# What is the momentum?

Finds the momentum p = m × v of a moving object from its mass and velocity, or the mass or velocity from the other two, with the kinetic energy.

- Page: https://www.acalculator.org/physics/momentum-calculator
- JSON spec: https://www.acalculator.org/physics/momentum-calculator.json
- Version: e08590aee3ed

## Default answer

Example with the default inputs (Mass 3,086.47167058829 lb, Velocity 33.554044380816 mph): The momentum is 21,000 kg·m/s.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Mass | The mass of the moving object. |
| v | Velocity | The speed in the direction of motion; a negative value means the opposite direction. |
| p | Momentum (kg·m/s) | Mass times velocity, in kilogram meters per second. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mass | Mass | The mass of the moving object. |
| velocity | Velocity | The speed in the direction of motion; a negative value means the opposite direction. |
| momentum | Momentum (kg·m/s) | p = m × v in kilogram meters per second. |
| lbFtS | Momentum (lb·ft/s) | The same momentum in pound feet per second: p ÷ 0.138254954376. |
| energy | Kinetic energy (J) | K = p² ÷ (2m) = ½mv², in joules. |

## Method

p = m × v; v = p ÷ m; m = p ÷ v. Kinetic energy K = p² ÷ (2m). Units are converted to kilograms and meters per second first.

## Assumptions

- Speeds are far below the speed of light, so the classical p = mv applies.
- The motion is along one line: a negative velocity or momentum points the opposite way. A mass is more than 0.
- Values run in kilograms, meters and seconds, in double precision.

## Worked examples

1. m = 1,400, v = 15 gives p = 21,000, energy = 157,500, lbFtS = 151,893.290875. Source: OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02).
2. m = 0, v = 500 gives p = 0. Source: OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02).
3. p = 21,000, m = 1,400 gives v = 15. Source: OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02).
4. p = 3,000, v = 26.8224 gives m = 111.846815. Source: OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv in kg·m/s; a 1,400 kg car at 15 m/s has p = 21,000 kg·m/s), https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02).

## FAQ

### How do I calculate momentum?

Multiply the mass by the velocity: p = m × v. With the mass in kilograms and the velocity in meters per second, the momentum is in kg·m/s. A 1,400 kg car at 15 m/s has p = 1,400 × 15 = 21,000 kg·m/s.

### What is the unit of momentum?

The SI unit is the kilogram meter per second (kg·m/s), which is the same as a newton second (N·s). In US units the page also shows pound feet per second: 1 lb·ft/s = 0.45359237 kg × 0.3048 m/s = 0.138254954376 kg·m/s.

### How do I find velocity from momentum?

Divide the momentum by the mass: v = p ÷ m. A momentum of 21,000 kg·m/s for a 1,400 kg car is 21,000 ÷ 1,400 = 15 m/s. Type the momentum and the mass and leave the velocity empty.

### Can momentum be negative?

Yes. Momentum is a vector: it points the same way as the velocity. On a line, a negative velocity gives a negative momentum, which means motion in the opposite direction. The mass is always positive.

### How are momentum and kinetic energy related?

Kinetic energy is K = ½mv², and since p = mv, K = p² ÷ (2m). The car above has K = 21,000² ÷ 2,800 = 157,500 J. Two objects with the same momentum can have very different kinetic energies if their masses differ.

### Why does a small, fast object have little momentum?

Momentum depends equally on mass and velocity. OpenStax compares an air molecule (6 × 10⁻²⁵ kg at 500 m/s, p = 3 × 10⁻²² kg·m/s) with a car (21,000 kg·m/s): the molecule is faster, but its mass is about 27 orders of magnitude smaller.

## Sources

- OpenStax, University Physics Volume 1, §9.1 Linear Momentum (p = mv; SI unit kg·m/s; the car and air molecule examples). https://openstax.org/books/university-physics-volume-1/pages/9-1-linear-momentum (retrieved 2026-10-02)
- NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (1 lb = 0.45359237 kg, 1 ft = 0.3048 m, exactly). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)