• $\begin{array}{l}L*=116f\left(Y/Y_{\text{n}}\right)-16\\ a*=500\left[f\left(X/X_{\text{n}}\right)-f\left(Y/Y_{\text{n}}\right)\right]\\ b*=200\left[f\left(Y/Y_{\text{n}}\right)-f\left(Z/Z_{\text{n}}\right)\right]\end{array}$

where

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

and

• $f\left(Y/Y_{\text{n}}\right)={\left(Y/Y_{\text{n}}\right)}^{1/3}$ 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

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

and X, Y, Z describe the colour stimulus considered and X_n, Y_n, Z_n describe a specified white achromatic stimulus

Note 1 to entry: Approximate correlates of lightness, 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 a, b chroma:

• $\Delta C_{\text{ab}}^{*}={\left(a^{*2}+b^{*2}\right)}^{1/2}$

CIE 1976 a, b hue angle:

• $h_{\text{ab}}=\arctan \left(b^{*}/a^{*}\right)$

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

Note 3 to entry: See also ISO/CIE 11664-4, Colorimetry – Part 4: CIE 1976 L*a*b* Colour Space.

Note 4 to entry: This entry was numbered 845-03-56 in IEC 60050-845:1987.