Planck function

The Planck function is a function of wavelength (or frequency) and temperature that describes a distribution of the intensity (aka radiance) at each wavelength or frequency (i.e., the specific intensity aka spectral radiance) in black-body radiation. The form for frequency:

         2hν3      1
B(ν,T) = ———— —————————————
          c2  ehν/(kBT) - 1

• B(ν,T) - spectral radiance (specific intensity).
• ν - frequency.
• h - Planck constant.
• T - temperature.
• c - speed of light in a vacuum.
• k_B - Boltzmann constant.

Note that the formula for the Plank function for the distribution over wavelength does not simply plug in c/wavelength into the above formula: the relation of their differentials must be taken into account.

Sometimes the equation is cited including π as an additional factor: the form with π produces the total energy emitted per unit area of the black body per wavelength or frequency, i.e., the spectral flux density a unit area produces.

Much of astrophysics uses the term intensity for the quantity of radiation emitted through a surface into a given solid angle, specific intensity being the radiance at a given wavelength or frequency. More common terms are radiance and spectral radiance.