How to Calculate Color Temperature

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All objects with a temperature above absolute zero radiate some energy. As the temperature of an object increases, the amount of radiation it emits also increases, and the average wavelength of the emitted radiation decreases. Some mammals, including humans, can distinguish wavelengths of radiation in the 400 to 700 nanometer range, and perceive them as colors. If we make a few assumptions, it becomes fairly straightforward to calculate the color of light emitted by a hot object based on its temperature.

    Assume the object in question is a black body, meaning that it does not preferentially absorb or emit any particular wavelength. This assumption will make your calculations much simpler.

    Determine the temperature of the object in Kelvins. If you're working this question as a problem for a physics class, this value will usually appear in the problem. If you need to convert from Fahrenheit or Celsius to Kelvins, use the following formulas:

    Degrees Celsius = (degrees Fahrenheit - 32) x 5/9 Degrees Kelvin = degrees Celsius + 273.15

    Plug the temperature into the following equation:

    2.9 x 10 ^ 6 Kelvins per nanometer / temperature = wavelength

    This calculation will give you the peak wavelength in nanometers, or billionths of a meter. Wavelengths of visible light are so small that we typically measure them in nanometers. Note that the object also emits radiation at other wavelengths, but this is the wavelength at which it radiates with maximum intensity.

    Click the NASA link under the “Resources” section of this article to access a chart that lists the wavelength corresponding to each color. Identify the color that corresponds with the peak wavelength for your black body object.

    Example: If we have a black body object with a temperature of 6000 degrees Kelvin, the peak wavelength would be equal to 2.9 x 10 ^ 6 Kelvins per nanometer / 6000 degrees Kelvin = 483 nanometers, which corresponds to the blue-green region of the spectrum.

    Tips

    • The surface temperature of the sun is about 5780 degrees Kelvin, so the peak intensity of solar radiation is about 501 nanometers, which corresponds to the blue-green region of the spectrum. The sun's actual color is white because the range of wavelengths it emits is broad. The sun’s light appears yellow to us, however, because of the way Earth's atmosphere scatters light.

    Warnings

    • You must convert temperatures to Kelvins. If you use Fahrenheit or Celsius, you'll get an answer that doesn't make any sense.

References

About the Author

Based in San Diego, John Brennan has been writing about science and the environment since 2006. His articles have appeared in "Plenty," "San Diego Reader," "Santa Barbara Independent" and "East Bay Monthly." Brennan holds a Bachelor of Science in biology from the University of California, San Diego.

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