Momentum Calculator

What Actually Determines How Hard Something Hits

Momentum captures something force alone doesn't: the combined effect of how much mass is moving and how fast. A slow-moving truck and a fast-moving bicycle can carry comparable momentum despite wildly different masses, which is exactly why momentum — not speed and not mass in isolation — is the quantity that's conserved in collisions and used to predict what happens when objects interact.

The Formula

p = m × v

Rearranged for the other two unknowns:

m = p / v
v = p / m

Momentum is a vector, carrying direction as well as magnitude, and its SI unit is kg·m/s. This calculator solves for momentum, mass, or velocity depending on which two values you already have.

Why Momentum Is the Quantity That's Conserved

  • Collision analysis — total momentum before a collision equals total momentum after, which lets investigators and engineers reconstruct crash dynamics from limited evidence.
  • Rocket propulsion — a rocket gains forward momentum precisely because it expels propellant with momentum in the opposite direction.
  • Sports biomechanics — the momentum a bat, racket, or fist transfers on contact determines how much velocity change the target object experiences.
  • Ballistics and recoil — a firearm's recoil momentum exactly matches the momentum of the fired projectile, just in the opposite direction.

Momentum Across Very Different Masses

Momentum for objects of very different mass and speed (p = m × v)
ObjectMassVelocityMomentum
Rifle bullet0.145 kg40 m/s5.8 kg·m/s
Compact car1,200 kg15 m/s18,000 kg·m/s
Mid-size car1,500 kg25 m/s37,500 kg·m/s

Despite its tiny mass, the bullet's high velocity gives it real momentum — but nowhere near what a car carries even at modest speed, illustrating how mass and velocity trade off differently for momentum (linear) than for kinetic energy (velocity-squared).

How to Use This Calculator

  1. Choose what to solve for: Find Momentum, Find Mass, or Find Velocity.
  2. For Find Momentum, enter Mass (kg) and Velocity (m/s).
  3. For Find Mass, enter Momentum (kg·m/s) and Velocity (m/s).
  4. For Find Velocity, enter Momentum (kg·m/s) and Mass (kg).
  5. Select Calculate to see the result along with the worked formula.

Related Calculations

To see how a force applied over time produces this exact momentum change, use the Impulse Calculator, or compare it against the kinetic energy of the same moving object with the Kinetic Energy Calculator.