How it works
When a moving object is brought to rest, its kinetic energy (½mv²) is absorbed over the stopping distance. Work equals force times distance, so the average force is the energy divided by that distance: F = ½mv² / d. The shorter the stop, the larger the force — which is the whole reason crumple zones, crash mats and packaging exist.
The lever you control is the stopping distance. Doubling how far the object decelerates halves the average force; halving it doubles the force. A fall onto concrete stops in millimetres and generates huge forces, while the same fall onto a thick crash mat stops over tens of centimetres and can cut the peak force a hundredfold.
This gives the average force over the stop; the peak force in a real collision is higher because the deceleration is not perfectly constant. The result also counts only the kinetic energy at impact — while the object is stopping, gravity keeps adding a small mg (for a vertical impact the true average is ½mv²/d + mg). Assumes a head-on stop and g ≈ 9.81 m/s².
Use it in real life
Falls and safety flooring: an 80 kg person hitting the ground at 10 m/s (a ~5 m fall) over a 1 cm stop feels about 400 kN; spreading that stop to 20 cm on a crash mat drops it to about 20 kN — the physics behind gym mats and playground surfacing.
Car crashes: a modern crumple zone extends the stopping distance from centimetres to nearly a metre, cutting the average force on the occupants by the same factor and turning a fatal deceleration into a survivable one.
Packaging and phone cases: foam and rubber work purely by lengthening the stopping distance, converting a hard millimetre-scale stop into a soft centimetre-scale one and slashing the force reaching the fragile part.
Frequently asked questions
How do you calculate impact force?
Find the kinetic energy at impact (½mv²) and divide by the stopping distance: F = ½mv² / d. This gives the average force over the collision. A shorter stopping distance means a proportionally larger force.
Why does a longer stopping distance reduce impact force?
The same kinetic energy has to be absorbed either way, and energy is force × distance. Spread the stop over more distance and the force needed for each metre drops. That is exactly how airbags, crumple zones and crash mats protect you.
Is this the peak force or the average force?
The average force across the stop. Real collisions decelerate unevenly, so the instantaneous peak force is higher — often roughly double the average. Use this figure for comparison and estimation, not for certifying safety limits.