BYTETOOLS

Momentum Calculator

Calculate momentum p = mv, impulse J = FΔt, and solve 1D elastic or perfectly inelastic collisions from conservation of momentum, all in your browser.

30,000 kg·m/s
Momentum
1,500 kg
Mass
20 m/s
Velocity

Working

p = m × v = 1,500 kg × 20 m/s = 30,000 kg·m/s

What is the Momentum Calculator?

The ByteTools Momentum Calculator has three modes. Momentum mode solves p = m × v for momentum, mass or velocity.

  • Solves p = mv for momentum, mass or velocity
  • Impulse–momentum theorem: J = FΔt = Δp
  • 1D elastic and perfectly inelastic collision solver
  • Momentum conservation check shown before vs after
  • Kinetic energy lost in inelastic collisions reported
  • 100% private — runs entirely in your browser

How to use the Momentum Calculator

  1. 1

    Pick a mode: momentum (p = mv), impulse (J = FΔt) or collision.

  2. 2

    Enter the known values — use negative velocities for opposite directions.

  3. 3

    In collision mode, choose elastic or perfectly inelastic.

  4. 4

    Read final velocities, momentum totals and kinetic energy lost.

  5. 5

    Copy the results with one click.

About the Momentum Calculator

The ByteTools Momentum Calculator has three modes. Momentum mode solves p = m × v for momentum, mass or velocity. Impulse mode uses the impulse–momentum theorem J = F × Δt = Δp to find impulse, average force, contact time or the change in momentum. Collision mode solves one-dimensional two-body collisions.

For collisions, enter both masses and initial velocities. The perfectly inelastic case (objects stick together) gives the shared final velocity v = (m₁u₁ + m₂u₂) ÷ (m₁ + m₂) from conservation of momentum alone. The elastic case also conserves kinetic energy, giving the standard v₁ and v₂ formulas — the tool reports final velocities, total momentum before and after, and how much kinetic energy was lost.

Signs carry direction: use negative velocity for motion to the left. Everything runs 100% locally in your browser — nothing is uploaded and it works offline.

Frequently asked questions

How do you calculate momentum?

Momentum is mass times velocity: p = m × v, measured in kg·m/s. A 1,500 kg car at 20 m/s has p = 30,000 kg·m/s. Momentum is a vector, so direction matters — in one dimension we carry it with a plus or minus sign.

What is impulse?

Impulse is force multiplied by the time it acts, J = F × Δt, and it equals the change in momentum it produces. That is why airbags and crumple zones work: stretching the stopping time lowers the average force for the same momentum change.

What is the difference between elastic and inelastic collisions?

Both conserve momentum. Elastic collisions also conserve kinetic energy — think billiard balls or colliding gas molecules. In a perfectly inelastic collision the objects stick together and the maximum possible kinetic energy is converted to heat and deformation.

What happens when two equal masses collide elastically?

They exchange velocities. If ball A at 5 m/s hits identical stationary ball B head-on elastically, A stops dead and B moves off at 5 m/s — the classic Newton's cradle result, which drops straight out of the elastic collision equations.

Is momentum always conserved?

In any collision with no external force, yes — total momentum before equals total momentum after, whether the collision is elastic or not. Kinetic energy, by contrast, is only conserved in perfectly elastic collisions; some is always lost in real-world impacts.

Related tools