Wien's Law Calculator

Wien's Displacement Law states that the blackbody radiation curve for different temperatures peaks at inversely proportional wavelengths. The primary formula for calculating peak wavelength is given by λ_max = b / T, where λ_max is the peak wavelength, b is Wien's displacement constant (approximately 2.89777195 × 10^-3 m·K), and T is the absolute temperature in Kelvin. Additionally, the peak frequency can be found using the relation ν_max ≈ (5.8789 × 10¹⁰) × T.

Consider a star with a surface temperature of 10,000 Kelvin, characteristic of a hot A-type star. To find the peak emission wavelength, apply Wien's displacement law formula: λ_max = b / T. Substituting the constants, we divide Wien's constant (0.00289777 m·K) by the temperature (10,000 K). This yields a peak wavelength of approximately 2.8978 × 10^-7 meters, or 289.78 nanometers, which falls squarely in the ultraviolet spectrum.

Always ensure your temperature inputs are in Kelvin rather than Celsius or Fahrenheit to maintain mathematical accuracy. Remember that Wien's law assumes an ideal blackbody radiator; real stars and objects have absorption features that slightly shift their apparent peak emission. Use the frequency equation when dealing with radio astronomy or high-energy astrophysics contexts where frequency is the preferred unit of measurement.