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Momentum Calculator

Momentum p = m·v, with kinetic energy alongside to show how differently the two scale, a stopping force from any stopping time, and a comparison object.

Momentum is mass in motion: p = m·v, in kg·m/s — the same units as impulse, because impulse is what changes it.

Mass m (kg)Velocity v (m/s)Stopping time (s) — optional

Compare against a second object

Its mass (kg)Its velocity (m/s)

The rectangle is mass against speed — both axes logarithmic, so a bullet and a tanker fit on one chart.

18,760 kg·m/s

momentum

Kinetic energy

125.69 kJ

½mv² — scales with v²

Speed a 1 kg object would need

18.76 km/s

Stopping force

6.25 kN

over 3.00 s

Stopping distance

20.10 m

Against the reference object

Its momentum3.6 kg·m/s

Its kinetic energy1.62 kJ

Momentum ratio0×

Energy ratio0.013×

Instant insight

18,760 kg·m/s of momentum
p = m·v = 1,400 × 13.4. Momentum is mass in motion, and its units are the same as impulse (N·s) because impulse is exactly what changes it. A body keeps its momentum until something exerts a force on it — that is Newton's first law restated.
But its kinetic energy is 125.69 kJ, and that is a different story
Momentum goes as v, kinetic energy as v². Double the speed and the momentum doubles while the energy quadruples. That is why momentum and energy are separate ideas rather than two names for the same thing: a collision conserves momentum always, and conserves energy only if it is elastic.
Compared with the reference object
It carries 0× the momentum and 0.01× the kinetic energy. Those two ratios being different is the whole point: they are not interchangeable measures of "how hard it hits".
A 1 kg object would need 18.76 km/s to match it
Equivalently, something moving at 1 m/s would need to mass 18,760 kg. The same momentum can be packed into almost any combination of the two, which is why a slow lorry and a fast bullet can be comparable on this measure and nothing alike on any other.
Stopping it in 3.00 s takes 6.25 kN
F = Δp/Δt — the impulse–momentum theorem again. It would travel 20.10 m while stopping under that constant force. Halve the time and you double the force; that trade is the entire design brief of a crumple zone.
The stopping distance is the average speed times the time, which is half the initial speed times the time when it decelerates uniformly.
What the model leaves out
One dimension, one body, no rotation. Real momentum is a vector, so two objects can each carry a great deal of it and have zero between them if they are heading in opposite directions — which is exactly what makes a head-on collision so much worse than hitting a parked car.

Worked out in your browser — nothing is sent anywhere.

Compare results

Save this result, change your inputs, and recalculate to compare scenarios side by side.

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Everyday Uses

Collision problems

Apply conservation of momentum to find an unknown velocity after impact.

Recoil and propulsion

Work out recoil velocity, or how expelling mass produces thrust.

Before and after a collision

Check momentum before and after, and see where energy is lost.

Sports impacts

Compare the momentum a heavier slower player carries against a lighter faster one.

Pool, snooker and Newton's cradle

Hit a stationary ball dead straight and the cue ball stops while the target moves off at the same speed. Equal masses swap momentum almost completely, which is what the cradle on the desk is demonstrating.

Why lorries need a longer gap

A 40-tonne truck at 50 km/h carries roughly the momentum of thirty cars. No amount of braking skill closes that gap, which is why tailgating a heavy vehicle is a different risk from tailgating a car.

Frequently Asked Questions

What is momentum?

Mass times velocity, measured in kilogram metres per second. It captures how hard something is to stop: a lorry at 20 mph and a car at 60 mph can carry similar momentum despite very different speeds. Because velocity is a vector, momentum has direction too — two objects of equal mass moving in opposite directions at the same speed have equal and opposite momentum, summing to zero.

What does conservation of momentum mean?

In any closed system with no external forces, total momentum before an interaction equals total momentum after. It holds in every collision, explosion and recoil, whether or not energy is conserved. It is why a rifle recoils, why a rocket accelerates by expelling gas, and why two skaters pushing apart move in opposite directions with momenta that cancel exactly.

What is the difference between elastic and inelastic collisions?

Momentum is conserved in both; kinetic energy only in elastic ones. In a perfectly elastic collision — billiard balls come close — objects bounce apart and total kinetic energy is unchanged. In an inelastic collision energy is lost to deformation, heat and sound. In a perfectly inelastic collision the objects stick together and move as one, which loses the most energy while still conserving momentum exactly.

How does momentum differ from kinetic energy?

Momentum is mass times velocity; kinetic energy is half mass times velocity squared. That squaring matters: doubling speed doubles momentum but quadruples kinetic energy. It is why impact damage rises so steeply with speed, and why a crash at 60 mph is four times as energetic as one at 30, not twice. Momentum tells you about stopping; energy tells you about damage.

What is impulse and how does it relate?

Impulse is force times the time it acts, and it equals the change in momentum. Rearranged, force equals change in momentum divided by time — so extending the duration of a stop reduces the force. Airbags, crash barriers, catching a ball with moving hands and gymnasts rolling on landing all exploit this. The momentum change is fixed; the force is not.

Can momentum be negative?

Yes, and the sign is meaningful rather than a quirk. Momentum is a vector, so once you choose a positive direction, anything moving the other way has negative momentum. Getting the signs right is essential in collision problems — treating both objects as positive is the most common source of wrong answers, because it makes a head-on collision look like a chase.