Best Elastic Collision Calculator to Solve Momentum and Energy Conservation

What is an Elastic Collision?

An elastic collision is one in which both momentum and kinetic energy are conserved. Perfect elastic collisions occur at the atomic/molecular level in ideal gas behavior. In everyday life, billiard balls and Newton's cradle approximate elastic collisions. Contrast with inelastic collisions, where kinetic energy is lost to heat or deformation.

🎱 Elastic Collision Calculator

Use our free calculator for instant, accurate results.

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📐 Formula

v₁' = (m₁−m₂)u₁/(m₁+m₂) + 2m₂u₂/(m₁+m₂)

Similarly: v₂' = (m₂−m₁)u₂/(m₁+m₂) + 2m₁u₁/(m₁+m₂). u = initial velocity, v = final velocity.

📝 Worked Example

m₁=2kg at 3m/s hits m₂=1kg at rest (u₂=0):
v₁' = (2−1)×3/(2+1) + 0 = 1 m/s
v₂' = 0 + 2×2×3/(3) = 4 m/s
Check: KE_before = ½×2×9 = 9J; KE_after = ½×2×1+½×1×16 = 1+8 = 9J ✓

📝 How to Use the Calculator

Enter Mass 1 & VelocityMass (kg) and initial velocity (m/s) of object 1.

Enter Mass 2 & VelocityMass (kg) and initial velocity of object 2 (0 if at rest).

CalculateView final velocities of both objects after collision.

Verify ConservationCheck that momentum and kinetic energy totals match before/after.

❓ FAQ

What happens in a perfectly inelastic collision?

Objects stick together after collision. Momentum is conserved but maximum kinetic energy is lost: v' = (m₁u₁ + m₂u₂)/(m₁+m₂).

Can two objects of equal mass exchange velocities in elastic collision?

Yes — if m₁=m₂, object 1 stops and object 2 takes the initial velocity of object 1. Newton's cradle demonstrates this perfectly.