Impulse Calculator
The airbag page: change of momentum equals force times time — the crash sets the change, and stretching the time is the only lever anyone has on the force.
Impulse Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Average force over the interval — peaks can exceed it several-fold
- One dimension; no rotational impulse
In short: A 70 kg occupant decelerating from 14 m/s to rest changes momentum by J = 70 × (0 − 14) = −980 kg·m/s. The crash fixed that number; the SURVIVABILITY question is how long the change takes. Over 0.1 s the average force is −980/0.1 = −9,800 N — a 14.276027-g stop. Stretch the same stop to 1 s — airbag, crumple zone, bent knees — and the force falls to −980 N: 1.427603 g. Exactly a tenth the force for ten times the time, because the change was never negotiable. Impulse is why safety engineering is the art of spending time.
Formula
J = F·Δt = m·Δv · F_avg = mΔv/Δt · g's = |F|/(m·9.80665)
Impulse is force accumulated over time — its unit, newton-second, is exactly a kg·m/s of momentum. The equation has two sides and only one is free: mΔv is fixed by the event, so Δt and F trade off inversely. Safety engineering never changes the left side of this equation; it only stretches the right side's denominator.
Worked Example
- Enter the mass, the velocity before and after (signs from one chosen direction).
- Read the impulse — the change is set by the event, not by your engineering.
- Read the average force and its g-quote for the duration you gave.
- Double the duration and watch the force halve: that inverse trade IS the airbag.
Defaults: −980 kg·m/s of change; at 0.1 s that is −9,800 N (14.276027 g); at 1 s, −980 N (1.427603 g). Same crash, tenth the force — the time did all the work.
Strengths & Limits Of This Model
Where this engine is strong
- The stretch trade (10×t → 1/10 F) computed from your own numbers
- g-quoted deceleration beside the newtons
Where it stops
- No force-time profiles or peak estimation
- No restitution — the after-velocity is typed, not modelled
Practical Use Cases
Safety
airbags, helmets, crumple zones — priced honestly
Sport
why you bend your knees landing a jump
Teaching
the FΔt = mΔv identity made live
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Impulse Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
If the change is fixed, what does engineering control?
Only the duration — and through it, the force. The crash decides mΔv; the airbag, helmet foam or crumple zone decides Δt, and F_avg follows as the quotient. That inverse trade is the whole of impact safety design, and this page computes it twice so the ratio is yours.
Why do airbags and crumple zones work?
Neither reduces the impulse — the car stops regardless. Both stretch the time over which the stop happens, cutting the peak and average force proportionally. The stretch card shows the exact exchange rate: 10× the time, a tenth the force, to the digit.
What does the g-quote mean?
The average deceleration as a multiple of standard gravity — |F|/(m·9.80665). Values around 5 g are commonly cited at the edge of untrained tolerance for brief loads; the 14.276027-g default stop is the survivable-with-restraints territory that real crashes straddle. Averages, not peaks: the peak force is always worse.
Why is a truly instant stop refused?
Because Δt = 0 demands an unbounded force — the equation says so and physics agrees: no stop is instant, only fast. The page declines the infinite rather than printing it; give the collision a duration, even a hostile 0.01 s, and the arithmetic returns an answer a wall can be built from.
Does the sign matter here?
Yes — impulse is a vector in 1-D clothing. A negative J with positive v₁ says the force opposed the motion: a stop or a slowdown. The signs let recoil and braking live in the same law without lying about direction.
How is this different from the momentum page?
That page owns the STATE (how much signed motion a mass carries); this page owns the CHANGE (what a force over a time does to it). Same units, different questions — and the impulse is precisely the difference between the momentum page's two readings.
What if the force is not constant?
Then F_avg is the honest average of a varying push — the impulse equals the area under the force-time curve, and peaks can be much higher than the average. Airbag design lives in that gap; this page quotes the average and names it as one.
Where do bent knees come in?
Landing from a jump, your legs choose Δt. Stiff-legged, the stop takes hundredths of a second and the force is bone-breaking; knees bending spend tenths of a second on the same change and divide the force accordingly. Your body discovered the stretch card first.