`rho = ( m_0 * "v" ) /sqrt(1 - ( "v" ^2 / c^2))`

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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)

Related Calculators

• Normal Momentum

The Math / Science

The formula for relativistic momentum is:

     `ρ = (m_0 * v)/sqrt(1 - v^2/c^2)`

where

• ρ is the relativistic momentum

This differs from the formula for momentum

      p = m • v

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.