Blackbody Temperature from peak wavelength

The Temperature of a Black body calculator computes the temperature (T) of a black body based on the wavelength (λ) of its strongest regular emissions. 

INSTRUCTIONS: Choose units and enter the following:

• (λ) This is the wavelength of the strongest emissions of light.

Temperature (T): The calculator returns the temperature (T) in degrees Kelvin.  However, this can be automatically converted to other units via the pull-down menu.  

The Math / Science

A blackbody at a fixed temperature emits most strongly at a particular wavelength that depends only on the temperature. This formula computes the temperature that corresponds to a given wavelength.

Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black body radiation as a function of wavelength at any given temperature. However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black body radiation toward shorter wavelengths as temperature increases.

Formally, Wien's displacement law states that the spectral radiance of black body radiation per unit wavelength, peaks at the wavelength λ_max.  Therefore the formula for the max wavelength of a black body is::

   ` λ_max = b /T `

where 

• λ_max is the maximum wavelength of the black body
• T is the black body absolute temperature in kelvins.
• b is a constant of proportionality called Wien's Dipsplacement constant , equal to 2.8977729(17)×10−3 m⋅K[1], or more conveniently to obtain wavelength in micrometers, b ≈ 2900 μm·K. 

If one is considering the peak of black body emission per unit frequency or per proportional bandwidth, one must use a different proportionality constant. However, the form of the law remains the same: the peak wavelength is inversely proportional to temperature (or the peak frequency is directly proportional to temperature).

Wien's displacement law may be referred to as "Wien's law", a term which is also used for the Wien approximation.

References

The general information above is, in part, from Wikipedia (en.wikipedia.org/wiki/Wien's_displacement_law).

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