Blackbody Radiation Calculator — Wien & Stefan-Boltzmann
Enter a surface temperature in kelvin and emitting area to find the peak emission wavelength (Wien's law), radiated intensity per square metre (Stefan-Boltzmann), and the full Planck spectral distribution.
K
m²
λ_max = 2.898 × 10⁻³ / T — peak emission in the green range
- 1
Apply Wien's displacement law
λ_max = 2.898×10⁻³ ÷ 5,778 K = 5.0156e-7 mWien's constant b = 2.898×10⁻³ m·K; peak wavelength = b / T. - 2
Convert to nanometres
5.0156e-7 × 10⁹ = 501.6
How does this calculator work?
A blackbody at temperature T emits most strongly at λ_max = 2.898 × 10⁻³ / T metres (Wien's law) and radiates σT⁴ watts per square metre in total (Stefan-Boltzmann). The Sun at 5 778 K peaks at 502 nm (visible); the human body at 310 K peaks at 9 350 nm (infrared). Real surfaces multiply output by their emissivity ε.
Formula
How this is calculated
A perfect blackbody absorbs all incoming radiation and re-emits it purely as a function of temperature. Wien's displacement law (λ_max = b / T, b = 2.898 × 10⁻³ m·K) gives the wavelength of peak emission — inversely proportional to temperature. At 5 778 K the Sun peaks near 502 nm (visible green); the human body at 310 K peaks at ≈ 9 350 nm (mid-infrared, invisible to the eye but detectable by thermal cameras).
The Stefan-Boltzmann law (M = σ T⁴, σ = 5.670 × 10⁻⁸ W·m⁻²·K⁻⁴) gives total radiated power per unit area across all wavelengths. Because power scales as T⁴, doubling temperature multiplies emission by 16. Total power = M × area.
The chart shows Planck's radiation law — the theoretical distribution of spectral intensity normalised to 100 at its peak. This calculator assumes ideal blackbody emissivity ε = 1. Real surfaces emit a fraction ε of this: polished metals ε ≈ 0.03–0.1; painted surfaces and human skin ε ≈ 0.90–0.98. Multiply power outputs by ε for real-surface estimates.
Frequently asked questions
The Sun emits strongly across the whole visible range; the brain perceives the mixture as near-white. Atmospheric scattering preferentially removes blue light at low elevations, making the Sun appear yellow or orange. The 502 nm peak is where spectral power density is highest, but it does not alone determine perceived colour.
σ = 5.670 × 10⁻⁸ W·m⁻²·K⁻⁴, derived analytically from Planck's constant h, Boltzmann's constant k and the speed of light c. At 300 K a perfect blackbody emits ≈ 459 W/m²; at 6 000 K it emits ≈ 73 MW/m².
Emissivity ε (0–1) is the fraction of blackbody power a real surface actually emits. Human skin ε ≈ 0.98; concrete ε ≈ 0.94; polished aluminium ε ≈ 0.05. Multiply both power outputs by ε. The peak wavelength is unchanged — Wien's law depends only on temperature.
Also known as
TG we-Calculate Editorial Team. (2026). Blackbody Radiation Calculator — Wien & Stefan-Boltzmann [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/blackbody-radiation-calculator
TG we-Calculate Editorial Team. "Blackbody Radiation Calculator — Wien & Stefan-Boltzmann." TG we-Calculate. 2026. https://we-calculate.com/calculator/blackbody-radiation-calculator.
TG we-Calculate Editorial Team, "Blackbody Radiation Calculator — Wien & Stefan-Boltzmann," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/blackbody-radiation-calculator
@misc{wecalculate_blackbody_radiation_calculator, title = {Blackbody Radiation Calculator — Wien & Stefan-Boltzmann}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/blackbody-radiation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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