Momentum Calculator
Linear momentum, p = mv, plus the impulse needed to stop it in a given time.
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Your details
Optional — gives the average force required.
Result
- Momentum
- 30,000 kg·m/s
- Kinetic energy
- 300,000 J
- Impulse to stop it
- 30,000 N·s
- Average force over that time
- 6,000 N
1500 kg at 20 m/s
Momentum is linear in speed; energy is quadratic
Equal in size to the momentum itself
Stopping in 5 s — halve the time and the force doubles
1500 kg moving at 20 m/s…
p = m × v
1500 × 20
p = 30,000 kg·m/s
Formula — written step by step
A 1500 kg car at 20 m/s…
p = m × v
1500 × 20
p = 30,000 kg·m/s
p is momentum, m mass in kilograms and v velocity in metres per second. Unlike energy, momentum is linear in speed — and unlike energy, it is conserved in every collision, whether or not the objects bounce.
A worked example
Why crumple zones work
- Car
- 1500 kg at 15 m/s
- Rigid stop
- 0.05 s
- With crumple zone
- 0.15 s
- p = 1500 × 15 = 22,500 kg·m/s
- Rigid: F = 22,500 ÷ 0.05 = 450,000 N
- Crumple: F = 22,500 ÷ 0.15 = 150,000 N
Tripling the stopping time cuts the force to a third
The momentum to be removed is fixed by the mass and speed — nothing about the car’s design changes it. What a crumple zone changes is the time over which it is removed, and force is momentum divided by time. This is the whole principle behind airbags, helmets and crash barriers.
How to use this calculator
- Enter the mass and speed with their units.
- Add a stopping time to see the average force required to bring the object to rest.
- Compare the momentum and kinetic energy rows — the same motion, measured two ways that behave very differently as speed rises.
- For a collision, work out each object’s momentum separately; the total before and after must match.
What momentum measures
Momentum is mass times velocity — a measure of how hard something is to stop. It is a vector, so direction matters: two objects of equal mass and speed moving towards each other have momenta that cancel exactly.
Its importance comes from conservation. In any collision, the total momentum of the system before equals the total after, provided no external force acts. This holds whether the objects bounce apart, stick together or shatter.
Impulse and why time matters
Impulse is the change in momentum, and it equals the average force multiplied by the time over which it acts. Rearranged, force is momentum divided by time — which is the most useful form for anything involving safety.
The momentum to be removed in a crash is fixed. What engineering can change is the time. A crumple zone, an airbag, a climbing rope’s stretch and a boxer riding a punch all do the same thing: extend the duration so the force falls in proportion.
Momentum is conserved, energy usually is not
This is the distinction that trips people up. Momentum is conserved in every collision. Kinetic energy is conserved only in perfectly elastic ones, which are rare outside of billiard balls and gas molecules.
In a typical car crash, momentum is conserved exactly while a large fraction of the kinetic energy is converted into deformation, heat and sound. Two cars meeting head-on with equal and opposite momentum have zero total momentum before and after — both stop — yet all their kinetic energy has gone somewhere.
Formula & methodology
What this calculator assumes
- Momentum is a vector; this treats motion along one line, so opposing directions must be entered with opposite signs.
- Conserved in every collision provided no external force acts. Kinetic energy is not, except in perfectly elastic collisions.
- The average force assumes the momentum is removed at a constant rate. Real impacts peak well above their average.
Sources
- Young & Freedman, University Physics, 15th edition, Pearson, 2019 — momentum, impulse and collisions.
Momentum against kinetic energy as speed doubles
| Speed | Momentum (1000 kg) | Kinetic energy |
|---|---|---|
| 10 m/s | 10,000 kg·m/s | 50 kJ |
| 20 m/s | 20,000 kg·m/s | 200 kJ |
| 40 m/s | 40,000 kg·m/s | 800 kJ |
| 80 m/s | 80,000 kg·m/s | 3,200 kJ |
Momentum doubles with speed; energy quadruples. Momentum governs what happens in the collision, energy governs how much damage it does.
Frequently asked questions
What is the difference between momentum and kinetic energy?
Momentum is mv and is conserved in every collision; kinetic energy is ½mv² and is conserved only in elastic ones. Momentum determines what happens, energy determines the damage.
Can momentum be negative?
Yes. Momentum is a vector, so the sign records direction. Two objects with equal and opposite momentum have a total of zero.
What units is momentum in?
Kilogram-metres per second, kg·m/s. Impulse uses newton-seconds, N·s, which is the same unit expressed differently.
How does this apply to a collision between two objects?
Add the momenta before, add them after, and the totals must match. Work out each object separately and remember that direction carries a sign.