Momentum Calculator

Formula

Momentum (p) equals mass (m) times velocity (v), in kg·m/s. For collisions, conservation of momentum states that total momentum before equals total momentum after: m₁v₁ + m₂v₂ = (m₁ + m₂)v_final for a perfectly inelastic collision where objects stick together.

How to use the Momentum Calculator

1. 1

   Enter your mass of object 1

   Value should be in kg.

2. 2

   Enter your velocity of object 1

   Value should be in m/s.

3. 3

   Enter your mass of object 2 (collision)

   Value should be in kg.

4. 4

   Enter your velocity of object 2 (collision)

   Value should be in m/s.

5. 5

   Read your results instantly

   Results update in real time as you type.

Why momentum is conserved

Conservation of momentum is one of the most fundamental laws in physics. It follows directly from Newton's Third Law: when two objects interact, they exert equal and opposite forces on each other for the same duration, so they exchange equal and opposite impulses. The total momentum of the system doesn't change.

This conservation law holds in all situations — rocket propulsion, collisions, explosions, and particle physics. A rocket in space accelerates by expelling mass backward; the backward momentum of the exhaust equals the forward momentum gained by the rocket. Total momentum of rocket + exhaust remains the same.

Elastic vs. inelastic collisions

In an elastic collision, both momentum and kinetic energy are conserved. Billiard ball collisions are approximately elastic. In a perfectly inelastic collision, objects stick together after impact, and kinetic energy is not conserved — some converts to heat, sound, and deformation. Real car crashes are inelastic.

This calculator computes the inelastic case. For elastic collisions, the equations are more complex: v₁' = (m₁-m₂)v₁/(m₁+m₂) + 2m₂v₂/(m₁+m₂), and v₂' = 2m₁v₁/(m₁+m₂) + (m₂-m₁)v₂/(m₁+m₂). Notice that a small ball hitting a much larger stationary ball bounces back, while the larger ball barely moves.

Impulse: changing momentum with force

Impulse is the change in momentum: J = Δp = F × t (force times time). A large force for a short time produces the same impulse as a small force for a long time. This is why airbags save lives: they extend the collision time from milliseconds (hard steering wheel) to tens of milliseconds, reducing the peak force on occupants even though the total impulse (change in momentum) is the same.

Sports equipment uses the same principle. A cricket bat following through on a shot extends contact time, increasing impulse and ball speed. Catching a fast ball by pulling your hand back 'gives' with the ball, extending contact time and reducing the peak force on your hand.

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