The centroid wavelength is the power-weighted mean wavelength:
λ c = 1 P total ∫ p ( λ ) λ d λ , {\displaystyle \lambda _{\text{c}}={\frac {1}{P_{\text{total}}}}\int p(\lambda )\lambda \,d\lambda ,}
and the total power is
P total = ∫ p ( λ ) d λ , {\displaystyle P_{\text{total}}=\int p(\lambda )\,d\lambda ,}
where p ( λ ) {\displaystyle p(\lambda )} is the power spectral density, for example in W/nm. The above integrals theoretically extend over the entire spectrum, however, it is usually sufficient to perform the integral over the spectrum where the spectral density p ( λ ) {\displaystyle p(\lambda )} is higher than a fraction of its maximum.
See also Dominant wavelength
References