Impulse Calculator
Solve the impulse–momentum theorem J = FΔt = Δp from any two of force, time and impulse, or from mass and the change in velocity. A live 3D puck shows a strike in action, and charts show impulse as the area under a force–time graph.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that trip students up
1. Impulse is the area under F–t
The stacked bars trace out a force-vs-time rectangle. Their combined volume is exactly J = FΔt — impulse is literally the area (here, volume) swept out while the force acts.
2. A struck object gains velocity
The red arrow shows the force hitting the puck; the green arrow shows the velocity change (Δv) it produces — the impulse–momentum theorem, drawn as two vectors.
Impulse graphs
How it works
The core idea in one line: impulse is what a force actually does to motion over time — it's the push, sustained, and it equals exactly the change in momentum it causes.
J = F · Δt
impulse from a constant (or average) force acting over a time interval
J = Δp = m(vf − vi)
impulse–momentum theorem — impulse equals the resulting change in momentum
J = area under F–t graph
for a varying force, impulse is the area under the curve, not just F×Δt
Rearranging the impulse–momentum theorem gives F = J/Δt: for a fixed impulse (a fixed momentum change), a longer contact time means a smaller average force. That single rearrangement explains airbags, padded gloves and why 'giving' with a catch doesn't hurt.
Worked example 1 — hockey puck slap shot
Given: A stick applies an average force of 400 N to a 0.17 kg puck for 0.015 s. Find the impulse and the resulting change in velocity (puck starts at rest).
Worked example 2 — catching a ball softly
Given: A 0.15 kg ball arrives at 18 m/s and is brought to rest. Compare a rigid catch (Δt = 0.01 s) with a soft "giving" catch (Δt = 0.15 s).
Same impulse, but a 15× longer catch time cuts the average force by 15× — why "giving" with a catch doesn't sting.
Typical impulses in sports and safety
Approximate values — impulse is what changes an object's momentum in a collision or strike.
| Event | ForceN (approx.) | Times | ImpulseN·s |
|---|---|---|---|
| Tennis serve | ~600 | 0.005 | ~3 |
| Football kick | ~1,500 | 0.008 | ~12 |
| Boxing punch (gloved) | ~2,500 | 0.015 | ~38 |
| Car airbag deployment | ~5,000 | 0.15 | ~750 |
| Car crash without airbag | ~50,000 | 0.02 | ~1,000 |
Impulse J = FΔt is the area of the force–time rectangle; real strikes have varying force, so these are average-force estimates.
Where impulse actually matters
🎈 Airbags and crumple zones
A crash must remove a fixed amount of momentum (a fixed impulse). Airbags and crumple zones extend the stopping time Δt, which — since F = J/Δt — sharply cuts the peak force on the occupant.
🥊 Padding and follow-through
Boxing gloves, catcher's mitts and crash mats all work the same way: spreading a fixed impulse over more time lowers the force. Follow-through in golf, tennis and batting does the opposite on purpose — it extends contact time to deliver more impulse (more Δp) to the ball.
🖐️ Catching a ball
"Giving" with your hands as you catch increases Δt for the same required impulse, reducing the sting compared to catching rigidly.
Common misconceptions
"Impulse and force are the same thing."
Force is measured in newtons; impulse is force accumulated over time, measured in newton-seconds. A small force applied for a long time can deliver the same impulse as a huge force applied briefly.
"J = FΔt works for any force."
It only gives the exact impulse for a constant force, or F as the average force. For a force that changes with time, impulse is the area under the F–t curve, which may not equal (peak F) × Δt.
"Longer contact time always means a bigger hit."
It depends on what you're trying to do. To reduce force for the same impulse (airbags, catching), you want a longer Δt. To increase impulse itself (a golf swing), you want a longer Δt at a sustained force — the goal, not the time alone, determines what "better" means.
"Impulse only matters in collisions."
Impulse describes any momentum change from a force over time — throwing a ball, a rocket burn, or a sustained push all involve impulse, not just crashes.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §9.2 "Impulse and Collisions" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 9, Center of Mass and Linear Momentum.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 9, Linear Momentum and Collisions.
Results are rounded for display. Impulse and momentum share units: 1 N·s = 1 kg·m/s.
How to use this calculator
Pick the mode
"Force & time" for J = FΔt; "Momentum change" for J = mΔv.
Enter two values
Fill any two of the three fields; the third solves live.
Watch the strike
Use the sliders to see how force and duration shape the impulse and the resulting velocity change.
Related tools
Frequently asked questions
What is impulse?
Impulse (J) is the change in momentum produced by a force acting over a time interval: J = FΔt for a constant force, and J = Δp = m(v_f − v_i) by the impulse–momentum theorem. Units are newton-seconds (N·s), the same as kg·m/s.
How is impulse different from momentum?
Momentum (p = mv) describes the motion an object has right now. Impulse is the change delivered to that momentum by a force over time — it is the "action" that alters momentum, not a property an object carries by itself.
What if the force is not constant?
Then J = FΔt only works with the average force. In general, impulse is the area under a force-vs-time graph: J = ∫F dt. This calculator assumes a constant (or average) force, which is exactly the area of a rectangle F × Δt.
Why do airbags and padded gloves reduce force?
The impulse needed to stop a given object at a given speed (Δp) is fixed. Since J = FΔt, stretching out Δt over a longer time reduces the average force F needed to deliver the same impulse — that is the entire principle behind airbags, crash mats and boxing gloves.
Can impulse be negative?
Yes. Impulse is a vector in the direction of the force. If a force decelerates an object, the impulse is opposite to the direction of motion, and Δp = m(v_f − v_i) comes out negative if v_f < v_i along your chosen positive axis.