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Physics

Blackbody Peak Wavelength Calculator.

Calculates the wavelength at which a blackbody emits the most radiation, based on its temperature, using Wien's displacement law.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the temperature of the blackbody in kelvin.

  2. 2

    The calculator applies Wien's displacement law: λ_max = b / T.

  3. 3

    The result is the peak wavelength in meters, with an additional value in nanometers.

2.897771955e-3 / temperature

Frequently asked questions

What is Wien's displacement law?

It states that the wavelength of maximum emission from a blackbody is inversely proportional to its temperature: λ_max = b / T, where b ≈ 2.898 × 10⁻³ m·K.

Why does the peak wavelength shift with temperature?

As temperature increases, the peak emission moves to shorter wavelengths (higher frequencies). This is why hot objects glow blue-white while cooler ones glow red.

What is the typical temperature of the Sun's surface?

About 5,800 K, which gives a peak wavelength around 500 nm, in the green part of the visible spectrum.

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Peak Wavelength

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Peak Wavelength (nm)0nm
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How it works

Calculates the wavelength at which a blackbody emits the most radiation, based on its temperature, using Wien's displacement law.

  1. Enter the temperature of the blackbody in kelvin.
  2. The calculator applies Wien's displacement law: λ_max = b / T.
  3. The result is the peak wavelength in meters, with an additional value in nanometers.

Formulas

The math behind this calculator, written out so you can verify the result.

Wien's Displacement Law

λ_max = b / T

The peak wavelength λ_max is inversely proportional to the absolute temperature T. The constant b is approximately 2.898 × 10⁻³ m·K.

Example:

Input: T = 5800 K

Calculation: λ_max = 2.898e-3 / 5800

Result: ≈ 5.0 × 10⁻⁷ m (500 nm)

Real-world use cases

Where this calculation shows up in everyday life.

Astronomy

Estimate the temperature of stars from their color or determine the peak emission wavelength of celestial bodies.

Example: A star with a peak at 400 nm has a temperature of about 7,245 K.

Thermal Imaging

Understand the infrared radiation emitted by objects at different temperatures for sensor design and calibration.

Example: A human body at 310 K peaks around 9.3 µm.

Lighting Design

Choose the color temperature of light sources to achieve desired visual effects.

Example: A warm white LED at 3000 K peaks near 966 nm.

Tips and common mistakes

Tips

  • Use kelvin for temperature; Celsius or Fahrenheit must be converted first.
  • The peak wavelength is in meters; multiply by 10⁹ to get nanometers.
  • For very hot objects (e.g., 10,000 K), the peak falls in the ultraviolet range.
  • Wien's law applies to ideal blackbodies; real objects may deviate slightly.

Common Mistakes to Avoid

  • Forgetting to convert temperature to kelvin.
  • Using the wrong value for Wien's constant (some sources use 2.9e-3).
  • Confusing peak wavelength with total emitted power, which follows the Stefan-Boltzmann law.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.