Momentum Calculator
This momentum calculator finds the linear momentum of a moving object from its mass and velocity, p = m v. Enter the mass and the velocity and the momentum calculator returns the momentum in kilogram metres per second. It is the quick way to work a momentum problem without doing the multiply by hand.
Results
The Momentum Calculator is part of our Motion & Force collection. Browse more motion & force to size, convert, and check your work alongside this tool.
What the momentum calculator shows
Momentum is how much motion an object carries, and it grows with both mass and speed. This momentum calculator multiplies the mass by the velocity to give the linear momentum, p = m v. A heavy truck at a low speed and a light bullet at a high speed can carry the same momentum, which is what the momentum calculator makes easy to compare.
How the momentum calculator works
The momentum calculator uses the linear momentum formula:
m is the mass and v is the velocity, so momentum rises in direct proportion to each. Because velocity is a vector, momentum has a direction too, pointing the same way the object moves. The unit is the kilogram metre per second, and there is no separate unit name for it.
Momentum calculator example
A 1500 kg car moving at 20 m/s. The momentum calculator gives:
So the car carries 30,000 kilogram metres per second of momentum. Change the speed and the momentum calculator updates the result at once.
How to use the momentum calculator
Enter the mass in kilograms and the velocity in metres per second, then the momentum calculator returns the momentum in kilogram metres per second. Velocity has a direction, so use a sign if the object moves backward. As a momentum solver it also echoes the mass and velocity you entered so you can check the inputs at a glance.
Reading the momentum calculator result
The momentum is the product of mass and velocity, and it is what a collision has to absorb or redirect. A larger momentum is harder to stop, which is why a fast or heavy object needs a bigger force or a longer time to bring to rest. That link is the impulse momentum idea: a force applied over time changes the momentum. Use the momentum calculator result as the starting point for collision and impulse problems.
When to use the momentum calculator
- Solving collision problems with the momentum calculator
- Comparing the momentum of two moving objects
- Setting up an impulse or change in momentum problem
- Checking physics homework quickly
Common momentum calculator mistakes
- Ignoring direction. Momentum is a vector, so use a sign for objects moving opposite ways.
- Confusing momentum with energy. Momentum is m v; kinetic energy is half m v squared and grows faster with speed.
- Mixing units. Use kilograms and metres per second for a result in kilogram metres per second.
Tips for momentum problems
- Keep mass in kilograms and speed in metres per second.
- Track direction with a sign in collision problems.
- Use impulse, force times time, for the change in momentum.
Change in momentum calculator and impulse
A change in momentum calculator answers the question a plain momentum figure cannot: how a force acting over time speeds up or slows an object. The impulse momentum theorem says the impulse, force times the time it acts, equals the change in momentum. That is why a long, gentle stop and a short, hard stop can remove the same momentum: a crumple zone stretches the time so the force stays low. An impulse momentum theorem calculator rearranges this to find any one of force, time, or momentum change from the other two. Start from the momentum of each state, then subtract to get the change, and divide by the time for the average force.
Bullet momentum calculator and momentum solver
A bullet momentum calculator shows why small, fast objects still hit hard. A 10 gram bullet at 400 m/s carries 4 kg·m/s, the same momentum as a 40 kg object walking at 0.1 m/s, but delivered in a tiny area over a tiny time, which is what makes it dangerous. As a general momentum solver, the tool works in reverse too: given a momentum and a mass, the velocity follows, and given a momentum and a velocity, the mass follows. The kinetic energy calculator then shows the energy that same motion carries, which grows with the square of the speed rather than in proportion to it.
Momentum calculator reference values
Linear momentum for several mass and speed pairs, from the momentum calculator:
| Mass | Velocity | Momentum |
|---|---|---|
| 1500 kg | 20 m/s | 30,000 kg·m/s |
| 1000 kg | 30 m/s | 30,000 kg·m/s |
| 0.01 kg | 400 m/s | 4 kg·m/s |
| 70 kg | 10 m/s | 700 kg·m/s |
Momentum Calculator FAQ
What is the momentum formula?
The momentum formula is p = m v, mass times velocity. The momentum calculator applies it and returns the result in kilogram metres per second.
What is change in momentum?
It is the difference between the final and starting momentum, equal to the impulse, force times time. A change in momentum calculator subtracts one momentum from the other.
Does momentum have a direction?
Yes. Velocity is a vector, so momentum points the same way the object moves. Use a sign to show direction in one dimension.
How does a bullet have large momentum?
A bullet has a small mass but a very high speed, so a bullet momentum calculator still returns a notable value because momentum is mass times velocity.