$$B_{\nu}(T) = \frac{2 h \nu^3}{c^2} \frac{1}{e^{h \nu / k_B T} – 1} ~~ {\rm [erg~s^{-1}~cm^{-2}~Hz^{-1}~sr^{-1}]} \,,$$
where ν is the frequency in [Hz], h is Planck’s constant, c is the speed of light in vacuum, and kB is Boltzmann’s constant. The spectrum is interesting in many ways. Its shape is characterized by only one parameter, the radiation temperature T. A spectrum with a higher T is greater in intensity at all frequencies compared to one with a lower T, and the integral over all frequencies is σ T4, where $$\sigma \equiv \frac{2\pi^5k_B^4}{15 c^2 h^3}$$ is the Stefan-Boltzmann constant. Other than that, the normalization is detached, so to speak, from T, and differences in source luminosities are entirely attributable to differences in emission surface area.
$$\nu_{\rm max} = 2.82 \frac{k_B T}{h}$$,
$$\lambda_{\rm max} = \frac{2.9\cdot10^4}{T} ~~ {\rm[\AA]} \,,$$