Momentum Calculator (p = mv)

Momentum Calculator works with linear momentum, the product of an object’s mass and its velocity. Enter any two of momentum, mass and speed and the third is worked out at once, with the formula and the working shown in SI units underneath. Each value has its own unit, so you can mix them: momentum in kilogram metres per second, newton seconds (the same unit, written the way impulse usually is), gram centimetres per second or pound feet per second; mass in kilograms, grams, tonnes or pounds; speed in metres per second, kilometres per hour, miles per hour, feet per second or knots. Alongside the answer it gives the kinetic energy that goes with that momentum, E = p² ÷ 2m, because the two are often needed together — in collision problems, for example, momentum is always conserved but kinetic energy usually is not.

1. Type two of the three values and pick their units.
2. Leave the third empty; it is worked out and highlighted.
3. Read the kinetic energy under the answer, and the working in base units.
4. Change any unit to see the answer another way. Clear all starts again.

• Momentum is a vector: it has a direction as well as a size. This page works with sizes. For a collision in a straight line, give one direction a minus sign in your own working and add the momenta before and after.
• It is the Newtonian formula. Near the speed of light momentum grows faster than m × v (it becomes γmv), so the result would be too small.
• Mass is taken as constant. A rocket losing fuel needs the rocket equation.
• Kinetic energy shown is for motion in a straight line; a spinning object also stores rotational energy.
• The calculation runs in your browser. Nothing you type is sent anywhere or saved.

A 1,200 kg car at 25 m/s (90 km/h) has 30,000 kg·m/s of momentum — the page opens with this example. Doubling the speed doubles the momentum but quadruples the kinetic energy.

Impulse is a change in momentum: the force on an object multiplied by how long it acts, F × t. That is why both are measured in newton seconds. A longer stopping time — an airbag, a crumple zone — means a smaller force for the same change in momentum.

Yes, in any collision or explosion where no outside force acts, the total momentum before equals the total after. Kinetic energy is conserved only in perfectly elastic collisions; in real ones some turns into heat, sound and bent metal.

Divide the momentum by the mass. Enter both, leave speed empty, and choose the unit you want the speed in — for example, 5.8 kg·m/s for a 145 g baseball gives 40 m/s.