# How do you calculate the momentum of a photon?

Mar 22, 2018

#### Answer:

The momentum of a photon is given by $\frac{E}{c} \hat{n}$ where $\hat{n}$ is the unit vector in the direction in which the photon is moving, $E$ is its energy, and $c$ is the speed of light.

#### Explanation:

For any particle of mass $m$ (this is the so called invariant mass of the particle, often called the rest mass and denoted by ${m}_{0}$), the energy and the momentum are related by

${E}^{2} - | \vec{p} {|}^{2} {c}^{2} = {m}^{2} {c}^{4}$

For the photon, the mass $m$ is zero and this leads to

$| \vec{p} | = \frac{E}{c}$

Note that the formula
$\vec{p} = \frac{m \vec{v}}{\sqrt{1 - {v}^{2} / {c}^{2}}}$
which is valid for massive particles, fails for the photon since both $m$ and $1 - {v}^{2} / {c}^{2}$ vanish for it.