Momentum Calculator

Calculate momentum using p = m × v

Momentum Calculator

Calculate momentum (p = m × v)

Momentum

p = m × v

Formula
p = m × v

What Is Momentum?

Momentum (p) is the product of an object's mass and velocity — a measure of how hard it is to stop a moving object. A large truck moving slowly and a small bullet moving fast can have the same momentum. Momentum is a vector quantity, meaning it has both magnitude and direction, and is measured in kilogram-meters per second (kg·m/s). The greater an object's mass or speed, the harder it is to bring to rest.

The law of conservation of momentum states that in a closed system with no external forces, the total momentum before a collision equals the total momentum after. This principle governs everything from billiard balls colliding on a table to rocket propulsion in outer space. This calculator also helps you compute impulse — the change in momentum caused by a force acting over a period of time.

How to Use the Momentum Calculator

  1. Enter the mass of the object in kilograms (kg).
  2. Enter the velocity in meters per second (m/s) — use a positive value for one direction, negative for the opposite direction.
  3. Click Calculate to get the result.
  4. Read the momentum in kg·m/s and the equivalent impulse if force and time are provided.

Momentum Formulas

Momentum: p = m × v Conservation of momentum (collision): m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' Impulse: J = F × Δt = Δp = m(v_final − v_initial) Elastic collision (kinetic energy conserved): v₁' = ((m₁−m₂)v₁ + 2m₂v₂) / (m₁+m₂) v₂' = ((m₂−m₁)v₂ + 2m₁v₁) / (m₁+m₂)

Momentum is always conserved in a closed system (no external forces). Kinetic energy is only conserved in elastic collisions — in inelastic collisions, some energy converts to heat, sound, or deformation of the objects involved.

Worked Examples

Car on the highway

A 1,000 kg car traveling at 20 m/s: p = 1,000 × 20 = 20,000 kg·m/s. It takes a significant braking force to stop this much momentum in a short time.

Baseball pitch

A 0.145 kg baseball thrown at 40 m/s: p = 0.145 × 40 = 5.80 kg·m/s. Despite being much lighter than a car, it packs serious momentum at speed.

Impulse from a bat

A 500 N force applied for 0.1 s: J = F × Δt = 500 × 0.1 = 50 N·s = 50 kg·m/s. This impulse equals the change in the baseball's momentum during the hit.

Frequently Asked Questions

What does conservation of momentum mean?▾
In a closed system — one with no outside forces acting on it — the total momentum of all objects stays constant. If two billiard balls collide, the momentum lost by one is gained by the other. The total before and after the collision is identical.
What is the difference between momentum and kinetic energy?▾
Momentum (p = mv) is a vector and is always conserved in collisions. Kinetic energy (KE = ½mv²) is a scalar and is only conserved in perfectly elastic collisions. In most real-world collisions, some kinetic energy is lost to heat or deformation, even though momentum is fully conserved.
What is impulse and how does it relate to momentum?▾
Impulse (J) is the product of a force and the time over which it acts: J = F × Δt. Impulse equals the change in momentum of an object (Δp). This is why airbags protect passengers — they increase the time of impact, reducing the peak force needed to change momentum.
What is the difference between elastic and inelastic collisions?▾
In an elastic collision, both momentum and kinetic energy are conserved — the objects bounce off each other with no energy loss (idealized billiard balls). In an inelastic collision, momentum is conserved but kinetic energy is not — some is converted to heat or sound. A perfectly inelastic collision is when the objects stick together after impact.
Why can rockets move in the vacuum of space?▾
Rockets work on the principle of conservation of momentum. By expelling exhaust gases at high velocity in one direction, the rocket gains an equal and opposite momentum in the other direction. No air or ground is needed — the reaction between the rocket and its own exhaust is enough to propel it forward.