Acceleration to force: what a crash actually loads
What this calculation does
It multiplies an acceleration by the mass being accelerated, giving the force required to produce it. A 75 kg occupant decelerating at 300 m/s² — a fairly ordinary frontal impact, and a little over thirty times the acceleration of free fall — experiences a force of 22,500 N. That figure is what the seat belt, the pretensioner and the mounting points are all designed around.
Why crash forces are so much larger than weight
A stationary occupant exerts a force on the seat equal to their weight, around 735 N. The same occupant in a crash is decelerated at many times gravity over a very short distance, and every multiple of gravity multiplies the force. The whole purpose of a crumple zone is to extend the distance over which that deceleration happens, because stretching the same change in speed over a longer time and distance lowers the acceleration, and lowers the force with it.
m/s² to newtons for a 75 kg occupant
Every row is computed for a mass of 75 kilograms, a common crash-test dummy figure. For a different occupant, multiply the row value by their mass divided by seventy-five; the interactive converter above takes any mass directly, in kilograms, grams or tonnes.
| Metre per second squared (m/s²) | Newton (N) |
|---|---|
| 0.1 | 0.1 |
| 1 | 1 |
| 2 | 2 |
| 5 | 5 |
| 9.80665 | 9.80665 |
| 10 | 10 |
Why the belt stretches, and why that is the point
A seat belt that did not stretch at all would stop the occupant almost instantly, which means an enormous acceleration and an enormous force. Real belts are woven so that they pay out a little under load, and load limiters allow a controlled amount of webbing to slip. Both are doing the same job as the crumple zone: converting a very large force over a very short distance into a smaller force over a longer one.
Gravity as a yardstick
Crash accelerations are usually quoted in multiples of g, and the unit selector offers standard gravity for exactly that reason. A deceleration of 30 g is 294 m/s², and the force on a 75 kg occupant is then thirty times their weight — around 22 kN, which is a number you can compare directly against the strength of the mounting hardware.
Frequently asked questions
How do I convert an acceleration into a force?
Multiply the acceleration in metres per second squared by the mass in kilograms. A 5 m/s² acceleration applied to 2 kg requires 10 N. The relationship is Newton second law exactly as it is usually written, F = m·a.
What force does a 30 g crash put on a person?
Roughly thirty times their weight. For a 75 kg occupant that is about 22 kN, or 22,500 N. The exact figure depends on the deceleration profile, which is why real measurements come from instrumented crash tests rather than from a single number.
Why does a longer crumple zone reduce the force?
Because the same reduction in speed spread over more distance takes more time and therefore involves a lower acceleration. Since force is proportional to acceleration at a fixed mass, lowering the acceleration lowers the force in the same proportion.
Is one g equal to 9.80665 m/s²?
Yes, that is the standard value by definition, and it is offered as a unit in the selector. It is the acceleration an object experiences in free fall near the Earth surface, and it is the natural yardstick for describing crash loads.
What about feet per second squared?
It is available in the selector for readings taken from American instrumentation. One foot per second squared is 0.3048 m/s², so a figure quoted in it converts to a smaller number of metres per second squared.