What this calculator does
Momentum is mass times velocity, and changing it requires a force applied for a period of time. That product of force and time is called impulse, and it is the reason crumple zones, airbags and crash mats all work the same way.
The total change in momentum in a collision is fixed by the speeds involved. What can be designed is the time over which the change happens, and stretching that time out is what reduces the force everything experiences.
The formula
Momentum is mass times speed, with speed converted to metres per second. The change in momentum between the initial and final speed is the impulse. Dividing that impulse by the time it takes gives the average force, and dividing that acceleration by gravity expresses it in g.
| Term | Meaning |
|---|---|
| Momentum (p) | Mass times velocity, in kilogram metres per second. A vector, so direction matters. |
| Impulse | The change in momentum, equal to force multiplied by the time it acts for. |
| Average force | The constant force that would produce the same change in momentum over the same time as the real, varying force did. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the object, in kilograms. |
| Initial speed (km/h) | The speed before the change, in kilometres per hour. |
| Final speed (km/h) | The speed after the change, in kilometres per hour. Use zero for coming to a complete stop. |
| Time of the change (s) | How long the change in speed takes, in seconds. This is the figure that determines the force. |
When to use it
Understanding why crumple zones work
Extending a collision from a twentieth of a second to a fifth cuts the average force by the same factor, which is the entire principle behind modern vehicle safety structures.
Working out an impact force
The force in a collision is not a property of the speed alone; it depends on how quickly the speed changes, and this makes that dependency explicit.
Comparing a hard surface with a soft one
Landing on concrete and landing on a mat involve the same change in momentum but very different stopping times, and therefore very different forces.
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 does stopping time change the force in a collision?
The same vehicle and the same change in speed, stopped over different times.
| Stopping time | Average force | In g of deceleration |
|---|---|---|
| 0.05 s | 416,667 N | 28.33 g |
| 0.15 s | 138,889 N | 9.44 g |
| 0.5 s | 41,667 N | 2.83 g |
| 1 s | 20,833 N | 1.42 g |
Questions
What is the difference between momentum and kinetic energy?
Momentum is mass times speed and has direction; kinetic energy is half mass times speed squared and does not. In a collision momentum is always conserved, while kinetic energy generally is not, because some of it goes into deformation and heat.
Why does a longer stopping time reduce the force?
Because the impulse needed is fixed by the change in momentum, and impulse is force times time. If the time doubles, the force needed to deliver the same impulse halves.
Why express force in g?
Because human tolerance to deceleration is usually discussed in g, and it makes the figure comparable regardless of the mass involved. A 9 g deceleration is severe for a person regardless of what vehicle they are in.
Is momentum conserved in every collision?
Yes, for the system as a whole, provided no outside force acts. That is what makes it such a useful quantity: the total before a collision equals the total after, even when the objects involved stick together or break apart.
For the energy involved rather than the momentum, see the kinetic and potential energy calculator. For the force and acceleration relationship on its own, see the force, mass and acceleration calculator.