# Blackbody Radiation Calculator

URL: https://speedycalculator.com/calculators/physics/blackbody-radiation/
Last updated: 2026-10-30

> The blackbody radiation calculator applies Planck's law to find the spectral radiance of a body at a given temperature and wavelength, the peak wavelength (Wien) and the total emitted power per area (Stefan–Boltzmann), with optional emissivity.

## Inputs

- Temperature T (K, °C, °F)
- Emissivity ε
- Wavelength λ (µm, nm, mm, m)

## Results

- Spectral radiance
- Spectral photon radiance
- Peak wavelength (Wien)
- Total emitted power per area
- Peak frequency (Wien)

## 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
```

## Explanation

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

FieldWhat to enterTemperature TUnits: K, °C, °FEmissivity εA numberWavelength λUnits: 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))2,889180.03974,333.54,986.83675,77826,375.88957,222.572,267.40398,667142,940.915711,556344,531.1902

## 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.

## FAQ

**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).


## Sources

- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)
- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)