This impulse calculator finds impulse from force and contact time — and the momentum (and velocity) change it buys: J = F·Δt = Δp.
Safety engineering is impulse management: the same Δp spread over more time means less peak force. Crumple zones, airbags, bent knees on landing and follow-through in sports all trade time against force at a fixed impulse — that trade is this entire page’s lesson.
Impulse Is Force With a Duration — and It Equals Δp Exactly
The impulse-momentum theorem is Newton’s second law integrated over time. The momentum side lives on our Momentum Calculator; what happens when impulses collide is the Collision Calculator. Part of our Physics Calculators collection.
Worked Example (Verified)
- 50 N for 0.20 s on a 2 kg mass (defaults): J = 10 N·s = Δp of 10 kg·m/s → Δv = 5.0 m/s
- The airbag arithmetic: stopping a head’s 25 kg·m/s in 0.01 s (dashboard) averages 2,500 N; over 0.15 s (airbag) it averages ~167 N — same impulse, survivable force
- Catching a fastball barehanded vs with a glove-and-give: the glove doesn’t change Δp; it rents the time to pay it gently
- Average vs peak: real force curves spike; J is the area under F(t), so “average force” is defined as J ÷ Δt — peak forces run roughly 1.5–2× the average in typical impacts
Where Impulse Rules
- Ballistic and crash testing (force plates integrate F·dt directly).
- Rocket science’s specific impulse — impulse per unit propellant weight, the field’s core metric.
- Sports technique: follow-through lengthens Δt on the ball (more Δp) and on your joints (less peak F).
- Impulse is a vector: direction matters as much as magnitude when Δv is the question.
Related Tools
- Momentum Calculator — p = mv, all directions
- Collision Calculator — elastic & perfectly inelastic outcomes
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate impulse?
J = average force × time = F·Δt, in newton-seconds — identically equal to the momentum change Δp. 50 N acting for 0.2 s delivers 10 N·s, which changes a 2 kg object’s velocity by 5 m/s. This calculator returns all three quantities.
What is the impulse-momentum theorem?
The net impulse on an object equals its change in momentum: F·Δt = m·Δv. It is Newton’s second law integrated over the interaction time — and the reason the same momentum change can be gentle (long Δt) or violent (short Δt).
Why do airbags and crumple zones help?
The momentum change of stopping is fixed; injuries track peak force, not impulse. Stretching Δt from ~0.01 s to ~0.15 s divides average force by 15 — the defaults’ numbers show the same division. Safety design is Δt procurement.
Is impulse a vector?
Yes — impulse points along the net force, and Δp points along Δv. A sideways impulse of 10 N·s turns motion rather than speeding it; this calculator reports magnitude for force applied along the motion.
Average force vs peak force — which does J use?
J = ∫F dt equals average force × Δt by definition of that average. Real impacts peak above the average (often ~2× for triangular force profiles). For injury and structural questions, peaks rule; for momentum accounting, the average suffices.
Is this impulse calculator free?
Yes — free, instant, no sign-up.