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Wien's displacement law states that within the black-body spectrum, the wavelength with the maximum specific intensity is inversely proportional to the temperature of the black body. Graphs of the wavelength-distribution of emitted energy within black-body radiation at various temperatures have the same general shape, but the peak is displaced within the graph, to a shorter wavelength if the temperature is higher, and vice versa:
wavelengthmax × temperature = b
In principle, this formula is used to determine the temperature of distant bodies such as stars. In practice, a rough determination would be done using a color index or brightness temperature, a more accurate determination would be done based upon the shape of the spectral energy distribution (SED) over some wavelength-range and an accurate temperature would take into account spectral features associated with temperatures and constituents both at and near the surface such as absorption lines.
Of note is that both the above constant and even the location of the peak are for graphs specifically mapping the wavelength to energy density per unit of wavelength of the EMR. An energy density per unit frequency peaks at a different wavelength, i.e., to a different wavelengthmax than the one described above. This latter peak is also inversely proportional to the black-body temperature, but the constant of proportionality used in this case must accommodate the differing type of units. Energy density distributions can also be taken according to other units, such as log wavelength, or wavelength squared, and other means of characterizing the distribution have been used, such as the median of the energy distribution or the average photon energy and each of these, an appropriate constant of proportionality must be used for its variant of Wien's displacement law. A particular type of instrument's sensitivity and resolution are oriented to just one of these (i.e., wavelength, or frequency, or whatever). Alternate constants (using the above formula with temperature and wavelength):
Some example peaks:
| temperature | distribution by wavelength | distribution by frequency or photon energy | distribution by log | band |
| 0.0285 K | 1 m 294 MHz | 1.8 m 1.68 MHz | 1.29 m 233 MHz | radio |
| 2.725 K | 1.06 mm 282 GHz | 1.87 mm 160 GHz | 1.34 mm 222 GHz | microwave |
| 273.15 K | 10 μm 28 THz | 18 μm 16 THz | 13 μm 22 THz | mid infrared |
| 300 K | 9.66 μm 31 THz | 17 μm 17 THz | 12.2 μm24.5 THz | mid infrared |
| 6000 K | 483 nm 621 THz | 850 nm 353 THz | 612 nm 490 THz | visible light |
| 100,000 K | 29 nm 10.3 PHz | 51 nm 5.8 PHz | 37 nm 8.2 PHz | extreme ultraviolet |
| 1,000,000 K | 2.9 nm 103 PHz | 5.1 nm 58 PHz | 3.7 nm 82 PHz | X-ray |