acalculator

What is the momentum?

Type the mass and velocity of a moving object to get its momentum, p = m × v. Or type the momentum and one of the others to find the mass or the velocity. The momentum calculator also gives the momentum in lb·ft/s and the kinetic energy.

Your numbers

Units
Momentum (kg·m/s)
21,000

The momentum is 21,000 kg·m/s.

Momentum (lb·ft/s)
151,893
Kinetic energy (J)
157,500

Momentum (kg·m/s): 21,000. The momentum is 21,000 kg·m/s.

How to calculate

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.

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

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

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Mass 3,086 lb, Velocity 33.55 mph gives Momentum (kg·m/s) 21,000, Kinetic energy (J) 157,500, Momentum (lb·ft/s) 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. Mass 0 lb, Velocity 1,118 mph gives Momentum (kg·m/s) 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. Momentum (kg·m/s) 21,000, Mass 3,086 lb gives Velocity 33.55 mph.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. Momentum (kg·m/s) 3,000, Velocity 60 mph gives Mass 246.6 lb.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)

How it works

For an object of mass m moving with velocity v along a line:

  • momentum p = m × v, in kg·m/s with m in kilograms and v in meters per second
  • velocity v = p ÷ m; mass m = p ÷ v
  • momentum in lb·ft/s = p ÷ 0.138254954376 (1 lb·ft/s = 0.45359237 × 0.3048 kg·m/s exactly)
  • kinetic energy K = p² ÷ (2m) joules, which equals ½mv² (worked out as p × (p ÷ 2m), so a tiny p² does not round to 0)

Type any two of mass, velocity and momentum. Masses are converted to kilograms (1 lb = 0.45359237 kg, 1 short ton = 2,000 lb, 1 t = 1,000 kg) and speeds to meters per second (1 mph = 1,609.344 m ÷ 3,600 s, 1 km/h = 1,000 m ÷ 3,600 s, 1 ft/s = 0.3048 m/s, 1 knot = 1,852 m ÷ 3,600 s) before the maths, which runs in double precision.

Rules

  • The mass is more than 0 and at most 10¹² kg. The velocity is from −3 × 10⁸ to 3 × 10⁸ m/s (about the speed of light) and the momentum from −10²¹ to 10²¹ kg·m/s; a negative value points the other way.
  • A mass solved from a momentum and a velocity of opposite signs, or from a velocity of 0, has no answer.
  • A derived value beyond the largest double-precision number is left out.

Output format. Momentum, lb·ft/s and kinetic energy to 6 significant figures.

Worked examples by hand

A 1,400 kg car at 15 m/s. p = 1,400 × 15 = 21,000 kg·m/s, or 21,000 ÷ 0.138254954376 = 151,893.29 lb·ft/s. K = 21,000² ÷ (2 × 1,400) = 157,500 J.

An air molecule of 6 × 10⁻²⁵ kg at 500 m/s. p = 6 × 10⁻²⁵ × 500 = 3 × 10⁻²² kg·m/s.

Velocity from momentum. v = 21,000 ÷ 1,400 = 15 m/s.

Mass from momentum. 3,000 kg·m/s at 60 mph: 60 mph = 60 × 1,609.344 ÷ 3,600 = 26.8224 m/s, so m = 3,000 ÷ 26.8224 = 111.85 kg.

Other questions people ask

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.