Elastic Collision Calculator

A perfectly elastic collision is the special case where two objects bounce off each other conserving both momentum and kinetic energy simultaneously — no energy is lost to heat, sound, or deformation, which real collisions like billiard balls or gas molecules only approximate but idealized physics problems assume outright. This calculator solves the standard textbook derivation for one-dimensional collisions: v1f = ((m1 − m2)v1i + 2m2·v2i) / (m1 + m2) and the mirrored expression for v2f, obtained by combining the two conservation equations (momentum and kinetic energy) and eliminating one unknown. It also reports total momentum and total kinetic energy both before and after, so you can directly verify that both quantities match — small differences you might see are just floating-point rounding, not physics. Sign convention matters here: velocities are signed along one axis, so a negative value means motion in the opposite direction from a positive one, and objects moving toward each other should have opposite signs.

Both masses must be positive and nonzero. A useful sanity check built into the results is the "KE transferred" figure, the amount of kinetic energy handed from object 1 to object 2 — in the special case of equal masses, this comes out to a full velocity swap (object 1 stops, object 2 takes on object 1's exact initial velocity), while a very heavy object colliding with a light one barely changes its own velocity but can send the light object away at nearly twice the heavy object's speed. This differs sharply from a perfectly inelastic collision, where the objects stick together and only momentum, not kinetic energy, is conserved.