Photon energy ($E=h\nu =\hslash \omega =hc/\lambda$)

The energy carried by one photon is proportional to its frequency $\nu$, with proportionality constant the Planck constant $h$. The equivalent forms use angular frequency $\omega =2\pi \nu$ and vacuum wavelength $\lambda =c/\nu$. Different observers can measure different photon energies because they measure different frequencies; the photon remains massless. In signature $(+---)$, an observer with four-velocity $u^{\mu }$ measures $E=p_{\mu }{u}^{\mu }$, where $p^{\mu }$ is the photon's four-momentum and $u^{\mu }{u}_{\mu }=c^2$.

A monochromatic beam of frequency $f$ and mean radiated power $P$ carries mean photon rate $\dot{N}=P/(hf)$. It follows by dividing energy per unit time by energy per photon. A broadband source instead requires integrating spectral power divided by the frequency-dependent photon energy; electrical input power must first be converted to radiated power.