Wien's Law Calculator
Calculate the peak wavelength of blackbody radiation from temperature using Wien's displacement law. Get the Planck spectrum, peak frequency, and photon energy instantly.
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About This Calculator
Wien's displacement law describes the fundamental relationship between the temperature of a blackbody and the wavelength at which it emits the most radiation. Named after German physicist Wilhelm Wien, who won the 1911 Nobel Prize for this discovery, the law states that the peak wavelength λmax is inversely proportional to the absolute temperature T: λmax = b / T, where b = 2.897771955 × 10−3 m·K is Wien's displacement constant.
This calculator works both ways: enter the temperature of any object (in Kelvin) to find its peak emission wavelength, peak frequency, and photon energy. Alternatively, enter a known peak wavelength (in nanometers) to compute the corresponding blackbody temperature — a technique widely used in astronomy to estimate stellar surface temperatures from spectroscopic observations.
The interactive Planck spectrum chart visualizes the full blackbody radiation curve for the entered temperature, showing how energy is distributed across wavelengths. As temperature increases, the peak shifts toward shorter wavelengths (blueshift), while cooler objects emit predominantly in the infrared (redshift).
How It Works
The calculator applies three fundamental equations:
- Wien's displacement law: λmax (nm) = 2.897772 × 106 / T (K) — gives peak wavelength in nanometers
- Peak frequency: fmax = 5.8789232 × 1010 × T — the frequency-domain analogue of Wien's law
- Photon energy: E = hc / λmax ≈ 1239.84 eV·nm / λmax (nm) — the energy of a single photon at the peak wavelength
Regional Notes
Global (IN/US/UK): Wien's law is a universal physical law independent of geography. Temperature is measured in Kelvin (SI unit), wavelength in nanometers, and frequency in Hertz. The calculator is used worldwide in physics education, astronomy, materials science, and climate research. Astronomers in all regions use the same formula to estimate star temperatures from their observed spectra.
Frequently Asked Questions
What is Wien's displacement law?
Wien's displacement law states that the peak wavelength of blackbody radiation is inversely proportional to the temperature of the object. The formula is λmax = b / T, where b = 2.897771955 × 10−3 m·K is Wien's displacement constant.
How do I calculate peak wavelength from temperature?
Enter the temperature in Kelvin and click Calculate. The calculator applies Wien's law λmax = b / T to find the peak wavelength, peak frequency via fmax = 5.8789232 × 1010 × T, and photon energy at that wavelength.
What is the peak wavelength of the Sun?
The Sun's surface temperature is approximately 5778 K, giving a peak wavelength of about 501.7 nm (green light). This explains why the Sun appears white-yellow to human eyes, as its spectrum peaks in the visible range.
Can I calculate temperature from peak wavelength?
Yes. Enter the peak wavelength in nanometers and the calculator will compute the temperature using T = b / λmax. This is how astronomers estimate the surface temperature of stars from their spectral observations.
What is the difference between Wien's law and the Stefan-Boltzmann law?
Wien's law tells you the peak wavelength where a blackbody emits the most energy. The Stefan-Boltzmann law tells you the total power radiated per unit area, proportional to T4. Both are derived from Planck's law of blackbody radiation.
What does the peak frequency tell us?
The peak frequency fmax = 5.8789232 × 1010 Hz/K × T is the frequency at which spectral radiance per unit frequency is maximum. This is useful in radio astronomy and infrared spectroscopy where frequency-domain measurements are standard.
Is Wien's law accurate for all objects?
Wien's law is exact for ideal blackbodies and a good approximation for most stars, planets, and heated objects. Real materials have emissivity less than 1, but the peak wavelength shift follows the same inverse relationship.