Momentum Calculator

1. Enter any two of momentum, mass and velocity.
2. Leave the one you want to find blank.
3. Read the result.
4. See which value was solved for and the formula used.

Here is what each result means:

Momentum is a measure of how much motion an object has. It equals the mass times the velocity, so a heavy object or a fast one carries a lot of momentum. A truck rolling slowly and a bullet flying fast can both have large momentum for very different reasons.

Momentum matters most in collisions and impacts, because it is conserved: the total momentum of a closed system stays the same before and after. That single rule lets you predict how objects move after they hit. In SI units momentum is measured in kilogram meters per second, and this calculator links it to mass and velocity.

Momentum also explains why it is harder to stop a heavy or fast object. Bringing something to rest means removing all of its momentum, and the more momentum it carries, the larger the force or the longer the time that takes. A slow oil tanker and a fast tennis ball can be equally stubborn to stop for very different reasons.

It rearranges one relation to solve for whichever value you leave blank.

1. For momentum, multiply mass by velocity.
2. For mass, divide momentum by velocity.
3. For velocity, divide momentum by mass.

Momentum, force and energy all build on mass; see the force calculator and kinetic energy calculator.

A 10 kilogram object moves at 5 meters per second.

Calculation: p = m v = 10 x 5 = 50 kilogram meters per second. To find the velocity that gives a momentum of 60 for a 12 kilogram mass, divide: 60 over 12 is 5 meters per second.

One relation, rearranged for whatever you need to find.

All three come from p equals m v, so any two of the values give the third. This makes the momentum rule one of the simplest and most useful in mechanics, since a single measurement of two quantities always pins down the last one.

Both describe a moving object, but they scale differently with speed.

Momentum is conserved in collisions and has a direction, while kinetic energy can turn into heat and is a single number. In a crash, the total momentum is preserved, but some kinetic energy is lost to sound, heat and deformation, which is why the two quantities behave so differently even for the same objects.

The Mass

A larger mass gives more momentum at the same velocity, since the two multiply.

The Velocity

A higher velocity gives more momentum in direct proportion. Doubling the velocity doubles the momentum.

The Direction

Momentum is a vector, so direction matters. Opposite directions can cancel when momentum is added.

Collisions

Work out momentum before and after an impact, where it is conserved.

Physics Homework

Solve for momentum, mass or velocity in a motion problem.

Sports and Vehicles

Compare how much motion different objects carry.

1. Confusing Momentum with Energy

Momentum is m v; kinetic energy is half m v squared. They behave differently with speed.

2. Ignoring Direction

Momentum has a direction. When adding momenta, opposite directions subtract.

3. Using Weight for Mass

Use mass in kilograms, not weight in newtons.

4. Mixed Units

Use consistent units, ideally kilograms and meters per second.

5. Zero in a Divisor

Solving for mass or velocity cannot divide by zero.

The relation is exact; only the displayed decimals are rounded.

Momentum is how much motion an object has, found by multiplying its mass by its velocity. A heavy or fast object has large momentum. It is measured in kilogram meters per second.

Multiply the mass by the velocity. A 10 kilogram object at 5 meters per second has a momentum of 10 times 5, which is 50 kilogram meters per second.

Divide the momentum by the mass. Leave the velocity field blank and enter momentum and mass, and the calculator solves for it.

Divide the momentum by the velocity. Leave the mass field blank and enter momentum and velocity to solve for the mass.

Yes, in a closed system with no outside forces. The total momentum before a collision equals the total after, which is why momentum is so useful for analyzing impacts.

Momentum is mass times velocity and doubles when speed doubles. Kinetic energy is half mass times velocity squared and quadruples when speed doubles. Momentum also has a direction.

Yes. Momentum is a vector, so it has both size and direction. When combining momenta, motions in opposite directions partly cancel.

The SI unit is the kilogram meter per second, when mass is in kilograms and velocity in meters per second. Keep the units consistent for a correct result.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Momentum (Wikipedia).
• Momentum explained (Maths Is Fun).
• Conservation of momentum (Wikipedia).