Solve p = mv for momentum, mass, or velocity with step-by-step. Free, exact, and mobile-friendly.
Momentum is the “oomph” of a moving object — the reason a slow truck is harder to stop than a fast tennis ball. Physicists define it simply: momentum equals mass times velocity. Our free Momentum Calculator solves p = m × v for momentum, mass, or velocity, showing every step so collisions, sports, and vehicle-safety problems become straightforward.
Momentum measures how much motion an object carries. A 0.06 kg tennis ball at 40 m/s has momentum 2.4 kg·m/s. A 1,200 kg car rolling at just 2 m/s has momentum 2,400 kg·m/s — a thousand times more, which is why you can catch the ball but must jump clear of the car. Both mass and velocity matter equally: doubling either doubles the momentum.
Momentum is a vector, meaning direction counts. Two objects with equal speed moving toward each other have opposite momenta, and their total can cancel to zero. This vector nature is what makes momentum conserved in collisions: the total momentum before a crash equals the total after, no matter how tangled the wreckage.
Key terms:
Momentum equals mass multiplied by velocity. Because velocity has direction, momentum points the same way the object moves. The closely related concept of impulse (F × t) equals the change in momentum — which is why airbags work: they stretch out the collision time, shrinking the force needed to cancel your momentum.
A 1,200 kg car travels at 25 m/s (about 90 km/h or 56 mph).
A 0.45 kg soccer ball is kicked with momentum 9 kg·m/s. How fast is it moving?
A 20,000 kg truck at 15 m/s carries momentum 300,000 kg·m/s; a 1,500 kg car at the same speed carries only 22,500. To stop, brakes must cancel all of it through impulse (force × time). The truck needs over thirteen times the braking impulse — the physical reason trucks need far longer stopping distances and why runaway-truck ramps exist on steep highways.
Conservation of momentum explains recoil. A 5 kg cannonball fired at 300 m/s carries 1,500 kg·m/s forward. The 500 kg cannon must gain 1,500 kg·m/s backward, so it recoils at 1,500 ÷ 500 = 3 m/s. The same math governs rocket propulsion: throwing mass one way pushes the rocket the other.
A final real-world note: rocket staging is momentum conservation in action. When a spent booster separates and falls away, the remaining spacecraft gains velocity — not from extra thrust, but because the same total momentum now belongs to less mass. Mission planners compute these velocity changes (delta-v) with the Tsiolkovsky rocket equation, which is essentially momentum bookkeeping for a continuously lightening vehicle. Every course correction burn is the same idea in miniature: eject a little mass one way, gain a little velocity the other.
Not all collisions treat momentum and energy the same way, and the distinction matters enormously. In a perfectly elastic collision — like two billiard balls striking — both momentum and kinetic energy are conserved. The balls rebound with the same total energy they had coming in, just redistributed. In a perfectly inelastic collision — like a lump of clay hitting a wall — the objects stick together; momentum is still conserved, but kinetic energy is not. The “missing” energy becomes heat, sound, and deformation.
Real crashes sit between these ideals. Car manufacturers exploit this deliberately: crumple zones are engineered to be as inelastic as possible, converting the car’s kinetic energy into crumpling metal rather than into the passengers’ bodies. The momentum still has to go somewhere — the car stops — but stretching the collision over extra milliseconds and extra centimeters keeps the peak force survivable. Airbags, seatbelts, and helmets all work on the same principle: manage the momentum change gently.
Sports equipment makes the opposite trade. A tennis racket’s strings, a baseball bat’s sweet spot, and a golf club’s face are all tuned to be as elastic as possible, returning maximum kinetic energy to the ball. The coefficient of restitution — the ratio of relative speeds after and before impact — quantifies this: 1.0 is perfectly elastic, 0 is perfectly inelastic, and a well-struck tennis ball is around 0.8.
Linear momentum p = m × v (kg·m/s), a vector in the direction of velocity. Rearrangements: m = p/v, v = p/m. Total momentum is conserved in closed systems; impulse F·t equals change in momentum. Source: Sigma Calculator, Momentum Calculator, https://sigmacalculator.net/math-calculators/momentum-calculator/
Cite this page as: Momentum Calculator, Sigma Calculator, https://sigmacalculator.net/math-calculators/momentum-calculator/
Last updated: October 12, 2026