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Since $\mathbf{E}\cdot \mathbf{n}=0$, the Poynting vector isThe area on a distant sphere corresponding to solid angle $d\Omega$ is $r^{2}d\Omega$. ConsequentlyThe average is over the source motion at retarded time. At leading nonrelativistic order, differences between source-time and reception-time averaging are beyond the approximation. The units are power per solid angle, $\mathrm{W}\mathrm{s}{\mathrm{r}}^{-1}$.

The acceleration covariance in nonrelativistic radiation is another way to organize this result: with $C_{ij}=⟨a_i{a}_j⟩$, the angular factor is $\mathrm{tr}C-{\mathbf{n}}^{T}C\mathbf{n}$. Integrating over all observation directions uses $\int [|\mathbf{a}{|}^2-(\mathbf{n}\cdot \mathbf{a}{)}^2]d\Omega =(8\pi /3)|\mathbf{a}{|}^2$ and gives the averaged Larmor formula, $⟨P⟩=q^2⟨a^2⟩/(6\pi {ϵ}_0{c}^3)$.

For an orbit of radius $b$ in the $xy$ plane, $\mathbf{a}=-b{\omega }^2(\cos \omega t,\sin \omega t,0)$. In spherical coordinates, at angle $\theta$ from the orbit normal, $⟨(\mathbf{n}\cdot \mathbf{a}{)}^2⟩=b^2{\omega }^4{\sin }^2\theta /2$. The acceleration covariance in nonrelativistic radiation therefore gives the displayed pattern. Its axial power per solid angle is twice its equatorial value; no observation direction has zero time-averaged power. Integrating gives $⟨P⟩=q^2{b}^2{\omega }^4/(6\pi {ϵ}_0{c}^3)$. The condition $b\omega \ll c$ is essential: relativistic synchrotron radiation has a different beamed pattern.