The color difference method of the Color Measurement Committee (the CMC) is a model using two parameters *l* and *c*,
typically expressed as CMC(*l:c*). Commonly used values for acceptability are CMC(2:1) and for perceptibility are CMC(1:1).

The color difference, or $\Delta E$, between a sample color ($L_2$, $a_2$, $b_2$) and a reference color ($L_1$, $a_1$, $b_1$) is:

$$\Delta E = \sqrt{ \left({{\Delta L} \over {l S_L}}\right)^2 + \left({{\Delta C} \over {c S_C}}\right)^2 + \left({{\Delta H} \over {S_H}}\right)^2 }$$where

$$\Delta C = C_1 - C_2$$ $$C_1 = \sqrt{{a_1}^2 + {b_1}^2}$$ $$C_2 = \sqrt{{a_2}^2 + {b_2}^2}$$ $$\Delta H = \sqrt{{\Delta a}^2 + {\Delta b}^2 - {\Delta C}^2}$$ $$\Delta L = L_1 - L_2$$ $$\Delta a = a_1 - a_2$$ $$\Delta b = b_1 - b_2$$ $$S_L = \cases{ 0.511 & \text{if }L_1 \lt 16 \\ {{0.040975 L_1} \over {1 + 0.01765 L_1}} & \text{if }L_1 \geq 16 }$$ $$S_C = {{0.0638 C_1} \over {1 + 0.0131 C_1}} + 0.638$$ $$S_H = S_C (FT+1-F)$$ $$T = \cases{ 0.56 + |0.2 \cos (H_1 + 168°)| & \text{if }164° \leq H_1 \leq 345° \\ 0.36 + |0.4 \cos (H_1 + 35°)| & \text{otherwise} }$$ $$F = \sqrt{{C_1^4} \over {C_1^4 + 1900}}$$ $$H = \arctan \left({b_1} \over {a_1}\right)$$ $$H_1 = \cases{ H & \text{if }H \geq 0 \\ H + 360° & \text{otherwise} }$$**Implementation Notes:**

- $H_1$ is in degrees, not radians.
- In computing $H$, be careful with the inverse tangent since $a_1$ could be zero. Instead, use special
math functions to do this. In the Standard C library and most other math libraries, this function is called
**atan2**and is used calling atan2(b, a). In Microsoft Excel, it is called**ATAN2**and its use is ATAN2(a, b).**Note the argument reversal!**These special functions will compute the proper inverse tangents without needing to worry about "divide by zero" conditions. Additionally, atan2 will also handle the quadrants for you. - Math libraries generally return inverse tangents in radians, not degrees. In Excel, use the DEGREES function to convert radians to degrees.
- Math libraries generally require the input to the cosine function to be in radians, not degrees. In Excel, use the RADIANS function to convert degrees to radians.