Spectral optical depth in frequency and spectral optical depth in wavelength of a material, denoted  and  respectively, are given by:
where
* is the spectral radiant flux in frequency transmitted by that material;
* is the spectral radiant flux in frequency received by that material;
* is the spectral transmittance in frequency of that material;
* is the spectral radiant flux in wavelength transmitted by that material;
* is the spectral radiant flux in wavelength received by that material;
* is the spectral transmittance in wavelength of that material.
Spectral absorbance is related to spectral optical depth by:
where
* is the spectral absorbance in frequency;
* is the spectral absorbance in wavelength.