${\displaystyle \underset{{\lambda }_1}{\overset{{\lambda }_2}{\int }}{\left[1-\frac{S_{\text{t}}(\lambda )}{a{S}_{\text{b}}(\lambda ,T)}\right]}^2\text{d}\lambda }$

where λ is the wavelength, S_t(λ) is the relative spectral distribution of the radiation being considered, S_b(λ, T) is the relative spectral distribution of the Planckian radiator at temperature T, and a is a scaling factor

Note 1 to entry: The scaling factor a is chosen to make the quotient ${\displaystyle \frac{S_{\text{t}}(\lambda )}{S_{\text{b}}(\lambda ,T)}}$ equal to unity at a convenient wavelength which, in photometry and colorimetry is typically 560 nm.

${\displaystyle S_{\text{b}}(\lambda ,T)=\frac{P(\lambda ,T)}{P(560\text{nm},T)}}$ with $P(\lambda ,T)={\lambda }^{-\text{5}}{\left({\text{e}}^{\frac{c_{\text{2}}}{\lambda T}}-\text{1}\right)}^{-\text{1}}$, where c₂ is the second radiation constant.

Note 2 to entry: Distribution temperature is a meaningful characteristic for radiators having a relative spectral distribution similar to that of a Planckian radiator, but only if calculated for an expanded wavelength range and for radiation whose spectral distribution of radiant flux is a continuous function of wavelength in that range.

Note 3 to entry: In photometry and colorimetry the wavelength range set by λ₁ and λ₂ is the visible spectral range, and in these cases the range from at least λ₁ = 400 nm to λ₂ = 750 nm is recommended.

Note 4 to entry: In practice, the integral is replaced by a summation. For incandescent lamps, equally spaced wavelength intervals of 10 nm will usually suffice. All values in the summation are treated with equal weight.

Note 5 to entry: The distribution temperature is expressed in kelvin (K).

Note 6 to entry: For further information, see CIE 114-1994, CIE Collection in Photometry and Radiometry – 114/4 Distribution Temperature and Ratio Temperature.

Note 7 to entry: This entry was numbered 845-04-14 in IEC 60050-845:1987.