Elastic Collision Calculator

Enter the mass and initial velocity of two different objects undergoing an elastic collision. The calculator will calculator the final velocities of each object and the total kinetic energy.

Elastic Collision Formula

The following formula is used to calculate the velocities of two objects after an elastic collision.

m1·vi1 + m2·vi2 = m1·vf1 + m2·vf2

vf1 = [(m1 – m2)·vI1 + 2 m2·vI2]/(m1 + m2)

vf2 = [2 m1·vI1 – (m1 – m2)·vI2]/(m1 + m2)

  • Where M1 and M2 are the masses of the objects
  • VI and VF are the initial and final velocities respect of the obejcts.

The first formula above is derived from the law of conservation of momentum. We can derive these formulas because elastic collisions conserve energy and therefore conserve momentum.

How to calculate an elastic collision

  1. First, determine the masses of each object

    Measure the masses of object 1 and 2 using an accurate scale or formula.

  2. Next, measure the initial velocities of each object

    Using a speed radar or another formula, calculate the initial velocities of the object.

  3. Calculate the final velocities

    Using the two formulas above, and then information measured in steps 1 and 2, calculate the final velocities of the objects after an elastic collision.


What is an elastic collision?

An elastic collision is a collision of 2 or more objects in which the object react perfectly elastically. This means that conservation of momentum and energy are both conserved before and after the collision.

elastic collision calculator

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