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Momentum Calculator

Physics

Calculate linear momentum using p = m × v. Enter mass and velocity to get the resulting momentum in kg·m/s instantly, with a clear step-by-step breakdown shown.

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Momentum

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This calculator computes your Momentum from the values you enter.

Inputs
MassVelocity
Outputs
Momentum

What is a Momentum?

The Momentum Calculator computes linear momentum using the formula p = m × v — mass multiplied by velocity. Enter a mass in kilograms and a signed velocity in meters per second, and the calculator instantly returns the resulting momentum in kilogram-meters per second (kg·m/s).

Momentum is one of the most important conserved quantities in physics — the total momentum of a closed system stays constant unless an external force acts on it, a principle that underlies the analysis of collisions, explosions, and any interaction between moving objects. Because momentum is a vector, this calculator correctly propagates the sign of velocity through to the result, so directional scenarios are handled automatically.

If you only have displacement and time rather than velocity directly, use the Velocity Calculator first to derive a signed velocity, then bring that result here.

How to use this Momentum calculator

  1. Enter the mass — the mass of the object in kilograms.

  2. Enter the velocity — the signed velocity of the object in meters per second. Use the Velocity Calculator first if you only have displacement and time.

  3. Read the momentum result — the highlighted result shows momentum in kg·m/s, correctly signed based on the direction of the velocity entered.

  4. Adjust and compare — change either mass or velocity to instantly see how momentum scales, useful for comparing multiple objects (like before-and-after a collision).

  5. Check the step-by-step breakdown — expand the calculation steps to see the exact formula substitution behind your result.

Formula & Methodology

Momentum formula:
p = m × v

Variable definitions:
- m — mass (kilograms)
- v — velocity (meters per second, signed)
- p — resulting momentum (kg·m/s)

Worked example:

A 1,500 kg car moving at 20 m/s.

Step 1 — Apply the formula: p = 1,500 kg × 20 m/s = 30,000 kg·m/s

This momentum value could be compared against another vehicle's momentum in a collision scenario, where the combined momentum before impact must equal the combined momentum after impact (conservation of momentum), regardless of how the collision itself unfolds.

Note: This calculator computes linear momentum for straight-line motion only. For rotating objects, a related but distinct quantity — angular momentum — uses moment of inertia and angular velocity instead of mass and linear velocity.

Frequently Asked Questions

Linear momentum is calculated as mass multiplied by velocity: p = m × v. It's a vector quantity, meaning it has both magnitude and direction, inherited directly from the direction of the velocity used in the calculation.
This calculator expresses momentum in kilogram-meters per second (kg·m/s), calculated from mass entered in kilograms and velocity entered in meters per second. There is no dedicated named SI unit for momentum, so kg·m/s is the standard way it's expressed.
Yes — since momentum is calculated directly from velocity, a negative velocity (indicating motion in the negative or 'backward' direction) produces a negative momentum. The sign of momentum always matches the sign of the velocity used, assuming mass is always entered as a positive value.
Use the [Velocity Calculator](/velocity-calculator/) first — enter displacement and time to get a signed velocity value, then bring that result into this Momentum Calculator along with the object's mass.
Momentum is central to one of the most powerful principles in physics: conservation of momentum, which states that the total momentum of a closed system remains constant unless acted on by an external force. This principle underlies the analysis of collisions, explosions, and any interaction between multiple objects.
Momentum (p = m × v) scales linearly with velocity and is a vector with direction, while kinetic energy (KE = ½mv²) scales with the square of velocity and is always a positive scalar with no direction. Two objects with equal and opposite momenta (which sum to zero) can still have substantial, non-zero total kinetic energy.
Impulse equals the change in momentum an object experiences: J = Δp = F × t. If a known force acts on an object for a known time, use the [Impulse Calculator](/impulse-calculator/) to find exactly how much its momentum changes as a result.
In any collision (assuming no external forces like friction), the total momentum of all objects involved before the collision equals the total momentum after — this is the conservation of momentum principle. This holds true whether the collision is elastic (kinetic energy also conserved) or inelastic (kinetic energy is not conserved, but momentum still is).
Momentum calculations are central to vehicle crash safety design (estimating impact forces and the effectiveness of crumple zones), sports equipment design (like understanding how a bat or racket transfers momentum to a ball), and rocket propulsion (where momentum conservation explains thrust generation).
A 1,500 kg car moving at 20 m/s (about 72 km/h) has a momentum of 30,000 kg·m/s. A baseball with a mass of about 0.145 kg thrown at 40 m/s has a momentum of about 5.8 kg·m/s — illustrating how much mass amplifies the momentum of even modestly fast-moving objects.
Yes — because momentum is calculated from velocity, and velocity is always measured relative to some reference frame (like the ground, or another moving object), momentum values differ depending on which reference frame you use. This calculator assumes you've already chosen a consistent frame of reference for your velocity input.
No — this calculator computes linear momentum only (p = m × v) for straight-line motion. Angular momentum, used for rotating objects, follows a related but distinct formula (L = I × ω, using moment of inertia and angular velocity) not covered by this tool.
Also known as
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