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Calculate color temperature (CCT) from CIE 1931 xy coordinates

Home /  Blog /  Tech & Color Science /  Calculate color temperature (CCT) from CIE 1931 xy coordinates
Color temperature can be approximated using just a pair of xy coordinates from CIE 1931. Use the formula below, or simply plug in the x and y values into our online calculator.

When performing this conversion, we recommend also including the Duv value as well (more on this below). See our CIE xy to Duv calculator here.

Looking to go the other way? See our CCT to CIE XY calculator.

 

CIE 1931 xy to CCT Calculator



CIE x:
 


CIE y:
 



Result: -





















Use caution when "correlating" color temperature


Color temperature is a useful metric when discussing approximately white color light sources only. Mathematically, however, it is possible to calculate a CCT value for light sources that are not even close to being white - for example, a saturated green LED from an RGB system can have a calculated CCT of approximately 7000K, even though its qualitative color appearance is vastly different from a white LED at 7000K.

Why is this?

Color temperature is an absolute, one-dimensional metric that describes a particular point along the black body curve. As the color temperature value increases, we move further down the curve (down and left, towards the blue region). But most light sources, including natural daylight, do not actually exhibit light color that is exactly on the black body curve. Instead, we see minor deviations from the black body curve due to atmospheric absorption (natural daylight) and manufacturing variability (artificial lamps).

When these deviations are minor, it can still be helpful to ask, "what is the color temperature value of the closest point along the black body curve?" - because it allows us to make simple, intuitive judgement about the color of a light source.

The word "correlated" in "correlated color temperature" (CCT) refers to the mathematical process that answers the question above.

But what if the deviations are not minor? Mathematically, the process of correlating to a color temperature value is still possible, and the formula (including our calculator) will produce a numerical result. But if the deviation is so large that the light source is no longer considered "white," the result is likely to be not meaningful.

It's important to note that in correlating a light source's measured CIE xy coordinate value to a color temperature value, we immediately lose information about the magnitude and direction of this correlation.

If using CCT and you are concerned about light quality, it is always best to also include information about the light source's Duv value, as it includes information about the distance and direction away from the black body curve.

Read more about why CCT is insufficient for film & photography lighting applications, as well as how to translate Duv values to green gel values.

 

Not all CCTs are equal!


If you've successfully grasped the concept behind color temperature correlation, you should now understand why not all light sources with the same CCTs will necessarily have the same color.

In the graphic below, you will find iso-CCT lines for various CCT values. Iso-CCT lines describe points whose CCT value are the same. For 3500K, you will see the line extend from a yellowish hue in the area above the black body curve, while it will transition towards a pink/magenta hue as you move down the same 3500K iso-CCT line below the black body curve.

In other words, just because two lights are both labeled (or even tested to have) "3500K CCT" without information about Duv or original CIE xy coordinates, we are unable to determine if their light color actually matches.

 

CIE 1931 xy to CCT Formula


See below for the formula used to approximate CCT using CIE 1931 xy values:

n = (x-0.3320)/(0.1858-y);
CCT = 437*n^3 + 3601*n^2 + 6861*n + 5517

(This is McCamy's approximation)