# Stefan–Boltzmann Radiation Calculator

> Calculate net thermal radiation between a grey surface and large surroundings with Q = εσA(Ts⁴ − Tsur⁴), plus emitted power and radiative coefficient.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/radiation-stefan-boltzmann-calculator

Every surface radiates in proportion to the fourth power of its absolute temperature. The net exchange with large surroundings is εσA(T_s⁴ − T_sur⁴).

Also called: Radiant heat calculator, Stefan–Boltzmann law calculator.

## Inputs
- Emissivity (ε) (default 0.9)
- Surface area (unit m²; default 1.5)
- Surface temperature (unit °C; default 60)
- Surroundings temperature (unit °C; default 20)

## Results
- Net radiant heat loss
- Emitted by the surface
- Absorbed from the surroundings
- Radiative heat transfer coefficient

## Formula

```
Q̇ = ε × σ × A × (T_s⁴ − T_sur⁴);  h_rad = εσ(T_s + T_sur)(T_s² + T_sur²)
```

Where:
- ε: emissivity (0–1)
- σ: Stefan–Boltzmann constant, 5.670374419 × 10⁻⁸ W/(m²·K⁴)
- A: surface area
- T_s, T_sur: absolute temperatures in K

## Worked example
1. T_s = 333.15 K, T_sur = 293.15 K.
2. Emitted = 0.9 × 5.670374419e-8 × 1.5 × 333.15⁴ = 942.99 W; absorbed = 0.9 × σ × 1.5 × 293.15⁴ = 565.33 W.
3. Net = 942.99 − 565.33 = 377.65 W.

**Result:** A 1.5 m² painted surface at 60 °C in a 20 °C room loses about 378 W by radiation.

## What the result means

Because of the fourth power, radiation dominates at high temperatures. The radiative coefficient lets you add radiation to convection: total h ≈ h_conv + h_rad.

## Assumptions and limits
- Grey, diffuse surface that is small compared with surroundings at a uniform temperature.
- Emissivity equals absorptivity.
- View factors between two finite surfaces are not included.
- Solar or other directed radiation is not included.

## Questions

### Why must temperatures be in kelvin?

The law depends on T⁴ measured from absolute zero; the calculator converts your °C values for you.

### Does a shiny surface lose less heat?

Yes. Low-emissivity surfaces such as polished metal or low-e glass radiate far less, which is why survival blankets are shiny.

## Sources
- [NIST: fundamental physical constants (CODATA)](https://www.nist.gov/)

## Related calculators
- [Convection Heat Transfer Calculator](https://calculators.geekmidst.com/calculators/convection-heat-transfer-calculator)
- [Conduction Heat Flow Calculator](https://calculators.geekmidst.com/calculators/conduction-heat-flow-calculator)
- [Temperature Converter](https://calculators.geekmidst.com/calculators/temperature-converter)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/radiation-stefan-boltzmann-calculator