Momentum formula: p = mv
Momentum = mass × velocity, or p = m v. The letter p is momentum in kilogram metres per second (kg m/s), m is mass in kilograms (kg) and v is velocity in metres per second (m/s). It is Higher tier only on all six GCSE specifications, where it sits on the recall list, and it is printed on each board's exam sheet.
Equation
p = m v
| Symbol | Quantity | Unit |
|---|---|---|
p | momentum | kg·m/s |
m | mass | kg |
v | speed | m/s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall · Higher tier only | p = m v |
| AQA Combined Science (8464) | Recall · Higher tier only | p = m v |
| Edexcel Physics (1PH0) | Recall · Higher tier only | p = m v |
| Edexcel Combined Science (1SC0) | Recall · Higher tier only | p = m v |
| OCR Gateway Physics A (J249) | Recall · Higher tier only | p = m v |
| OCR Twenty First Century Physics B (J259) | Recall · Higher tier only | p = m v |
Calculator: p = m v
What momentum is
Momentum measures how hard it is to stop something that is moving. A loaded lorry at 10 m/s has far more momentum than a cyclist at the same speed. A bullet has a tiny mass, but its huge velocity still gives it a lot of momentum.
Momentum has a direction, because velocity does. If two trolleys roll towards each other, give one a positive velocity and the other a negative one. Their momentums then partly cancel when you add them.
In a collision or an explosion with no outside forces, the total momentum before equals the total momentum after. This is called conservation of momentum. It lets you work out how fast things move after they crash or push apart.
Tier and board details
AQA, Edexcel and OCR all print p = m v, with the words momentum = mass × velocity. In AQA 8463 and 8464, Edexcel 1PH0 and 1SC0, and OCR J249 and J259, it is marked as Higher tier content. Foundation papers do not ask you to use it.
Every one of these specifications puts p = m v in its recall group. Exam papers since 2025 have carried a sheet with both the recall and the given equations, so Higher tier students find it there. The Edexcel list and the full comparison of boards show where it sits.
Rearranging and next steps
- m = p ÷ v
- v = p ÷ m
Momentum links to force. A force acting for a time changes the momentum, which is the idea behind the force and momentum equation. Airbags and crumple zones make the change happen over a longer time, so the force on you is smaller.
Do not confuse momentum with kinetic energy. Both depend on mass and speed, but only momentum is always conserved in a collision. Some kinetic energy usually turns into heat and sound.
Worked examples
p
- Change the mass to kilograms: 58 g = 0.058 kg
- p = m × v
- p = 0.058 × 40
- p = 2.32 kg m/s
2.32 kg m/s
v
- v = p ÷ m
- v = 30 000 ÷ 1500
- v = 20 m/s
20 m/s
m
- Change the velocity to m/s: 90 ÷ 3.6 = 25 m/s
- m = p ÷ v
- m = 250 000 ÷ 25
- m = 10 000 kg
10 000 kg
Common mistakes
- Ignoring direction in a collision. A ball moving left must have negative momentum if right is positive, or the totals will not balance.
- Writing the unit as N or J. Momentum is mass times velocity, so its unit is kg m/s.
- Using the mass of only one object after two objects stick together. After they join, use their total mass with their shared velocity.
- Squaring the velocity, as you would for kinetic energy. Momentum uses v once.
Practise getting v or m on its own in the Equation Rearranger.
Questions people ask
Why does a cannon roll back when it fires?
Before firing, nothing moves, so the total momentum is zero. The ball flies forwards with momentum in one direction. The cannon must gain the same amount in the opposite direction to keep the total at zero.
Can a small object have more momentum than a big one?
Yes, if it moves fast enough. A 0.01 kg pellet at 300 m/s has 3 kg m/s, while a 60 kg person creeping along at 0.04 m/s has only 2.4 kg m/s.