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In color theory, the Planckian locus is generally the path or locus that the color of a black body would take in a particular color space as the blackbody temperature changes. Generally, a color space is a set of three numbers (X, Y, and Z, for example) which specify the color and brightness of a particular homogeneous visual stimulus. Sometimes we may only wish to deal with the chromaticity (color) of a visual stimulus. This is a two-dimensional space of two numbers (x and y) which leave out the brightness information. In this case the Planckian locus is the path that the color of a black body takes in this chromaticity space as the blackbody temperature changes.

CIE1964 Supplementary Standard Colorimetric Observer functions X, Y, and Z functions between 380 nm and 780 nm (at 5 nm intervals).

In the CIE XYZ color space, the three coordinates defining a color are given by X, Y, and Z where

where I(λ) is the spectral radiance of the light being viewed, and X(λ), Y(λ) and Z(λ) are the CIE standard observer functions shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting the black body spectral radiance into the above equations. The black body spectral radiance is given by

where:

I is the black body spectral radiance (power per unit area per unit solid angle per unit wavelength)

T is the temperature of the black body

h is Planck's constant

c is the speed of light

k is Boltzmann's constant

Planckian locus in the (1964) CIE chromaticity diagram

This will give the Planckian locus in XYZ space. If these coordinates are X(T), Y(T), Z(T) where T is the temperature, then in the CIE chromaticity coordinates will be

The Planckian locus in xy space is shown in the diagram on the left.

While it is possible to compute the CIE xy(Y) coordinates exactly given the above formulas, it is typically faster to compute these using polynomial approximations.

• Luminosity function

• Wyszecki, Günter and Stiles, W.S. (2000). Color Science - Concepts and Methods, Quantitative Data and Formulae, 2nd edition, Wiley-Interscience. ISBN 0-471-39918-3. 

• Blackbody color datafile — Numerical table of color temperature and the corresponding CIE xy coordinates and sRGB coordinates.