Impulse CalculatorJ = FΔt = Δp
Impulse is force multiplied by the time it acts (J = FΔt), and it always equals the change in momentum (Δp = m(v − u)). Find the impulse from a force and contact time, from a mass and two velocities, or work out the average force of an impact. That last one shows why airbags and crumple zones save lives.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Collision data
Use signs for direction: a ball bouncing back has a negative final velocity.
Step-by-step working
What is impulse?
Impulse is the product of a force and the time it acts, and it equals the change in an object’s momentum. It is measured in newton-seconds (N·s).
Impulse explains why stopping slowly is safer than stopping suddenly. The momentum you must lose is fixed, so spreading the stop over more time means a smaller force.
Quick answers
How do I calculate the impact force of a collision?
Find the momentum change and divide by the stopping time: F = m(v − u) ÷ Δt. A 75 kg person stopping from 50 km/h in 0.1 s feels about 10.4 kN on average.
What is the unit of impulse?
Newton-seconds (N·s), which is identical to kg·m/s, the unit of momentum. That equality is the impulse–momentum theorem in unit form.
Why do airbags reduce injury?
They don’t change the impulse, because your momentum still has to drop to zero. They stretch the stopping time, which lowers the average force in proportion. Try the two crash presets side by side.
How is impulse related to momentum?
Impulse equals the change in momentum, J = Δp. To get the momentum itself, use the momentum calculator.
Impulse formula
This is the impulse–momentum theorem: the net impulse on an object equals its change in momentum.
| Symbol | Meaning | SI unit |
|---|---|---|
| J | Impulse | N·s |
| F̄ | Average net force | N |
| Δt | Time the force acts | s |
| Δp | Change in momentum | kg·m/s |
| m | Mass | kg |
| u, v | Initial and final velocity | m/s |
How to calculate impulse
- Pick a positive direction and give each velocity its sign.
- Find the momentum change: Δp = m(v − u).
- That change is the impulse, in N·s.
- Divide by the contact time to get the average force.
Worked example: a baseball off the bat
A 145 g baseball arrives at 40 m/s and leaves the bat at 50 m/s in the opposite direction. Contact lasts about 0.7 ms.
F̄ = J ÷ Δt = 13.05 ÷ 0.0007 = 18,643 N ≈ 18.6 kN
That is roughly the weight of a 1.9-tonne car, acting for less than a thousandth of a second.
Why stopping time matters: a 75 kg person stopping from 50 km/h
Same impulse (1,042 N·s), very different forces.
| Stopping method | Stopping time | Average force | Average deceleration |
|---|---|---|---|
| Rigid wall | ≈ 10 ms | ≈ 104 kN | ≈ 142 g |
| Seatbelt only | ≈ 150 ms | ≈ 6.9 kN | ≈ 9.4 g |
| Airbag + seatbelt | ≈ 100–200 ms | ≈ 5–10 kN | ≈ 7–14 g |
| Crumple zone + belt + airbag | ≈ 200 ms | ≈ 5.2 kN | ≈ 7.1 g |
Common mistakes to avoid
- Dropping the signs on a bounce. 40 m/s in and 50 m/s out is a change of 90 m/s, not 10.
- Confusing impulse with force. Impulse has units of N·s; it is force accumulated over time.
- Treating the average force as the peak force. Real impacts peak at about twice the average.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Impulse Calculator: frequently asked questions
J = F̄Δt, average force times contact time. By the impulse–momentum theorem, J also equals Δp = m(v − u).
Yes. Impulse points in the direction of the net force, and that is the direction of the momentum change.
Calculate the area under the curve. For a constant force it is a rectangle, F × Δt; for a triangle-shaped pulse it is ½ × Fpeak × Δt.
Keeping the bat or racket in contact longer increases Δt for a given force, so more impulse and therefore more momentum is delivered to the ball.
No. Momentum is what a moving object has (p = mv). Impulse is what changes it (J = Δp). They share the same units.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 9.2, Impulse and Collisions
- HyperPhysics, Georgia State University — impulse and momentum
- NHTSA — Air Bags — how airbags work
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.