Momentum Calculator — linear momentum (p = mv)

How it works

The momentum of an object is defined as the product of its mass and its velocity (OpenStax University Physics):

p = m × v

Mass is measured in kilograms and velocity in metres per second, so momentum comes out in kilogram-metres per second (kg·m/s). Because velocity is a vector, momentum is too — it points the same way the object moves. A car heading east and an identical car heading west have equal and opposite momenta.

Momentum captures why a slow, heavy object can be as hard to stop as a fast, light one: a 1,500 kg car at 20 m/s and a 0.01 kg bullet at 400 m/s differ enormously in speed but both carry real momentum. It is also the conserved quantity in collisions — the total momentum of an isolated system stays constant, which is what makes it so useful in physics.

Worked example

For a mass of 5 kg moving at 10 m/s:

p = 5 × 10 = 50 kg·m/s

Double the velocity to 20 m/s and the momentum doubles to 100 kg·m/s; momentum scales in direct proportion to both mass and speed.

Frequently asked questions

What is momentum?

Momentum is a measure of the motion of an object — the product of its mass and velocity. A heavier or faster object has more momentum, and it takes a larger impulse (force over time) to change it.

What is the formula for momentum?

Momentum equals mass times velocity, p = m × v. With mass in kilograms and velocity in metres per second, the result is in kilogram-metres per second (kg·m/s).

Is momentum a vector?

Yes. Momentum has both magnitude and direction, pointing the same way as the velocity. In one dimension you track direction with a sign — for example, motion to the right positive and to the left negative.

How is momentum different from kinetic energy?

Both depend on mass and velocity, but momentum (m × v) is a vector proportional to speed, while kinetic energy (½ × m × v²) is a scalar proportional to speed squared. Momentum is conserved in all collisions; kinetic energy is conserved only in elastic ones.

What are the units of momentum?

In SI units, kilogram-metres per second (kg·m/s), which is equivalent to newton-seconds (N·s) — the unit of impulse, the change in momentum.

How do you change an object's momentum?

By applying an impulse — a force acting over time. The change in momentum equals force × time, so a small force applied for a long time changes momentum as much as a large force applied briefly. This is why airbags and crumple zones reduce injury: they extend the stopping time, lowering the force.