Skip to main content

Momentum Calculator

Our mechanics calculator computes momentum accurately. Enter measurements for results with formulas and error analysis.

Reviewed by Manoj Kumar, Mathematics Educator

Reviewed by Manoj Kumar, Mathematics Educator

Formula

p = m × v

Momentum equals mass times velocity.

Worked Examples

Example 1: Collision of Two Carts

Problem:A 4 kg cart moving at 3 m/s collides with a stationary 2 kg cart and they stick together (perfectly inelastic collision). What is the final velocity?

Solution:Initial momentum = m1*v1 + m2*v2 = (4)(3) + (2)(0) = 12 kg*m/s\nAfter sticking together, combined mass = 6 kg\nFinal velocity = total momentum / combined mass = 12 / 6 = 2 m/s

Result:Final velocity = 2 m/s (momentum conserved: 12 kg*m/s before and after)

Example 2: Rifle Recoil

Problem:A 4 kg rifle fires a 0.01 kg bullet at 400 m/s. What is the rifle's recoil velocity?

Solution:Bullet momentum = 0.01 kg x 400 m/s = 4 kg*m/s (forward)\nBy conservation of momentum, rifle momentum must be -4 kg*m/s\nRecoil velocity = -4 / 4 = -1 m/s

Result:Recoil velocity = 1 m/s backward

Frequently Asked Questions

What is momentum and why does it matter?

Momentum (p) is the product of an object's mass and velocity, p = mv, measured in kg·m/s. It matters because in a closed system with no external forces, total momentum is always conserved — this single rule lets you solve collision and recoil problems without ever knowing the details of the forces involved during impact.

How do you calculate momentum for a moving object?

Multiply mass in kilograms by velocity in meters per second. A 10 kg object moving at 5 m/s has momentum p = 10 × 5 = 50 kg·m/s. Because velocity is a vector, momentum also has direction — two objects with equal mass and speed but opposite directions have equal and opposite momentum.

How is momentum different from kinetic energy?

Momentum (p = mv) scales linearly with velocity, while kinetic energy (KE = ½mv²) scales with velocity squared. Doubling an object's speed doubles its momentum but quadruples its kinetic energy. This is why a car crash at twice the speed is far more than twice as destructive — the energy that must be dissipated rises much faster than the momentum.

What is conservation of momentum used for?

Conservation of momentum lets you find unknown velocities after a collision or explosion without needing to know the forces involved. In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision (like a car crash where vehicles crumple together) momentum is still conserved but kinetic energy is lost as heat and deformation.

References

Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy