# Momentum Calculator (p = mv)

Calculate linear momentum with p = mv. Enter mass and velocity to find momentum in kg·m/s. Also shows kinetic energy. Free physics calculator.

## What this calculates

Momentum is a fundamental quantity in physics that measures the "quantity of motion" of an object. Defined as the product of mass and velocity (p = mv), momentum is a vector quantity, meaning it has both magnitude and direction. The conservation of momentum is one of the most powerful principles in physics, governing everything from billiard ball collisions to rocket propulsion.

## Inputs

- **Mass** (kg) — min 0
- **Velocity** (m/s)

## Outputs

- **Momentum** (kg·m/s) — Linear momentum in kg·m/s
- **Kinetic Energy** (J) — Associated kinetic energy (KE = p²/2m)

## Details

The momentum formula p = mv connects an object's mass to its velocity. Momentum is conserved in all isolated systems, making it invaluable for analyzing collisions and explosions.

  - Momentum (p) is measured in kg·m/s (no special unit name)

  - Mass (m) is measured in kilograms

  - Velocity (v) is measured in meters per second (includes direction)

Key principles:

  - Conservation of momentum: In an isolated system, total momentum before = total momentum after any interaction

  - Impulse-momentum theorem: Force × time = change in momentum (FΔt = Δp)

  - Relationship to kinetic energy: KE = p²/(2m)

Examples: A 0.145 kg baseball at 40 m/s has a momentum of 5.8 kg·m/s. A 2,000 kg car at 30 m/s has a momentum of 60,000 kg·m/s. Despite the car being much slower than a bullet, its enormous mass gives it far more momentum.

## Frequently Asked Questions

**Q: What is momentum?**

A: Momentum is the product of an object's mass and velocity (p = mv). It is a vector quantity that represents the 'quantity of motion' of an object.

**Q: What is conservation of momentum?**

A: The law of conservation of momentum states that in an isolated system (no external forces), the total momentum before an event equals the total momentum after. This applies to collisions, explosions, and all interactions.

**Q: What is the difference between momentum and kinetic energy?**

A: Momentum (p = mv) is a vector quantity proportional to velocity. Kinetic energy (KE = ½mv²) is a scalar quantity proportional to velocity squared. Momentum is conserved in all collisions; kinetic energy is only conserved in perfectly elastic collisions.

**Q: Can momentum be negative?**

A: Yes. Since momentum is a vector, its sign indicates direction. If you define rightward as positive, an object moving leftward has negative momentum. The magnitude is always positive.

**Q: What is impulse?**

A: Impulse is the change in momentum of an object. It equals force multiplied by the time over which the force acts: J = FΔt = Δp. This is why airbags work—they increase the time of impact, reducing the force.

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Source: https://vastcalc.com/calculators/physics/momentum
Category: Physics
Last updated: 2026-04-21