• $\begin{array}{l}{L}^{\ast }=116f\left(Y/Y_{\text{n}}\right)-16\\ u^{\ast }=13L^{\ast }\left(u^{\prime }-{u^{\prime }}_{\text{n}}\right)\\ v^{\ast }=13L^{\ast }\left(v^{\prime }-{v^{\prime }}_{\text{n}}\right)\end{array}$

where

• $f\left(Y/Y_{\text{n}}\right)={\left(Y/Y_{\text{n}}\right)}^{1/3}$ if $\left(Y/Y_{\text{n}}\right)>{\left(6/29\right)}^3$
• $f\left(Y/Y_{\text{n}}\right)=\left(841/108\right)\left(Y/Y_{\text{n}}\right)+4/29$ if $\left(Y/Y_{\text{n}}\right)\le {\left(6/29\right)}^3$

and Y, u′, v′ describe the colour stimulus considered and Y_n, u′_n, v′_n describe a specified white achromatic stimulus

Note 1 to entry: Approximate correlates of lightness, saturation, chroma, and hue can be calculated as follows:

CIE 1976 lightness:

• $L^{\ast }=116f\left(Y/Y_{\text{n}}\right)-16$

where

• $f\left(Y/Y_{\text{n}}\right)={\left(Y/Y_{\text{n}}\right)}^{1/3}$ if $\left(Y/Y_{\text{n}}\right)>{\left(6/29\right)}^3$
• $f\left(Y/Y_{\text{n}}\right)=\left(841/108\right)\left(Y/Y_{\text{n}}\right)+4/29$ if $\left(Y/Y_{\text{n}}\right)\le {\left(6/29\right)}^3$

CIE 1976 u, v saturation:

• $s_{\text{uv}}=13{\left[{\left(u^{\prime }-{u^{\prime }}_n\right)}^2+{\left(v^{\prime }-{v^{\prime }}_n\right)}^2\right]}^{1/2}$

CIE 1976 u, v chroma:

• $\Delta C_{\text{uv}}^{*}={\left(u^{*2}+v^{*2}\right)}^{1/2}=L^{*}{s}_{\text{uv}}$

CIE 1976 u, v hue angle:

• $h_{\text{uv}}=\text{arctan}\left[\left(v^{\prime }-{v^{\prime }}_n\right)/{\left(u^{\prime }-{u^{\prime }}_n\right)}^2\right]=\arctan \left(v^{*}/u^{*}\right)$

Note 2 to entry: See also CIE 15, Colorimetry.

Note 3 to entry: See also ISO/CIE 11664-5, Colorimetry – Part 5: CIE 1976 L*u*v* Colour Space and u', v' Uniform Chromaticity Scale Diagram.

Note 4 to entry: This entry was numbered 845-03-54 in IEC 60050-845:1987.