# Momentum - Relativistic

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MichaelBartmess.Momentum - Relativistic
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The Relativistic Momentum calculator computes the momentum (ρ) of a mass (m0) at velocity (v) at relativistic speeds.

INSTRUCTIONS: Choose units and enter the following:

• (m0) This is  the rest mass
• (v) This is the velocity

Relativistic Momentum (ρ): The calculator returns the momentum (ρ) in kilogram meters per second (kg•m/s)

#### The Math / Science

The formula for relativistic momentum is:

ρ = (m_0 * v)/sqrt(1 - v^2/c^2)

where

This differs from the formula for momentum

Note that in the relativistic equation, as the speed approaches the speed of light, the denominator decreases, which has the result of increasing the momentum.   Also note that when v is equal to the speed of light, the momentum is infinite, and when v is zero, the equation matches that of normal momentum (p = m • v)

The velocity is restricted to be less than the speed of light.