Elastic Collision Calculator
Calculate post-collision velocities in a 1D elastic collision.
Enter both masses and initial velocities to find final speeds and verify energy conservation.
A perfectly elastic collision conserves both momentum and kinetic energy. No energy is lost to heat, deformation, or sound. Real-world collisions between billiard balls, gas molecules, and subatomic particles come close to this ideal.
Two conservation laws constrain the outcome simultaneously:
Conservation of momentum: m1v1 + m2v2 = m1v1’ + m2v2' Conservation of kinetic energy: (1/2)m1v1² + (1/2)m2v2² = (1/2)m1v1’² + (1/2)m2v2’²
Solving these two equations simultaneously for the final velocities:
v1’ = ((m1 - m2) x v1 + 2 x m2 x v2) / (m1 + m2) v2’ = ((m2 - m1) x v2 + 2 x m1 x v1) / (m1 + m2)
Special cases worth knowing:
- Equal masses (m1 = m2): the objects exchange velocities completely. Object 1 stops; object 2 moves at object 1’s original speed. This is why Newton’s cradle works.
- Very heavy hitting very light (m1 » m2): the heavy object barely slows down; the light object flies off at nearly twice the heavy object’s speed.
- Very light hitting very heavy (m1 « m2): the light object bounces back at nearly the same speed; the heavy object barely moves.
Enter positive velocity for rightward motion and negative for leftward. The calculator verifies that momentum and kinetic energy are conserved to confirm the results are correct.
These equations assume a one-dimensional (head-on) collision. For oblique 2D collisions, the vector components must be handled separately along each axis.