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
Rearranged for the other two unknowns:
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
| Object | Mass | Velocity | Momentum |
|---|---|---|---|
| Rifle bullet | 0.145 kg | 40 m/s | 5.8 kg·m/s |
| Compact car | 1,200 kg | 15 m/s | 18,000 kg·m/s |
| Mid-size car | 1,500 kg | 25 m/s | 37,500 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
- Choose what to solve for: Find Momentum, Find Mass, or Find Velocity.
- For Find Momentum, enter Mass (kg) and Velocity (m/s).
- For Find Mass, enter Momentum (kg·m/s) and Velocity (m/s).
- For Find Velocity, enter Momentum (kg·m/s) and Mass (kg).
- 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.