Momentum and Collision Calculator
Enter the mass and velocity of two objects to calculate their velocities after an elastic or perfectly inelastic collision.
Last updated: September 5, 2026
Frequently asked questions
What's the difference between elastic and inelastic collisions?
In an elastic collision, both momentum and kinetic energy are conserved (objects bounce apart cleanly). In a perfectly inelastic collision, momentum is conserved but kinetic energy is not - the objects stick together and move as one, with some energy lost to heat, sound, or deformation.
How do I calculate velocities after an elastic collision?
v1f = ((m1−m2)×v1 + 2×m2×v2) / (m1+m2), and v2f = ((m2−m1)×v2 + 2×m1×v1) / (m1+m2) - these formulas come from solving the conservation of momentum and conservation of kinetic energy equations together.
Why is momentum always conserved, even in inelastic collisions?
Momentum conservation comes directly from Newton's third law (equal and opposite forces during the collision) and doesn't require energy to be conserved - it holds for any collision as long as no external forces act on the system.
What happens to the 'lost' kinetic energy in an inelastic collision?
It converts to other forms of energy - heat from friction and deformation, sound from the impact, and permanent structural deformation of the colliding objects - rather than disappearing, consistent with the overall conservation of energy.
What if the two objects have equal mass in an elastic collision?
They simply exchange velocities - the elastic collision formulas simplify so that v1f = v2 and v2f = v1 when m1 = m2, a classic result you can see with equal-mass billiard balls or Newton's cradle.
How do I find the final velocity of a perfectly inelastic collision?
v_final = (m1×v1 + m2×v2) / (m1+m2), since the objects stick together and move at one shared velocity. For a 2 kg object at 5 m/s hitting a stationary 3 kg object: (2×5 + 3×0)/(2+3) = 10/5 = 2 m/s.
Does this calculator handle collisions in two dimensions, like an angled impact?
No - this calculator only solves 1D (head-on) collisions along a single line of motion. A 2D collision requires separately conserving momentum along two perpendicular axes, which needs the objects' angles as additional inputs.