An elastic collision is the special case where two objects bounce off each other without losing any kinetic energy to heat, sound, or deformation. This calculator solves the standard 1D elastic-collision equations for the final velocities of both objects, and shows the momentum and kinetic-energy bookkeeping that proves the collision really is elastic.
How the Elastic Collision Calculator works
The calculator solves two equations at once: conservation of momentum (m1v1 + m2v2 = m1v1' + m2v2') and conservation of kinetic energy (1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 m1v1'^2 + 1/2 m2v2'^2). Solving that pair of equations for the two unknown final velocities gives the closed-form formulas shown in the Formula section, so the result appears instantly with no iteration needed.
The calculation assumes the collision is one-dimensional (both objects move along the same line, before and after) and perfectly elastic. Real-world collisions — car crashes, most sports impacts — lose some energy to heat and deformation and are only approximately elastic; billiard balls, gas molecules, and hard-sphere collisions in physics problems are the closest real examples.
Inputs and what they mean
Enter each object's mass in kilograms (always positive) and its velocity in meters per second, using a consistent sign convention for direction — for example, moving right is positive and moving left is negative. Object 2's velocity is commonly set to 0 to model a stationary target, but any signed value works.
The mass ratio between the two objects has an outsized effect on the result: when the masses are equal, the objects trade velocities exactly; when one mass dominates, the lighter object absorbs most of the velocity change while the heavier object barely notices the collision.
Limits and edge cases
This calculator only models 1D (head-on) elastic collisions — it does not handle 2D or 3D collisions at an angle, where the final velocities depend on the impact angle as well as the masses and speeds. It also assumes momentum and kinetic energy are exactly conserved, so it should not be used to model real inelastic impacts like car crashes.
If both masses are zero, or the numbers you enter aren't valid, the calculator flags the input rather than showing a result — a total mass of zero has no physical collision to solve for. For a collision where the objects stick together instead of bouncing apart, use a perfectly inelastic collision calculation instead of this one.