Linear momentum tool

Momentum Calculator

Solve momentum, mass, or velocity from two known values using p = m × v.

Enter two known values

Solve a momentum problem

Free tool
kg·m/s

This is the value being calculated.

kg

Amount of matter in the object.

m/s

Speed and direction of the moving object.

Use kilograms for mass, meters per second for velocity, and kilogram-meters per second for momentum.

Try an example:

Your momentum result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Momentum Calculator determines the linear momentum of moving objects using mass and velocity. It helps physics students, engineers, researchers, and laboratory users analyze motion, collisions, force interactions, and mechanical systems using momentum principles.

Formula explanation

Momentum describes the quantity of motion and is calculated using p = mv.

Formula

Momentum = Mass × Velocity

Worked example

Example: A 10 kg object moving at 3 m/s has momentum of 30 kg·m/s.

Assumptions

  • Classical mechanics is used for ordinary speeds.
  • Object mass remains constant during calculation.
  • Mass and velocity values use compatible scientific units.
  • External relativistic effects are ignored in the ideal model.

Examples

  • Example: Calculate the momentum of an object when its mass and velocity are known.
  • Example: Engineers analyze momentum changes when studying impacts and mechanical systems.

Common mistakes

  • Ignoring velocity direction.
  • Using energy formulas instead.
  • Mixing mass units.

Variables

  • Object mass
  • Object velocity
  • Linear momentum
  • Direction of motion
  • Collision conditions
  • Measurement units

Limitations

  • Does not include relativistic effects at extremely high speeds.
  • Results depend on accurate mass and velocity measurements.

Scientific references

  • OpenStax University Physics: Linear Momentum and Collisions
  • NIST SI Units and Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Collision and impact analysis
  • Mechanical engineering studies
  • Vehicle safety analysis
  • Laboratory motion experiments
  • Scientific research applications

Frequently asked questions

How is momentum calculated?

Momentum is calculated using p = mv, where momentum equals mass multiplied by velocity.

How does velocity affect momentum?

Momentum increases as velocity increases because momentum is directly proportional to velocity.

What is the SI unit of momentum?

The SI unit of momentum is kilogram meter per second (kg·m/s).

Why is momentum important in collisions?

Momentum helps scientists and engineers analyze how objects interact, transfer motion, and behave during collisions.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Motion and mass

What is momentum?

Linear momentum describes the quantity of motion carried by an object. It depends on both the object's mass and its velocity.

Formula

Momentum formula

Momentump = m × v

  • p is momentum in kilogram-meters per second.
  • m is mass in kilograms.
  • v is velocity in meters per second.

Worked example

A 12 kg object moves at 5 m/s

  1. Write the formula: p = m × v.
  2. Substitute the values: p = 12 × 5.
  3. Calculate the momentum: p = 60 kg·m/s.

Rearranged equations

Solve for mass or velocity

Mass

m = p ÷ v

Divide momentum by a non-zero velocity. Momentum and velocity must have matching signs.

Velocity

v = p ÷ m

Divide momentum by a positive mass.

Direction

Positive and negative momentum

Momentum is a vector quantity. Its sign represents direction relative to the positive axis selected for the problem. A negative velocity therefore produces negative momentum when mass is positive.

Stationary objects

When momentum equals zero

An object with zero velocity has zero momentum, regardless of its positive mass. Momentum may also become zero at the instant an object changes direction.

Units

Standard SI units

Use kilograms for mass and meters per second for velocity. Convert grams, kilometers per hour, and other units before entering values.

Momentum unitkg·m/s

Calculation checks

Important input requirements

  • Mass must be greater than zero.
  • Velocity cannot be zero when solving for mass.
  • Momentum and velocity must have matching signs when calculating mass.
  • All entered values must be finite numbers.
  • The calculator does not automatically convert units.

Related tools

Use the Force Calculator to solve Newton's second law problems involving force, mass, and acceleration.

Use the Acceleration Calculator to calculate velocity change over time, and review the Tables and Graphs Guide when presenting motion data.

Questions and answers

Calculator FAQ

How is momentum calculated?

Momentum is calculated using p = mv, where momentum equals mass multiplied by velocity.

How does velocity affect momentum?

Momentum increases as velocity increases because momentum is directly proportional to velocity.

What is the SI unit of momentum?

The SI unit of momentum is kilogram meter per second (kg·m/s).

Why is momentum important in collisions?

Momentum helps scientists and engineers analyze how objects interact, transfer motion, and behave during collisions.