MotionLab

Impulse Calculator

Force applied over time — equal to the resulting change in momentum.

Force (N)

Time (s)

Impulse (N·s)

J = F · t

What you entered

Force (N): 50Time (s): 0.5

1
J = F × t
50 × 0.5= 25 N·s

Result

Impulse (N·s): 25

A 50N force applied for 0.5s delivers an impulse of 25 N·s.

Impulse from force applied over time

Impulse is force times the time it acts for, and it equals the change in momentum it produces.

Force (N)	Time (s)	Impulse (N s)	Situation
10	1	10.00	Gentle steady push
50	2	100.00	Sustained shove
100	0.5	50.00	Kicking a ball
500	0.02	10.00	Bat striking a ball
1000	0.1	100.00	Crash over 0.1 s

Rows one and four give the same 10 N s from wildly different forces, because a small force for a long time equals a large force for a short one. That equivalence is the entire principle behind airbags, crumple zones and crash mats: the momentum change is fixed by the collision, so the only way to reduce the peak force is to stretch the time over which it happens. Doubling the stopping time halves the force. Impulse has the same units as momentum, since it is precisely the change in it.

Impulse equals change in momentum

The impulse-momentum theorem says J = Δp — this is why airbags and crumple zones work: spreading a collision over more time reduces the peak force needed to produce the same change in momentum.

Same impulse, different force

A small force over a long time can deliver the same impulse as a large force over a short time — this is the core idea behind cushioning and safety equipment design.

Frequently asked questions

A baseball (0.145 kg) hits a bat and reverses from -40 m/s to +50 m/s. What's the impulse?

J = Δp = m(v₂ − v₁) = 0.145 × (50 − (−40)) = 0.145 × 90 = 13.05 N·s. The contact lasts about 1 ms, so the average force is J/Δt ≈ 13,050 N — over 1.3 tonnes of force.

Why do airbags reduce injury if the momentum change is the same?

The impulse (Δp) is identical whether you hit the dashboard or an airbag. But J = F × Δt — the airbag extends the collision time from ~5 ms to ~50 ms, reducing peak force by roughly 10×. Same impulse, much less damaging force.

How is impulse different from momentum?

Momentum is a property of a moving object at a moment (p = mv). Impulse is the change in momentum caused by a force over time (J = FΔt = Δp). Think of momentum as a bank balance and impulse as a deposit or withdrawal. See the momentum calculator.

Can impulse be negative?

Yes — impulse is a vector. Negative impulse means the force was applied opposite to the chosen positive direction. A ball bouncing off a wall receives negative impulse in the original direction of travel, reversing its momentum.