What this calculator does
Impact force is the average force experienced during a collision as an object's kinetic energy is brought to a stop over some distance. The impact force formula used here comes from the work-energy theorem: average force equals kinetic energy divided by stopping distance, F = ½mv² / d.
What is impact force in practice is best understood through that stopping distance. The same mass and speed carry the same kinetic energy no matter how the object stops, but a shorter stopping distance concentrates that energy into a much larger average force, while a longer stopping distance spreads it out into a smaller one. This is the entire logic behind crumple zones, airbags and padded surfaces.
The formula
Kinetic energy is worked out first as ½mv², then divided by the stopping distance (how far the object travels while decelerating to a stop, such as the crush distance of a car's crumple zone) to give the average impact force over that distance.
| Term | Meaning |
|---|---|
| F | Average impact force during the collision. |
| m | Mass of the object involved in the impact. |
| v | Speed of the object at the moment impact begins. |
| d | Stopping (or deformation) distance: how far the object travels while coming to a stop. |
| KE | Kinetic energy at impact, ½mv², all of which the stopping distance must absorb. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the object involved in the collision. |
| Speed at impact (m/s) | Its speed at the instant impact begins. |
| Stopping (deformation) distance (m) | How far it travels while decelerating to a stop; a crumple zone's crush distance, a padded surface's give, or similar. |
When to use it
Explaining why crumple zones work
Increasing the stopping distance in this impact force formula while holding mass and speed fixed shows the average force dropping sharply, which is exactly why vehicles are designed to crumple over a longer distance rather than stop instantly.
Comparing a fall onto a hard surface versus a soft one
The same fall height and mass give the same kinetic energy at impact regardless of the surface, but a soft surface with more give increases the stopping distance and lowers the resulting impact force considerably.
Estimating force in a packaging or drop-test scenario
Given a known drop speed and the crush distance of a package's cushioning material, this estimates the average force the contents would experience.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How impact force changes with stopping distance at a fixed mass and speed
A fixed 70 kg mass moving at 5 m/s, brought to a stop over a range of distances.
| Stopping distance | Average impact force | Kinetic energy at impact |
|---|---|---|
| 0.01 m | 87,500.00 N | 875.00 J |
| 0.02 m | 43,750.00 N | 875.00 J |
| 0.05 m | 17,500.00 N | 875.00 J |
| 0.1 m | 8,750.00 N | 875.00 J |
| 0.2 m | 4,375.00 N | 875.00 J |
| 0.5 m | 1,750.00 N | 875.00 J |
How impact force changes with speed at a fixed mass and stopping distance
A fixed 70 kg mass and a 5 cm stopping distance, across a range of impact speeds.
| Speed at impact | Average impact force | Kinetic energy at impact |
|---|---|---|
| 2 m/s | 2,800.00 N | 140.00 J |
| 4 m/s | 11,200.00 N | 560.00 J |
| 6 m/s | 25,200.00 N | 1,260.00 J |
| 8 m/s | 44,800.00 N | 2,240.00 J |
| 10 m/s | 70,000.00 N | 3,500.00 J |
| 15 m/s | 157,500.00 N | 7,875.00 J |
Questions
What is impact force?
It is the average force an object experiences while its kinetic energy is absorbed over a stopping distance during a collision or sudden stop, distinct from the peak instantaneous force, which can be higher or lower depending on how that force varies through the impact.
What is the impact force formula used here?
F = ½mv² / d, derived from the work-energy theorem: the kinetic energy an object carries must equal the work done stopping it, and work is force multiplied by distance, so force equals energy divided by distance.
Why does a shorter stopping distance mean a bigger force?
For a fixed amount of kinetic energy, force and stopping distance are inversely related: spreading the same energy absorption over a shorter distance means each unit of distance has to absorb more energy, which shows up as a larger average force.
How is this different from the acceleration calculator on this site?
The acceleration calculator starts from an initial velocity and a deceleration rate to find stopping distance and time. This calculator goes the other way, starting from a known or estimated stopping distance to find the resulting average force.
To find a deceleration rate and stopping distance from initial velocity, see the acceleration calculator. For a related but distinct combination of forces, see the resultant force calculator.