Momentum Calculator

Linear momentum quantifies how hard it is to stop a moving object. A slow freight train and a fast baseball can carry the same momentum if mass and velocity balance — which is why catching a hard line drive stings even though the ball weighs only 145 grams. Momentum is conserved in isolated systems, making it the go-to quantity for collision analysis in physics labs, vehicle crash reconstruction, and sports science.

Linear momentum:

p = m × v

Where p is momentum (kg·m/s), m is mass, and v is velocity. Impulse — the momentum transferred by a force over time:

J = F × Δt = Δp

Where J is impulse, F is average force, Δt is time interval, and Δp is momentum change. In elastic collisions kinetic energy is also conserved; inelastic collisions objects may stick together sharing final momentum.

Enter mass and velocity for momentum magnitude, or force and contact time for impulse. Vector direction matters in two-dimensional collisions — head-on versus glancing — but scalar magnitudes suffice for introductory straight-line problems. Momentum increases linearly with speed but also grows with mass, explaining why heavy trucks need long braking distances.

Worked example: A 1,400 kg car at 20 m/s has p = 1,400 × 20 = 28,000 kg·m/s. Stopping in 3 s requires average force F = Δp/Δt = 28,000/3 ≈ 9,333 N (about 0.68 g deceleration). A 0.05 kg tennis ball at 50 m/s carries p = 2.5 kg·m/s — small mass but high speed still delivers noticeable impulse on a racket.

Link to the kinetic energy calculator to compare energy-based and momentum-based collision outcomes, and to the force calculator for average impact forces. Conservation problems often pair with the projectile motion tool when fragments separate after an explosion.