Impulse Calculator — J = FΔt and Momentum Change
Calculate impulse from force and time, or from momentum change. Covers J = FΔt, impulse-momentum theorem, sports physics, and airbag safety examples.
Why does catching a fast ball hurt less when you let your hand move with it? Why do airbags save lives? Both come down to impulse — the relationship between force, time, and change in momentum. Extending the time of a collision reduces the peak force dramatically, even when momentum change is identical.
The CalcHub impulse calculator connects force, time, and momentum change in one tool.
The Formulas
Impulse: J = F × Δt Impulse-momentum theorem: J = Δp = m × Δv = m(v_f − v_i)- J = impulse (N·s, or kg·m/s — same unit)
- F = average force (N)
- Δt = time over which force acts (s)
- Δp = change in momentum (kg·m/s)
The Force-Time Tradeoff
For a fixed change in momentum (say, stopping a moving car), the impulse J = Δp is fixed. But:
F = J / Δt = Δp / ΔtDoubling the time halves the force. This is the engineering principle behind:
| Safety feature | How it increases Δt |
|---|---|
| Airbag | Inflates, extends collision time from 1 ms to ~30 ms |
| Crumple zone | Car body deforms progressively |
| Foam helmet padding | Compresses during impact |
| Catching technique | Arm moves with ball |
| Gymnastics mat | Cushions landing |
Worked Example
A 70 kg person running at 4 m/s stops in 0.5 seconds (gradual deceleration). What average force acts on them?
Δp = mΔv = 70 × (0 − 4) = −280 kg·m/s
J = −280 N·s
F = J/Δt = −280/0.5 = −560 N (opposing motion)
If they stopped in 0.05 seconds (hard collision): F = −280/0.05 = −5600 N — ten times more force. That's why fall technique matters in sports.
Is impulse a vector?
Yes. Impulse has the same direction as the applied force, which is the same direction as the momentum change. A ball bouncing straight back reverses its momentum, so the impulse points opposite to the initial velocity.
How does a rocket use impulse?
Rocket thrust is a continuous impulse — the engine exerts force over time, continuously increasing momentum. Total Δv (delta-v) = J/m = F×t/m. Rocket scientists use specific impulse (impulse per unit weight of propellant) as a measure of fuel efficiency.
What's the difference between impulse and momentum?
Momentum (p = mv) is a property of a moving object at a given instant. Impulse (J = FΔt) is the cause of momentum change — it's what one object does to another during a collision or interaction. They have the same units (N·s = kg·m/s) but represent different physical ideas.