Britannica Sources used in this answer

How is momentum calculated from mass and velocity?

Created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

A diagram of a cylindrical vessel containing gas, with a movable piston held down by a weight. Countless small dots beneath the piston represent gas particles in rapid, random motion, illustrating Bernoulli's model of gas pressure. — physics As conceived by Daniel Bernoulli in *Hydrodynamica* (1738), gases consist of numerous particles in rapid random motion. He assumed that the pressure of a gas is produced by the direct impact of the particles on the walls of the container.

In classical physics, momentum (specifically linear momentum) is calculated as the product of an object's mass and its velocity. This relationship is expressed by the formula:123

$p = m v$

In this equation, $p$ represents momentum, $m$ is the mass, and $v$ is the velocity. Because velocity is a vector quantity—meaning it has both magnitude and direction—momentum is also a vector quantity.425

In the context of special relativity, the same formula applies, though the mass used is the relativistic mass, which increases as an object's velocity approaches the speed of light. For a collection of particles, the total momentum is the vector sum of the individual momenta of each particle.42