Conservation of Momentum Calculator
Use conservation of momentum to find the resulting velocities of two objects after a collision, for elastic or perfectly inelastic cases.
What conservation of momentum means
In any collision with no external forces, total momentum before the collision equals total momentum after. This calculator applies that principle to find the resulting velocities for two common idealized collision types.
The formulas
Total momentum is p = m1v1 + m2v2, which is conserved regardless of collision type. For a perfectly inelastic collision (objects stick together), the combined final velocity is v = (m1v1 + m2v2) / (m1 + m2). For a perfectly elastic collision (kinetic energy also conserved), the final velocities are v1′ = ((m1-m2)v1 + 2m2v2)/(m1+m2) and v2′ = ((m2-m1)v2 + 2m1v1)/(m1+m2).
Real collisions usually fall somewhere between these two idealized extremes. This calculator is for general physics education.