Conservation of Momentum Calculator — Elastic & Inelastic
Apply conservation of momentum to a one-dimensional collision. Choose elastic (kinetic energy also conserved) or perfectly inelastic (objects stick together), enter the two masses and initial velocities, and get the final velocities plus a momentum and energy check.
Collision type
kg
kg
m/s
m/s
Velocity of mass 1 after the collision
- 1
Total momentum before
2 × 5 + 3 × -1 = 7 kg·m/s - 2
Numerator for v₁
(2 − 3) × 5 + 2 × 3 × -1 = -11 - 3
Total mass
2 + 3 = 5 kg - 4
Final velocity v₁
-11 ÷ 5 = -2.2000
How does this calculator work?
Momentum is conserved in all collisions: m₁u₁ + m₂u₂ = constant. For elastic collisions KE is also conserved, giving v₁ = ((m₁−m₂)u₁+2m₂u₂)/(m₁+m₂). For perfectly inelastic collisions the bodies stick, giving vf = (m₁u₁+m₂u₂)/(m₁+m₂) with KE loss shown.
Formula
How this is calculated
Conservation of momentum states that in the absence of external forces the total momentum of a system is constant: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. This single equation has two unknowns (the final velocities), so a second constraint is needed to obtain a unique solution.
For an elastic collision the second constraint is conservation of kinetic energy. Solving the two equations simultaneously yields closed-form expressions for v₁ and v₂. When the masses are equal the objects exchange velocities; when a very light object strikes a much heavier stationary one it bounces back with nearly the same speed.
For a perfectly inelastic collision the two objects stick together and share a common final velocity vf = (m₁u₁ + m₂u₂)/(m₁+m₂). Kinetic energy is not conserved — some is converted to heat, sound, and deformation. The energy lost equals KE_before − KE_after. The calculator reports both momentum (which must be equal before and after) and kinetic energy so you can verify conservation. Velocities may be negative to represent motion in the leftward direction.
Frequently asked questions
In an elastic collision both momentum and kinetic energy are conserved — the objects bounce off each other without deformation. In a perfectly inelastic collision momentum is still conserved but the maximum possible kinetic energy is lost, because the objects merge and move together. Most real collisions fall somewhere between these extremes.
By Newton's third law, the force object 1 exerts on object 2 is equal and opposite to the force object 2 exerts on object 1. The impulses cancel, so the total momentum of the two-body system cannot change — it is a conserved quantity regardless of the collision type.
Yes. A negative final velocity means the object is moving in the opposite direction to the positive axis you chose. For example, a light ball bouncing off a heavy wall rebounds with a velocity close to −u₁ (opposite direction, similar speed).
Also known as
TG we-Calculate Editorial Team. (2026). Conservation of Momentum Calculator — Elastic & Inelastic [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/conservation-of-momentum-calculator
TG we-Calculate Editorial Team. "Conservation of Momentum Calculator — Elastic & Inelastic." TG we-Calculate. 2026. https://we-calculate.com/calculator/conservation-of-momentum-calculator.
TG we-Calculate Editorial Team, "Conservation of Momentum Calculator — Elastic & Inelastic," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/conservation-of-momentum-calculator
@misc{wecalculate_conservation_of_momentum_calculator, title = {Conservation of Momentum Calculator — Elastic & Inelastic}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/conservation-of-momentum-calculator}}, year = {2026}, note = {TG we-Calculate} }
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