Blackbody Radiation Calculator

Compute a surface's radiant power output, net radiative heat transfer, and peak emission wavelength from its temperature using the Stefan-Boltzmann and Wien's displacement laws.

Quick Facts

Stefan–Boltzmann Law
Radiant exitance M = εσT⁴, with σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴)
Doubling absolute temperature multiplies emitted power by 2⁴ = 16.
Wien's Displacement Law
Peak emission wavelength λmax = b / T, with b = 2.897771955 × 10⁻³ m·K
Hotter objects peak at shorter, bluer wavelengths.

Your Results

Calculated
Radiant Exitance
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Power emitted per unit area (Stefan–Boltzmann)
Total Radiated Power
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Radiant exitance × surface area
Net Power vs. Surroundings
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Accounts for radiation absorbed back from the environment
Peak Wavelength
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Wien's Law: where emission is strongest

Ready

Enter a temperature, surface area, and emissivity, then press Calculate.

About the Blackbody Radiation Calculator

An ideal blackbody absorbs all radiation that strikes it and re-emits energy purely as a function of its temperature. This calculator applies the two classical results that describe that emission: the Stefan-Boltzmann law, which gives the total power radiated per unit area, and Wien's displacement law, which gives the wavelength where that emission peaks.

The Stefan-Boltzmann law

The radiant exitance (power emitted per unit surface area) of a surface at absolute temperature T is M = εσT⁴, where σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant and ε is the surface's emissivity — 1 for an ideal blackbody, less than 1 for real materials. Multiplying M by the surface area A gives the total radiated power, P = εσAT⁴. Because power scales with the fourth power of temperature, doubling T multiplies the output by 16.

Real surfaces also absorb radiation emitted by their surroundings. If the environment sits at temperature Tsurr, the net radiative power exchanged is Pnet = εσA(T⁴ − Tsurr⁴). A positive value means the object is a net emitter and loses heat by radiation; a negative value means it is a net absorber because the surroundings are warmer.

Wien's displacement law

The wavelength at which emission is strongest is λmax = b / T, where b = 2.897771955 × 10⁻³ m·K is Wien's displacement constant. Cool objects around a few hundred kelvin peak in the infrared; the Sun's roughly 5,778 K surface peaks near 500 nanometers, in visible light; very hot plasmas peak in the ultraviolet or beyond.

Assumptions and limits

  • The object is treated as a gray body with a single, wavelength-independent emissivity ε — real materials can have emissivity that varies with wavelength, angle, and surface finish.
  • Temperature must be entered in kelvin (K); convert from Celsius with K = °C + 273.15.
  • The net power formula assumes the object is fully surrounded by an isothermal environment at Tsurr, with no reflected or transmitted radiation from other sources.

Frequently Asked Questions

What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law states that the radiant exitance (power per unit area) of a surface scales with the fourth power of its absolute temperature: M = εσT⁴, where σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant and ε is emissivity. Multiplying by surface area gives total radiated power.
What is Wien's displacement law used for?
Wien's displacement law finds the wavelength where a blackbody's emission is strongest: λmax = b / T, where b = 2.897771955 × 10⁻³ m·K. Hotter objects peak at shorter, bluer wavelengths — a few hundred kelvin peaks in the infrared, while the Sun's roughly 5,778 K surface peaks near 500 nanometers, in visible light.
What is emissivity and why does it matter?
Emissivity (ε) measures how efficiently a real surface radiates compared to an ideal blackbody, on a scale from 0 to 1. A perfect blackbody has ε = 1. Polished metals are often around 0.05–0.1, while most painted, oxidized, or organic surfaces sit around 0.85–0.95. Emissivity multiplies directly into the Stefan-Boltzmann power calculation.
Why is net radiated power different from total radiated power?
A real object also absorbs radiation emitted by its surroundings. Total radiated power (P = εσAT⁴) ignores that; net power (P = εσA(T⁴ − Tsurr⁴)) subtracts what the object absorbs back from an environment at temperature Tsurr, giving the actual heat lost or gained by radiation.

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Common Measurement Conversions for Everyday Use

QuantityUS / ImperialMetric Equivalent
1 cup8 fl oz237 mL
1 pint16 fl oz473 mL
1 quart32 fl oz946 mL
1 gallon128 fl oz3.785 L
1 lb16 oz453.6 g
1 ft12 in30.48 cm

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