Impulse is the change in momentum. The same impulse can be delivered by a large force for a short time or a small force for a long time – which is why airbags, crumple zones and bending your knees on landing reduce injury.
How to use the Impulse and Momentum Calculator
- Calculate from…
- Mass m
- Initial velocity v₁
- Final velocity v₂
- Average force F
- Time interval Δt
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose your data. From velocities, the impulse is the momentum change, and if you add the contact time you also get the average force. From force and time, the final velocity follows from the impulse.
Inputs explained
| Field | What to enter |
|---|---|
| Calculate from… | Choose one: Mass and velocity change, Force and time |
| Mass m | Units: kg, g, mg, t, lb, oz |
| Initial velocity v₁ | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Final velocity v₂ | Units: m/s, km/h, mph, ft/s, knots, km/s |
| Average force F | Units: N, kN, MN, mN, lbf, kgf … |
| Time interval Δt | Units: ms, s, µs |
What each result means
- Initial momentum p₁ = [Mass m]×[Initial velocity v₁]
- Final momentum p₂ = [Initial momentum p₁] + [Impulse J]
- Final velocity = [Final momentum p₂]÷[Mass m]
- Average force = [Impulse J]÷[Time interval Δt]
Example values
How the main result changes when Mass m changes and everything else stays at the example values above:
| Mass m (kg) | Impulse J (kg·m/s) |
|---|---|
| 0.075 | -5.25 |
| 0.1125 | -7.875 |
| 0.15 | -10.5 |
| 0.1875 | -13.125 |
| 0.225 | -15.75 |
| 0.3 | -21 |
Formula
J = Δp = m(v₂ − v₁) = F·Δt
Worked example
Inputs — Calculate from…: Mass and velocity change; Mass m: 0.15 kg; Initial velocity v₁: 30 m/s; Final velocity v₂: -40 m/s; Time interval Δt: 0.005 ms.
Results — Impulse J = -10.5 kg·m/s; Initial momentum p₁ = 4.5 kg·m/s; Final momentum p₂ = -6 kg·m/s; Final velocity = -40 m/s; Average force = -2,100,000 N.
Key terms
- Impulse
- Force integrated over time; equals momentum change.
Frequently asked questions
What is the unit of impulse?
Newton-seconds (N·s), the same as kg·m/s.
Why do airbags save lives?
They extend the stopping time, which reduces the average force for the same impulse.
Can impulse be negative?
Yes – it points opposite to the chosen positive direction.
What is the impulse–momentum theorem?
The impulse on an object equals its change in momentum.