Hong Life CalculatorsUnderstanding the car crash force calculator — concept and principle
How hard is a crash? This calculator estimates the average deceleration, stopping time and force on an occupant and a vehicle when they stop from a given speed over a given distance. It shows why crumple zones, seat belts and airbags save lives by lengthening that distance.
How it is calculated
- Constant deceleration from speed v to rest over distance d: a = v² ÷ (2d).
- Stopping time t = 2d ÷ v.
- Average force F = m × a; g-force = a ÷ 9.80665, which is also force as a multiple of body weight.
- Vehicle kinetic energy = ½ m v²; equivalent fall height h = v² ÷ (2g).
The principle
To stop, all of the moving body's kinetic energy must be absorbed over the stopping distance: force × distance = ½mv². So the average force is inversely proportional to the distance. Halving the stopping distance doubles the force. Crumple zones deform to lengthen the vehicle's stop, and seat belts and airbags let the occupant ride down that deformation instead of hitting the interior over a few centimetres.
Worked example
Default inputs: 50 km/h, occupant stopping distance 0.6 m, occupant 75 kg, vehicle 1,500 kg.
- v = 50 ÷ 3.6 ≈ 13.89 m/s.
- a = 13.89² ÷ (2 × 0.6) ≈ 161 m/s² = 16.4 g.
- Stopping time = 2 × 0.6 ÷ 13.89 ≈ 86 ms.
- Force on the occupant = 75 × 161 ≈ 12.1 kN, 16.39× body weight; on the vehicle ≈ 241 kN.
- Vehicle kinetic energy ≈ 145 kJ; equivalent fall height ≈ 9.8 m, about a three-storey fall.
| Speed at impact (km/h) | Average deceleration (g) |
|---|---|
| 12.5 | 1 |
| 25 | 4.1 |
| 37.5 | 9.2 |
| 50 | 16.4 |
| 62.5 | 25.6 |
| 75 | 36.9 |
| 100 | 65.6 |
How to read the result
Real crash pulses are not constant: peak decelerations are well above these averages. The fall-height comparison helps people grasp speed: crashing at 50 km/h is like falling from about 10 m. Doubling speed quadruples energy and the equivalent height.
Common mistakes
- Using the vehicle's crush distance for an unbelted occupant, who stops over a much shorter distance against the interior.
- Forgetting that energy grows with the square of speed.
- Treating average force as peak force.
- Mixing km/h and m/s.
Frequently asked questions
What g-force is a 50 km/h crash?
With 0.6 m of stopping distance, about 16 g on average; less distance means more.
Why do crumple zones help?
They lengthen the stopping distance and time, which lowers the force.
How high a fall equals a 50 km/h crash?
About 9.8 m, because h = v² ÷ (2g).
Sources: OpenStax, College Physics 2e, Chapter 8 Linear Momentum and Collisions (impulse and stopping distance) · NHTSA, seat belt and airbag safety information