Momentum & Impulse Calculator
Solve p = mv, or switch to impulse mode for Δp = FΔt. A live 3D block carries a momentum arrow that grows with mass and speed, and charts show how impulse and collision time trade off.
Reviewed by the ToolNestr Editorial Team — July 2026
Live 3D momentum
Bigger mass = bigger block; faster velocity = faster motion. The green arrow length is the momentum p = mv. Drag to orbit (touch works too).
Momentum & impulse graphs
How momentum and impulse are calculated
The core idea in one line: momentum measures "how hard something is to stop," and impulse is how you change it — a force applied for a length of time.
p = m · v
Momentum — mass times velocity. A vector: it points the way the object moves. Units kg·m/s.
J = F · Δt = Δp
Impulse — average force times the time it acts, which equals the change in momentum. Units N·s (same as kg·m/s).
Rearranging the impulse–momentum theorem gives the result behind every piece of crash safety: F = Δp / Δt. Because Δp is fixed by how fast and heavy the object is, the only way to cut the force in a collision is to increase the stopping time — exactly what airbags, crumple zones, crash mats and bent knees all do.
Worked example 1 — kicking a football
Given: a 0.45 kg ball is kicked from rest to 20 m/s, with the boot in contact for 0.05 s. Find the impulse and the average force.
Worked example 2 — why the airbag helps
Given: a 70 kg driver moving at 14 m/s (~50 km/h) is brought to rest. Compare a hard stop against a dashboard (0.02 s) with an airbag stop (0.20 s).
Two ideas that trip students up
1. Total momentum is conserved
A light fast block meets a heavy slow one. Whatever happens in the crash, the sum of their momenta afterwards equals the sum before — the momentum just gets redistributed, never lost.
2. Impulse is force × time (the area)
The tall thin block (big force, short time) and the short wide one (small force, long time) have the same area — the same impulse, so the same change in momentum.
Momentum of some everyday things
Approximate values, for a sense of scale of "how hard to stop."
| Object | Masskg | Speedm/s | Momentumkg·m/s |
|---|---|---|---|
| Thrown tennis ball | 0.06 | 25 | 1.5 |
| Kicked football | 0.45 | 20 | 9 |
| Sprinter | 70 | 10 | 700 |
| Car on the motorway | 1500 | 30 | 45,000 |
| Loaded lorry | 30,000 | 25 | 750,000 |
Where momentum actually matters
🚗 Vehicle crash safety
Crumple zones, airbags and seatbelts all exist to stretch the collision time. Since F = Δp/Δt, a longer stop turns a lethal force into a survivable one — the single most important application of the impulse–momentum theorem.
🚀 Rockets and recoil
A rocket throws mass (exhaust) backwards and gains equal and opposite momentum forwards. The same conservation law explains gun recoil and why you drift backwards when you throw something on a skateboard.
⚾ Sport technique
"Follow through" is impulse in action: keeping the bat, racquet or boot in contact longer increases Δt and so delivers more momentum to the ball. Catching softly ("giving with the ball") does the reverse to protect the hands.
Common misconceptions
"Momentum and kinetic energy are the same thing."
Momentum p = mv is linear in speed and is a vector; kinetic energy ½mv² is quadratic and a scalar. In an inelastic collision momentum is conserved but kinetic energy is not — they behave differently.
"A big force always means a big change in motion."
Only if it acts long enough. A huge force for a tiny time can deliver a small impulse; a gentle force sustained for a long time can deliver a large one. It's the product FΔt that changes momentum.
"Momentum is destroyed when something stops."
It's transferred, not destroyed. A ball stopped by a wall passes its momentum to the wall and the Earth; the total momentum of the whole system is unchanged.
"Direction doesn't matter for momentum."
Momentum is a vector. Two objects with equal and opposite momenta have a total of zero. When adding momenta you must include sign or direction — this calculator works with magnitudes, so track direction yourself.
Formula sources & further reading
Momentum and the impulse–momentum theorem are standard introductory mechanics, traceable to:
- • OpenStax, University Physics Volume 1 — §9.1–9.2 "Linear Momentum" and "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. Momentum and impulse share units: 1 N·s = 1 kg·m/s.
How to use this calculator
Choose the mode
Momentum (p = mv) for standard problems, or Impulse (Δp = FΔt) for force–time work. The fields and labels switch automatically.
Enter any two
Fill two of the three fields and the third solves live.
Explore in 3D
Use the mass and velocity sliders to feel how momentum grows, and watch the impulse–time trade-off in the charts.
Related tools
Frequently asked questions
What is momentum?
Momentum (p) is mass times velocity: p = mv. It is a vector with units kg·m/s (equivalently N·s). The heavier or faster an object, the more momentum it carries, and the harder it is to stop.
What is impulse?
Impulse is the change in momentum produced by a force acting over a time interval: J = FΔt = Δp. It equals the area under a force–time graph, and shares momentum’s units (N·s = kg·m/s).
Why is momentum conserved in collisions?
By Newton's third law the force each object exerts on the other is equal and opposite, and they act for the same time, so the impulses are equal and opposite. The total momentum of the system therefore does not change.
What is the difference between elastic and inelastic collisions?
Momentum is conserved in both. In an elastic collision kinetic energy is also conserved; in an inelastic collision some kinetic energy is converted to heat, sound or permanent deformation.
How do airbags use the impulse–momentum theorem?
The change in momentum in a crash is fixed. Airbags and crumple zones stretch out the stopping time Δt, and since F = Δp/Δt, a longer time means a much smaller average force on the occupant — that is what reduces injury.
Is momentum the same as kinetic energy?
No. Momentum p = mv is linear in velocity and is a vector; kinetic energy KE = ½mv² is quadratic in velocity and is a scalar. Doubling speed doubles momentum but quadruples kinetic energy.