Wien's Law Calculator
Calculate Wien's displacement law — the relationship between the temperature of a blackbody and the wavelength at which it emits the most radiation. Find peak wavelength, frequency, photon energy, and blackbody temperature.
What Is Wien's Displacement Law?
Wien's displacement law is a fundamental law of physics that describes the relationship between the temperature of a blackbody and the wavelength at which it emits the most radiation. The law states that the peak wavelength (λmax) is inversely proportional to the absolute temperature (T) of the blackbody.
λmax = b / T
Where:
λmax = Peak wavelength (m)
T = Absolute temperature (K)
b = Wien's displacement constant = 2.897771955 × 10⁻³ m·K
The law explains why hotter objects appear bluer (shorter wavelengths) and cooler objects appear redder (longer wavelengths). For example, the Sun has a surface temperature of about 5778 K, which gives a peak wavelength of approximately 502 nm — in the visible (green) portion of the spectrum.
How Does the Wien's Law Calculator Work?
The calculator supports two modes:
- Temperature → Wavelength: Enter the temperature (in K, °C, or °F) to calculate the peak wavelength, frequency, photon energy, and radiation type.
- Wavelength → Temperature: Enter the peak wavelength (in nm, µm, mm, or m) to calculate the temperature of the blackbody, along with frequency, photon energy, and radiation type.
The calculator uses the exact Wien's displacement constant and automatically converts between units. It also displays the radiation type based on the peak wavelength.
Why Use This Wien's Law Calculator?
- Two Modes: Calculate from temperature to wavelength, or from wavelength to temperature.
- Multiple Units: Enter temperature in K, °C, or °F, and wavelength in nm, µm, mm, or m.
- Complete Physics: Get peak wavelength, frequency, photon energy, and radiation type.
- Visual Spectrum: See the blackbody spectrum plot for your calculated temperature.
- Free & Private: No registration, no data storage.
Common Wien's Law Applications
- Astronomy: Determining the temperature of stars from their spectra.
- Thermal Imaging: Understanding the emission spectrum of objects.
- Lighting Design: Selecting appropriate color temperatures for lighting.
- Remote Sensing: Analyzing thermal emission from Earth's surface.
- Cosmology: Understanding the cosmic microwave background radiation.
❓ Wien's Law Calculator FAQ
What is Wien's displacement law?
Wien's displacement law states that the wavelength at which a blackbody emits the most radiation is inversely proportional to its temperature: λmax = b/T, where b = 2.897771955 × 10⁻³ m·K.
What is Wien's constant?
Wien's constant (b) is 2.897771955 × 10⁻³ m·K. It is the proportionality constant in Wien's displacement law. It relates the peak wavelength of a blackbody to its temperature.
How do I calculate the peak wavelength from temperature?
Use the formula λmax = b/T. For example, at 5778 K (the Sun's surface temperature), λmax = 2.897771955 × 10⁻³ / 5778 = 5.02 × 10⁻⁷ m = 502 nm.
How do I calculate temperature from peak wavelength?
Use the formula T = b/λmax. For example, if the peak wavelength is 502 nm, T = 2.897771955 × 10⁻³ / (502 × 10⁻⁹) = 5778 K.
What is the peak wavelength of the Sun?
The Sun's surface temperature is about 5778 K, so its peak wavelength is approximately 502 nm, which is in the visible (green) portion of the spectrum.
What is the cosmic microwave background (CMB) temperature?
The CMB has a temperature of approximately 2.725 K, corresponding to a peak wavelength of about 1.06 mm (microwave radiation).
What is the peak wavelength of a human body?
A human body at 310 K (37°C) has a peak wavelength of about 9.35 µm, which is in the infrared region. This is why thermal cameras can detect body heat.
What is the relationship between temperature and color?
As temperature increases, the peak wavelength shifts to shorter wavelengths. Cooler objects appear red (longer wavelengths), and hotter objects appear blue or white (shorter wavelengths). This is why stars have different colors.
What is the difference between Wien's law and Planck's law?
Planck's law gives the full spectral radiance of a blackbody at all wavelengths. Wien's displacement law gives only the wavelength at which the Planck curve peaks. Wien's law can be derived from Planck's law by differentiating with respect to wavelength.
What is the frequency form of Wien's law?
The frequency form of Wien's law is νmax = αT, where α is a different constant (approximately 5.879 × 10¹⁰ Hz/K). This gives the frequency at which the blackbody spectrum peaks.
What is the photon energy at the peak wavelength?
The photon energy is E = hν = hc/λ, where h is Planck's constant and c is the speed of light. At 502 nm, the photon energy is about 2.47 eV.
What is the difference between Wien's law and the Stefan-Boltzmann law?
Wien's law gives the peak wavelength of the spectrum. The Stefan-Boltzmann law gives the total power emitted over all wavelengths: P = σAT⁴. Both describe blackbody radiation but from different perspectives.
Can I use this calculator for real materials?
Real materials are not perfect blackbodies. However, many objects (including stars, incandescent bulbs, and the human body) approximate blackbody behavior well enough for Wien's law to be useful.
What is the radiation type for a given wavelength?
The calculator identifies the radiation type based on the peak wavelength: gamma (<0.01 nm), X-ray (0.01-10 nm), UV (10-400 nm), visible (400-700 nm), IR (700 nm-1 mm), microwave (1 mm-1 m), radio (>1 m).
What is the Planck constant?
The Planck constant is h = 6.62607015 × 10⁻³⁴ J·s. It is used to calculate photon energy from frequency: E = hν.
What is the speed of light?
The speed of light in vacuum is c = 2.99792458 × 10⁸ m/s. It is used to convert wavelength to frequency: ν = c/λ.