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Impulse Calculator
Calculate impulse J = F·Δt, or use the impulse–momentum theorem J = m(v₂ − v₁). Solve for impulse, average force or contact time, and see how stretching out the contact time lowers the force of an impact.
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Signed: negative = opposite direction
Enter your values to see the result.
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How to use the Impulse Calculator
- Choose what to calculate: impulse, force, time, impulse from momentum change, or average impact force.
- Enter the known values and pick units.
- Use signs for direction: a ball bouncing back has a negative velocity on one side.
- Press Calculate to see the answer with the formula and your numbers.
- Check the table to see how much a longer contact time reduces the force.
Impulse formulas
| Find | Formula | Example |
|---|---|---|
| Impulse | J = F · Δt | 500 N × 0.05 s = 25 N·s |
| Impulse (momentum) | J = m · (v₂ − v₁) | 0.6 kg × (4.5 − (−6)) m/s = 6.3 N·s |
| Average force | F = J ÷ Δt = m · Δv ÷ Δt | 1,500 kg × 13.9 m/s ÷ 3 s ≈ 6.9 kN |
| Contact time | Δt = J ÷ F | 10 lbf·s ÷ 20 lbf = 0.5 s |
For a force that changes during the contact, impulse is the area under the force–time graph, J = ∫F dt. The calculator's "average force" is the constant force that would deliver the same impulse in the same time; the peak force in a real impact is usually higher.
Typical contact times
| Event | Approximate contact time |
|---|---|
| Bat hitting a baseball | 0.5–1 ms |
| Golf club striking a ball | about 0.5 ms |
| Kicking a soccer ball | 8–12 ms |
| Landing a jump with bent knees | 0.1–0.3 s |
| Car stopping in a crash with crumple zones | 0.07–0.15 s |
Sign convention: pick one direction as positive. A velocity, force or impulse in the opposite direction is negative, so a rebound changes momentum more than a dead stop.
Frequently asked questions
What is impulse in physics?
Impulse is the effect of a force acting over time: J = F·Δt for a constant (or average) force. It is a vector measured in newton-seconds (N·s), which is the same unit as momentum (kg·m/s).
How is impulse related to momentum?
By the impulse–momentum theorem, the impulse on an object equals its change in momentum: J = Δp = m(v₂ − v₁). A 0.145 kg baseball going from −40 m/s to +45 m/s receives an impulse of 0.145 × 85 = 12.3 N·s.
How do I calculate average force from impulse?
Divide impulse by contact time: F = J ÷ Δt. If that baseball is in contact with the bat for 0.7 ms, the average force is 12.3 ÷ 0.0007 ≈ 17,600 N.
Why do airbags and crumple zones reduce injuries?
The impulse needed to stop you is fixed by your mass and speed, but airbags, padding and crumple zones make the stop last longer. Since F = J ÷ Δt, doubling the stopping time halves the average force.
Why does a bouncing ball get a bigger impulse than one that sticks?
Its velocity reverses direction, so the change in momentum includes both stopping and moving back: m(v₂ − v₁) with v₁ and v₂ of opposite sign. A perfect bounce gives twice the impulse of a ball that simply stops.
What are the units of impulse?
The SI unit is the newton-second (N·s = kg·m/s). In US customary units it is the pound-force second (lbf·s); 1 lbf·s ≈ 4.448 N·s.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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