Momentum Calculator
Momentum is mass multiplied by velocity, and it is the quantity that decides how hard something is to stop. It is a vector, so direction matters, and unlike kinetic energy it grows in a straight line with speed.
Momentum in kilogram metres per second
30,000
- Kinetic energy in joules
- 300,000
- Stopping time in seconds
- 5
- Stopping distance in metres
- 50
- Impulse needed to stop in newton seconds
- 30,000
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
p = m v
- m
- Mass in kilograms
- v
- Velocity in metres per second, with a sign for direction
- p
- Momentum in kilogram metres per second
- F
- Force in newtons, when working through impulse
How to check the result by hand
- 1
Write the velocity with its sign
Momentum inherits the direction of the velocity, so decide which way is positive before substituting. A car rolling backwards at 20 metres per second carries minus 30000 kilogram metres per second, not plus.
- 2
Multiply mass by velocity
1500 kilograms times 20 metres per second gives 30000 kilogram metres per second. Both inputs must be in SI units; a mass in grams or a speed in kilometres per hour breaks the result silently.
- 3
Convert speed if it was given in kilometres per hour
Divide by 3.6 first. A 100 kilometre per hour figure becomes 27.7777778 metres per second, and feeding the raw 100 would inflate the momentum by a factor of 3.6.
- 4
Use impulse to reach force or time
Divide the momentum change by the force to get the contact or stopping time, or divide by the time to get the average force. Rebounding doubles the change, because the momentum reverses rather than merely reaching zero.
- 5
Check the total before and after a collision
Add the signed momenta of every object. If an external force is absent the sum must be identical before and after, which is the quickest way to catch a sign error or a forgotten mass.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Momentum page.