Impulse and Momentum Calculator
The force needed to change momentum over a given time — the calculation behind crumple zones, airbags and every landing technique.
Why stopping slowly hurts less.
How the impulse and momentum calculator works
Impulse is force × time, and it equals the change in momentum: FΔt = mΔv. Rearranged, F = mΔv/Δt.
The momentum change is fixed by the collision; only the *time* is negotiable. Stretching a stop from 0.01 s to 0.1 s cuts the force tenfold, which is the entire principle of crumple zones, airbags, helmets, crash mats and bending your knees.
Formula: J = F Δt = m Δv
Worked examples
| Inputs | Average force | Note |
|---|---|---|
| 75 kg stopping from 10 m/s in 0.2 s | 3,750 N | 3,750 N |
| The same stop in 0.02 s | 37,500 N | ten times the force |
| A gentle stop | 375 N | 375 N — barely noticeable |
FAQFrequently asked questions
What is impulse?
Force multiplied by the time it acts. It equals the change in momentum, which is why the two are always discussed together.
Why do crumple zones work?
They extend the stopping time. The momentum change is fixed by the crash; stretching it from 0.02 s to 0.15 s cuts the peak force by a factor of seven.
Why bend your knees when landing?
Same reason. Landing stiff-legged stops you in perhaps 0.05 s; bending stretches it to 0.3 s and cuts the force sixfold.
What force can a person survive?
Brief decelerations above about 50 g are usually fatal, though restrained subjects have survived far more for very short durations.
Does a bouncing object need more force than one that stops?
Yes — reversing direction is a bigger momentum change than simply stopping, which is why a bouncing ball hits harder than a lump of clay.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.