Caption: Wien's law illustrated.

Features:

1. Wien's law is an exact result for blackbody radiation. It is a relationship between the temperature of the blackbody radiator and the peak of the blackbody spectrum.

2. The other famous simple blackbody radiation law is the Stefan-Boltzmann law that gives the wavelength-integrated flux of a blackbody spectrum.

3. Wien's law in terms of general physical constants is
   
   

   λ_max = (1/4.96511423 ...)*[hc/(kT)]   ,

   where h is the Planck constant h = 6.62607015*10**(-34) J·s = (4.135667696 ...) *10**(-15) eV·s (exact), c is the vacuum light speed c = 2.99792458*10**8 m/s = 2.99792458*10**5 km/s (exact) ≅ 3*10**5 km/s, k is the Boltzmann contant k = 1.380649*10**(-23) J/K = 8.617333262 ... )*10**(-5) eV/K (exact) ≅ 10**(-4) eV/K, T is the Kelvin temperature of the radiating body, and the coefficient (1/4.96511423 ...) is a dimensionless number (it is an irrational number) that follows from the derivation of Wien's law from Planck's law). For reference, see also NIST: Fundamental Physical Constants.

4. Wien's law is an inverse relationship: as temperature rises, the maximizing wavelength decreases. In shorthand: T ↑ λ_max ↓.

5. Note that wavelength goes to infinity if temperature goes to zero. This indeterminate result is rendered harmless by the fact that at T = 0 K (which is absolute zero), there is no blackbody radiation emitted. We know this from the Stefan-Boltzmann law.

6. Wien's law and its inverse (which can also be called Wien's law or the inverse Wien's law) in terms of fiducial values are, respectively,

            2897.771955 ... μm·K   2897.771955 ... Å·K
    λ_max = -------------------- = -------------------
                     T                   T/10**4
    and
        2897.771955 ... μm·K     (2897.771955 ...)*10**4 Å·K
    T = --------------------  =  ---------------------------  ,
               λ_max                       λ_max 

   where wavelength λ_max is in microns (μm) for the first versions and angstroms (Å) for the second versions, and the Wien's law constant (with ellipsis ... to show the value is an exact irrational number) is from CODATA: Fundamental Physical Constants --- Complete Listing.

   Compact forms are Wien's law λ_max = 2897.7729(17) μm·K/T = 2.8977729(17) Å·K/(T/10**7) = (1/4.96511423 ...)*(hc/k)/T and Wien's law inverse T = 2897.7729(17) μm·K/λ_max = 2.8977729(17)*10**7 Å·K/λ_max.

7. A temperature obtained by an application of the inverse Wien's law to the peak of the spectrum of a general radiator (one NOT necessarily a blackbody radiator) is a color temperature.
   Note that the general definition of color temperature for a radiator is the temperature of a perfect blackbody radiator that radiates electromagnetic radiation (EMR) with a spectrum comparable in shape in some sense to that of said radiator.

   Using the inverse Wien's law is simple way to get a color temperature. Another and often more easily obtained color temperature is the astronomical color temperature.

8. A color temperature is a characteristic (i.e., rough average) photospheric temperature for stars.

   However, the standard characteristic photospheric temperature is what is called the effective temperature. A discussion effective temperature and color temperature is given at Effective Temperature and Color Temperature.