Radiation energy density ($U/V={\int }_0^{\infty }u(\omega )d\omega$)

The spectral radiation energy density $u(\omega )$ is defined per unit angular frequency and physical volume. Thermal Planck law convention excludes the vacuum zero-point term. A density per ordinary frequency instead obeys $u_{\omega }=u_{\nu }/(2\pi )$, evaluated at $\nu =\omega /(2\pi )$; Einstein coefficients multiplying these densities must be converted correspondingly.