentum, impulse, and the principle behind crumple zones. States its idealisation instead of hiding it.
Optional — gives the force of the impact.
Momentum (kg·m/s)
30,000
Stopping force 150,000 N
Momentum is mv and kinetic energy is ½mv², which is why they behave so differently. Doubling the speed doubles the momentum but quadruples the energy — a collision at twice the speed has twice as much momentum to absorb and four times as much energy to dissipate. Stretching the stopping time is the whole principle behind crumple zones and airbags: the same impulse spread over longer means less force.
How the Momentum Calculator works
Momentum is mv and kinetic energy is ½mv², which is why they behave so differently: doubling the speed doubles the momentum but quadruples the energy. Stretching the stopping time is the whole principle behind crumple zones and airbags — the same impulse spread over longer means less force.
Also known as: momentum formula · impulse calculator · p = mv calculator · how to calculate momentum
Momentum against energy
Momentum is mv; kinetic energy is ½mv². Doubling the speed doubles one and quadruples the other, which is why they answer different questions.
Momentum tells you what it takes to stop something. Energy tells you how much damage stopping it will do.
Why crumple zones work
A 1,500 kg car at 20 m/s carries 30,000 kg·m/s of momentum. Stopping it requires exactly 30,000 N·s of impulse, no matter how the stop happens — that quantity is fixed.
What is not fixed is the time. Stop in 0.02 seconds against a rigid barrier and the force is 1.5 million newtons. Stretch it to 0.2 seconds with a crumple zone and the force falls to 150,000 — a tenth, for the same impulse.
Airbags, helmet foam, crash mats and the instinct to bend your knees on landing are all the same idea: the impulse is what it is, so the only variable left to control is how long you take to absorb it.
Frequently asked questions
What is the momentum formula?
p = mv — mass times velocity. A 1,500 kg car at 20 m/s carries 30,000 kg·m/s.
What is impulse?
The change in momentum, equal to force times the time it acts. Stopping that car requires 30,000 N·s however it is done.
How do crumple zones work?
By extending the stopping time. The impulse is fixed by the momentum, so spreading it over 0.2 seconds instead of 0.02 cuts the peak force by a factor of ten.
How is momentum different from kinetic energy?
Momentum is linear in speed and energy is quadratic. A collision at twice the speed has twice the momentum to absorb and four times the energy to dissipate.
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