Momentum Calculator

Momentum measures how hard it is to stop a moving object. The simple formula p = mv says momentum equals mass times velocity, with units of kg·m/s. A heavy slow object and a light fast object can carry the same momentum, but they don't behave identically in collisions because energy and momentum scale with velocity differently.

The companion concept is impulse, J = F × Δt, which equals the change in momentum delivered by a force acting over a time interval. Together they explain why a follow-through matters in baseball, why airbags work, and why two objects rebounding from each other still obey a conservation law: total momentum before a collision always equals total momentum after, as long as no external force interferes.

A 1,200 kg car traveling at 25 m/s rear-ends a stationary 1,800 kg car. They lock bumpers and slide together. What's their combined velocity right after impact?

• Initial momentum: p = 1,200 × 25 + 1,800 × 0 = 30,000 kg·m/s
• Combined mass: 1,200 + 1,800 = 3,000 kg
• Final velocity: v = 30,000 ÷ 3,000 = 10 m/s

Now an impulse example: a tennis player returns a 0.058 kg ball that arrived at 30 m/s and leaves at 35 m/s in the opposite direction. Change in momentum is 0.058 × (35 − (−30)) = 3.77 kg·m/s. If the racket contacts the ball for 4 ms (0.004 s), the average force is 3.77 ÷ 0.004 ≈ 943 N.

• Collision problems — predicting velocities after a crash, billiard hit, or sports impact using conservation of momentum.
• Rocket and propulsion math — thrust comes from changing the momentum of expelled gas.
• Safety engineering — designing crumple zones and airbags by extending Δt to lower peak force for the same Δp.
• Recoil calculations — a fired bullet and the gun must have equal and opposite momentum changes.
• Sports analysis — comparing how mass, swing speed, and contact time interact in a hit.

• Treating momentum as a scalar. Direction matters; opposite velocities partially or fully cancel.
• Confusing impulse with momentum. Impulse is the change in momentum (Δp), not the momentum itself.
• Mixing units. Use kilograms and meters per second. Pounds, mph, and ft/s give wrong answers unless you convert first.
• Assuming kinetic energy is conserved in every collision. Momentum is conserved in all collisions, but KE is only conserved in elastic ones; cars sticking together lose KE to deformation.
• Forgetting about external forces. Conservation of momentum assumes a closed system — friction, gravity along the motion, or other outside forces will change the total.