Momentum and Impulse Calculator

This momentum and impulse calculator helps you work out two closely linked quantities in classical mechanics quickly and reliably. Linear momentum is the product of an object's mass and its velocity, written as p equals m times v, and it measures how much motion an object carries. Impulse is the change in momentum produced by a force acting over a period of time, written as impulse equals force times time, and by the impulse momentum theorem it equals the change in momentum. You enter the mass in kilograms, the velocity in metres per second, the applied force in newtons and the time in seconds, and the tool returns momentum in kilogram metres per second and impulse in newton seconds. The units of newton seconds and kilogram metres per second are equivalent, which is why a steady force over time can be compared directly with a change in momentum. Students, teachers and engineers use this calculator to check homework, design simple experiments and reason about collisions, rocket thrust and sports impacts. A few good habits make your results trustworthy. Always work in consistent SI units before you start, since mixing grams with kilograms or kilometres per hour with metres per second is the most common source of error. Remember that momentum is a vector, so direction matters when objects move in different directions and you may need to treat one direction as positive. Finally, check that your impulse and your change in momentum agree, because they should be equal for a single object, and any mismatch usually points to a unit slip or a sign mistake that is worth tracking down before you trust the answer.

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50.00 kg m/s
Momentum
Impulse60.00 N s

Momentum p = m v. Impulse = F t = change in momentum.

How it works

Momentum is mass multiplied by velocity, so 5 kilograms at 10 metres per second gives 50 kilogram metres per second. Impulse is force multiplied by time, so 20 newtons over 3 seconds gives 60 newton seconds. Impulse equals the change in momentum the force would produce.

Worked example

With a mass of 5 kilograms moving at 10 metres per second, momentum is 5 times 10, which is 50.00 kilogram metres per second. With a force of 20 newtons acting for 3 seconds, impulse is 20 times 3, which is 60.00 newton seconds.

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Frequently asked questions

What is the difference between momentum and impulse?

Momentum is the quantity of motion an object has, equal to mass times velocity. Impulse is the change in that momentum, equal to force multiplied by the time it acts. Impulse and the change in momentum are always equal for a single object.

Why are the units kg m/s and N s the same?

A newton is one kilogram metre per second squared. Multiplying that by seconds cancels one second, leaving kilogram metres per second. So newton seconds and kilogram metres per second describe the same physical quantity.

Does direction matter for momentum?

Yes. Momentum is a vector, so it has both size and direction. When objects move in opposite directions you must assign signs, treating one direction as positive and the other as negative before adding.