Every object glows with a spectrum set by its temperature: the Sun (5,800 K) peaks in visible light, a person (310 K) in the infrared, and the cosmic background (2.7 K) in microwaves. Planck’s law, which started quantum mechanics, describes this spectrum exactly.
How to use the Blackbody Radiation Calculator
- Temperature T
- Emissivity ε
- Wavelength λ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the temperature, emissivity (1 for a perfect blackbody) and the wavelength at which to evaluate the spectrum. Photon radiance counts photons instead of energy.
Inputs explained
| Field | What to enter |
|---|---|
| Temperature T | Units: K, °C, °F |
| Emissivity ε | A number |
| Wavelength λ | Units: µm, nm, mm, m |
What each result means
- Spectral radiance = [Emissivity ε]×2×6.62607e-34×2.99792e+08^2÷[Wavelength λ]^5÷(exp([x]) – 1)×1e-9
- Spectral photon radiance = [Emissivity ε]×2×2.99792e+08÷[Wavelength λ]^4÷(exp([x]) – 1)×1e-9
- Peak wavelength (Wien) = 2.897771955e-3÷[Temperature T]
- Total emitted power per area = [Emissivity ε]×5.670374419e-8×[Temperature T]^4
- Peak frequency (Wien) = 5.878925757e10×[Temperature T]
Example values
How the main result changes when Temperature T changes and everything else stays at the example values above:
| Temperature T (K) | Spectral radiance (W/(m²·sr·nm)) |
|---|---|
| 2,889 | 180.0397 |
| 4,333.5 | 4,986.8367 |
| 5,778 | 26,375.8895 |
| 7,222.5 | 72,267.4039 |
| 8,667 | 142,940.9157 |
| 11,556 | 344,531.1902 |
Formula
B_λ = ε·(2hc²/λ⁵) / (e^{hc/(λkT)} − 1)
λ_max = b/T (b = 2.898 × 10⁻³ m·K), M = ε·σ·T⁴
Worked example
Inputs — Temperature T: 5,778 K; Emissivity ε: 1; Wavelength λ: 0.5 µm.
Results — Spectral radiance = 26,375.889538 W/(m²·sr·nm); Spectral photon radiance = 6.6390e22 photons/(s·m²·sr·nm); Peak wavelength (Wien) = 0.50152 µm; Total emitted power per area = 63,200,699.73479 W/m²; Peak frequency (Wien) = 339,684,330,239,460 Hz.
Key terms
- Planck's law
- The spectral distribution of blackbody radiation.
Frequently asked questions
What is a blackbody?
An ideal object that absorbs all radiation and emits the maximum possible at each wavelength.
Why does hot metal glow red, then white?
The peak shifts to shorter wavelengths as temperature rises.
What is the Sun's peak wavelength?
About 500 nm (green-blue), though it looks white.
What is emissivity?
The fraction of blackbody radiation a real surface emits (0–1).