Wien's Law Calculator — Peak Wavelength, Temperature & Frequency of Black Body Radiation

Wien's Law Calculator — Peak Wavelength & Temperature of Any Black Body

Use this Wien's law calculator to estimate the temperature of a black body from its peak emission wavelength (or frequency), or to find the peak wavelength and frequency from a known temperature. Based on Wien's displacement law, this tool is used in astrophysics, spectroscopy, and everyday physics.

What Is Wien's Displacement Law?

Wien's displacement law describes the relationship between the temperature of a black body and the wavelength at which it emits most strongly. The higher the temperature, the shorter the peak wavelength — hotter objects emit more blue/violet light, cooler objects emit more red/infrared light.

λ_max = b / T

• λ_max — peak wavelength of the emission spectrum (m)
• T — absolute temperature of the black body (Kelvin)
• b = 2.8977719 × 10⁻³ m·K — Wien's displacement constant

Wien's Law Formula for Peak Frequency

Although wavelength and frequency are related by c = λ × f, the peak frequency cannot be derived from the peak wavelength using this relation. This is because spectral radiance has a different shape when expressed in frequency terms:

f_max = k × T

• f_max — peak frequency of the emission spectrum (Hz)
• T — absolute temperature (Kelvin)
• k = 5.8789232 × 10¹⁰ Hz/K — Wien's frequency displacement constant

How to Use This Wien's Law Calculator

1. Choose your input mode: temperature, peak wavelength, or peak frequency
2. Enter a value and select the appropriate unit (K, °C, or °F for temperature; nm, μm, Å, mm, m for wavelength; THz, GHz, Hz for frequency)
3. Click Calculate
4. The calculator returns temperature in K, °C, and °F; peak wavelength in nm, μm, mm, Å, and m; peak frequency in THz, GHz, and Hz; plus the electromagnetic spectrum region

Temperature Units: Metric vs. American System

• Kelvin (K) — scientific standard; used for all calculations internally
• Celsius (°C) — metric system (widely used internationally)
• Fahrenheit (°F) — American system (used in the United States)

This calculator accepts and displays results in all three temperature units for convenience.

Example: Temperature of the Sun's Surface

1. The Sun's peak emission wavelength is approximately 501.7 nm (green-yellow light)
2. Using Wien's law: T = b / λ_max = 2.8977719 × 10⁻³ m·K / 501.7 × 10⁻⁹ m ≈ 5,778 K
3. In Fahrenheit: 5,778 K ≈ 9,941 °F

Example: Infrared Emission of Human Body

1. Human body temperature ≈ 37 °C = 310 K
2. Peak wavelength: λ_max = 2.8977719 × 10⁻³ / 310 ≈ 9,347 nm ≈ 9.35 μm (mid-infrared)
3. This is why thermal cameras detect human body heat in the infrared spectrum

Common Reference Temperatures

FAQs

Why can't I use f = c/λ to find the peak frequency from the peak wavelength?

The spectral radiance function has a different mathematical form depending on whether it's expressed per unit wavelength or per unit frequency. Maximizing each gives a different answer. The peak in the wavelength distribution and the peak in the frequency distribution do not correspond to the same point on the spectrum.

Does Wien's law apply to all objects?

Wien's law applies exactly to black bodies — idealized objects that absorb all radiation and emit perfectly. Real objects are gray bodies with emissivity ε < 1, so their actual emission is slightly lower, but the peak wavelength prediction from Wien's law is still a good approximation for many purposes.

What is the Wien's displacement constant?

The Wien's displacement constant b = 2.8977719 × 10⁻³ m·K is a physical constant derived from Planck's radiation law. It relates the peak wavelength of a black body's emission to its absolute temperature.

What is the relationship between Wien's law and the Stefan-Boltzmann law?

Wien's law tells you where the peak of the emission spectrum is (the wavelength or frequency of maximum emission). The Stefan-Boltzmann law tells you how much total power is radiated (P = εσAT⁴). Both laws originate from Planck's distribution function.