Impulse Calculator
Compute impulse two equivalent ways. Enter a force (N or lbf) and contact time (s or ms), or switch modes and enter a mass (kg, g, or lb) and its velocity change (m/s, mph, or ft/s) — either way you get J in N·s and lbf·s, since impulse equals the change in momentum.
Example: with Compute from Force × time (J = F·Δt) · Force (if force × time) 1200 · Force unit N (newtons) · Contact time 8 · Time unit ms (milliseconds) → Impulse J: 9.6 N·s (= kg·m/s).
- In pound-seconds2.158 lbf·s
- What that impulse can doEnough to take a 1 kg mass from rest to 9.6 m/s
Computed by the calculator below using its default values. Change any input to see your own numbers.
J = F·Δt = Δp = m·Δv — the impulse–momentum theorem, a direct restatement of Newton's second law integrated over time.
One quantity, two doors in
Impulse is force accumulated over time: J = F·Δt. Newton's second law says that accumulation exactly equals the change in momentum, J = m·Δv — which is why this calculator has two modes that always agree. A 1,200 N hit lasting 8 milliseconds delivers 9.6 N·s; so does anything that changes a 0.24 kg object's speed by 40 m/s. If you know the collision details, use force × time; if you only know what the object did, use mass × Δv.
The units tell the same story twice: newton-seconds and kilogram-meters-per-second are identical, 1 N·s = 1 kg·m/s.
Why airbags, crumple zones, and follow-through work
For a given momentum change, the impulse is fixed — but the force is not. Stretch the stop over more time and the average force drops in exact proportion: F = J/Δt. A 70 kg driver going 15 m/s carries 1,050 N·s of momentum; stopped by a rigid dashboard in 20 ms that is a 52,500 N average force, while an airbag spreading the same impulse over 150 ms cuts it to 7,000 N. Catching a ball 'soft' with retreating hands, bending your knees on a landing, and a boxer rolling with a punch are all the same trade: same J, longer Δt, smaller F.
How it’s calculated
J = F × Δt (force mode) or J = m × Δv (momentum mode), reported in N·s. Conversions: 1 lbf = 4.4482216153 N (exact), 1 ms = 0.001 s, 1 lb = 0.45359237 kg (exact), 1 mph = 0.44704 m/s (exact), 1 ft/s = 0.3048 m/s (exact); 1 N·s = 0.2248089431 lbf·s.
Force mode assumes the force is the average over the contact interval — real impacts peak well above their average, often by 2× or more.
Everyday impulses (computed as m × Δv)
| Event | Mass × Δv | Impulse |
|---|---|---|
| Golf drive | 45.9 g × 70 m/s | 3.2 N·s |
| Baseball catch (fastball) | 145 g × 40 m/s | 5.8 N·s |
| Soccer kick | 0.43 kg × 25 m/s | 10.8 N·s |
| Sprinter leaving the blocks | 70 kg × 10 m/s | 700 N·s |
| Car stopping from 60 mph | 1,500 kg × 26.8 m/s | 40,200 N·s |
Computed with J = mΔv from typical published masses and speeds; rounded.
Common mistakes
- Entering the peak force where the formula wants the average — J = FΔt only holds with the mean force over the contact.
- Leaving milliseconds as seconds: an 8 ms bat-ball contact entered as 8 s inflates the impulse 1,000×.
- Using Δv as the final speed when the object bounces — a ball arriving at 10 m/s and leaving at −8 m/s changed velocity by 18 m/s, not 2.
- Confusing impulse with force or with energy: N·s is momentum transfer; multiply-by-distance quantities (joules) answer different questions.
Frequently asked questions
What is the impulse formula?
J = F × Δt, and equivalently J = m × Δv. Both give newton-seconds: a 100 N force applied for half a second delivers 50 N·s, exactly enough to change a 5 kg mass's velocity by 10 m/s.
Is impulse the same as momentum?
Impulse is the change in momentum, not momentum itself — same units (kg·m/s), different meaning. An object can carry huge momentum while experiencing zero impulse if no net force acts on it. That distinction trips up most homework.
Why do airbags reduce injury if the impulse is the same?
They lengthen the stopping time. Since J is fixed by your mass and speed, F = J/Δt shrinks as Δt grows — spreading a crash over 150 ms instead of 20 ms cuts the average force about 7-fold.
What units does impulse use?
Newton-seconds (N·s) in SI, identical to kg·m/s. In US customary work you'll see pound-force-seconds; 1 N·s = 0.2248 lbf·s. Rocket engineers rate total motor output the same way.
How do I find the force from an impulse?
Divide by the contact time: F_avg = J/Δt. A 5.8 N·s catch absorbed over 0.1 s means about 58 N on your glove hand — and ten times that if you stop it rigidly in 0.01 s.