Blackbody Radiation Calculator
Peak wavelength by Wien's law, radiated power by the Stefan–Boltzmann law and Planck spectral radiance at any wavelength, for a body at a given temperature.
Result…
How it's calculated
Wien: λ_peak = b ÷ T, b = 2.897771955 × 10⁻³ m·K Stefan–Boltzmann: P = ε σ A T⁴, σ = 5.670374419 × 10⁻⁸ W·m⁻²·K⁻⁴ Planck: B(λ, T) = 2hc² ÷ λ⁵ × 1 ÷ (e^(hc ÷ λkT) − 1)
Every object above absolute zero glows with thermal radiation. For an ideal blackbody the spectrum depends only on temperature: Planck's law gives the radiance at each wavelength, its peak moves to shorter wavelengths as the body heats up (Wien's displacement law), and the total power per square metre grows with the fourth power of the absolute temperature (Stefan–Boltzmann law). The constants are the exact CODATA 2018 values published by NIST: h = 6.62607015 × 10⁻³⁴ J·s, c = 299792458 m/s, k = 1.380649 × 10⁻²³ J/K, σ and b as in the formula. Temperatures are converted to kelvin first.
Your numbers, step by step
About the Blackbody Radiation calculator
This blackbody radiation calculator applies three laws to a body at a given temperature. Wien's displacement law gives the peak wavelength λ = b ÷ T. The Stefan–Boltzmann law gives the radiated power P = ε σ A T⁴. Planck's law gives the spectral radiance at any wavelength you choose, along with the radiance at the peak for comparison. The constants are the exact CODATA values published by NIST for the Wien constant and the Stefan–Boltzmann constant, together with Planck's constant, the speed of light and Boltzmann's constant. Enter the temperature in K, °C or °F, an emissivity for a real (grey) surface, the area in m², cm², mm², ft² or in², and a wavelength in nm, µm or mm. Astronomy and physics students, and anyone checking thermal sensors, can follow every step.
How to use it
- Enter the “Temperature” and pick the “Temperature unit”.
- Set the “Emissivity”: 1 for an ideal blackbody, lower for a real surface.
- Enter the “Surface area” and its unit to get the total power.
- Enter the “Wavelength for the spectral radiance” and pick its unit.
- Read the peak wavelength, the power, the power per square metre and the radiance values.
Worked example
A blackbody at 3000 K peaks at 2.897771955 × 10⁻³ ÷ 3000 ≈ 966 nm, in the near infrared. It emits 5.670374419 × 10⁻⁸ × 3000⁴ ≈ 4.59 MW per m², so a 1 cm² patch radiates about 459 W. At 1 µm its spectral radiance is about 992 W/(m²·sr·nm), 99.7% of the peak value.
Updated
Questions people ask
How do I find the peak wavelength of a blackbody?
Divide Wien's constant, 2.897771955 × 10⁻³ m·K, by the absolute temperature in kelvin. Doubling the temperature halves the peak wavelength.
What is the Stefan–Boltzmann law formula?
The power radiated is P = ε σ A T⁴, with σ = 5.670374419 × 10⁻⁸ W·m⁻²·K⁻⁴ and T in kelvin. Because of the fourth power, doubling the temperature multiplies the power by 16.
Why must I use kelvin and not °C?
Both laws need the absolute temperature. Raising a temperature in °C to the fourth power gives nonsense. The calculator converts °C and °F to kelvin first.
What does spectral radiance measure?
It is the power per square metre of surface, per steradian of direction and per nanometre of wavelength. Comparing it at your wavelength with the peak shows how much of the glow falls there. To relate a wavelength to its frequency, use the wavelength calculator.
Is the radiated power the heat a hot object actually loses?
No. It is what the surface emits; it also absorbs radiation from its surroundings, so the net loss is ε σ A (T⁴ − T_surroundings⁴). Real emissivity also varies with wavelength, so treat a single value as an approximation.