Key takeaways
- Momentum is p = m × v, measured in kilogram-metres per second (kg·m/s).
- A heavier object always carries more momentum at the same speed.
- Momentum has a direction — momentum in opposite directions can cancel out.
- Momentum grows in direct proportion to speed, unlike kinetic energy, which grows with speed squared.
In this guide
What is momentum?
Momentum combines how much mass an object has and how fast it's moving. The more momentum something has, the harder it is to stop or change its direction.
Why does momentum matter?
Momentum is the reason a heavy truck needs a much longer braking distance than a small car moving at the same speed. It's also the core idea behind how engineers study collisions.
A 1,200 kg car at 15 m/s has a momentum of 18,000 kg·m/s, roughly 180 times the momentum of a person walking briskly, even though the car isn't moving especially fast.
The formula
| Symbol | What it means | Example |
|---|---|---|
| p | The momentum, in kilogram-metres per second (kg·m/s) | 18,000 kg·m/s |
| m | The mass, in kilograms (kg) | 1,200 kg |
| v | The velocity, in metres per second (m/s) | 15 m/s |
How to calculate momentum step by step
- 1Find the mass. Weigh the moving object in kilograms.
- 2Find the velocity. Measure its speed in metres per second.
- 3Multiply mass by velocity.
m × vgives you the momentum. - 4Write the answer in kg·m/s.
Try the calculator below with your own mass and velocity to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Ignoring direction. Momentum has a direction, so a car moving north and one moving south don't simply add together — they can partly cancel out.
- Using weight instead of mass. Always use mass in kilograms, not a weight measurement in newtons.
- Forgetting units. Keep mass in kg and velocity in m/s so the answer comes out in kg·m/s.
Tips and tricks
- Working backwards from momentum to velocity? Divide by mass:
v = p ÷ m. - Momentum is closely related to kinetic energy, which also depends on mass and velocity, just with velocity squared instead.
- Compare two objects' momentum before assuming the faster one is automatically "harder to stop" — a heavier, slower object can carry just as much.
Where you'll use it in real life
- Road safety: car safety testing studies momentum to understand crash forces.
- Sport: a heavier player moving at the same speed carries more momentum, which matters in contact sports.
- Space: rocket engines work by throwing exhaust gas out fast to gain momentum in the opposite direction.
- Everyday physics: it's why a bowling ball is harder to redirect mid-roll than a tennis ball at the same speed.
Quick summary
To find momentum, multiply an object's mass in kilograms by its velocity in metres per second. The result, in kg·m/s, describes how hard the object is to stop or turn. Use the calculator above to check your own numbers.
Worked example
A 1,200 kg car is travelling at 15 m/s on a straight road. What is its momentum?
- 01p = m × v
- 02p = 1200 × 15
- 03p = 18000 kg·m/s
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate momentum?
Multiply the object's mass in kilograms by its velocity in metres per second: p = m × v. The result is in kg·m/s.
Why do heavy objects have more momentum?
Momentum is directly proportional to mass, so at the same speed, a heavier object always carries more momentum than a lighter one.
What's the difference between momentum and kinetic energy?
Momentum (m × v) grows in direct proportion to speed, while kinetic energy (½mv²) grows with the square of speed, so it increases much faster as speed rises.
Can momentum be negative?
Yes. Since momentum has direction, an object moving in the negative direction, however you define it, has negative momentum.
