# Heat Radiation Calculator (Stefan-Boltzmann Law, Q=εσA·T⁴)

Compute thermal radiation from a blackbody/grey body (Stefan-Boltzmann law): blackbody emissive power E_b = σ·T⁴ (W/m²), total radiated power Q_rad = ε·σ·A·T⁴ (W); with an optional surrounding temperature T₀ it also computes the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) (W). σ = 5.670374419e-8 W/(m²·K⁴); ε is the emissivity (0 < ε ≤ 1, blackbody ε=1); T is the ABSOLUTE temperature (K) — °C and °F are first converted to K (this is an absolute temperature, not a difference); A is the radiating area. Area in m²/cm².

> Canonical page: https://elysiatools.com/en/tools/heat-radiation-calculator

- **Category:** Math & Numbers

- **Keywords:** heat radiation, thermal radiation, Stefan-Boltzmann law, blackbody, grey body, emissivity, emissive power, radiated power, net radiation, radiative heat transfer, σT⁴, absolute temperature, thermal

## Overview

The Heat Radiation Calculator uses the Stefan-Boltzmann law to calculate blackbody emissive power, total radiated power, and optional net radiative exchange. Enter emissivity, absolute temperature, and radiating area, with temperature available in K, °C, or °F and area in m² or cm².

## Inputs

- **Emissivity ε** (number): Emissivity ε of the surface (0 < ε ≤ 1). Use ε = 1 for an ideal blackbody.
- **Temperature T** (number): ABSOLUTE temperature T of the radiating surface, in the selected Temperature Unit. Must be > 0 K after conversion.
- **Temperature Unit** (select): Unit of the surface temperature. This is an ABSOLUTE temperature, not a difference: °C→K adds 273.15, °F→K uses (T-32)·5/9+273.15.
- **Radiating Area A** (number): Radiating surface area A, in the selected Area Unit.
- **Area Unit** (select)
- **Surrounding/Cold Temperature T₀ (optional, for net radiation)** (number): Optional surrounding (cold) temperature T₀, in the same Temperature Unit as T. When provided, the net radiative exchange Q_net = ε·σ·A·(T⁴-T₀⁴) is also computed. Leave blank to skip.
- **Decimal Places** (number)

## When to use

- Estimate thermal radiation from an ideal blackbody or grey surface.
- Calculate total radiated power from a surface with a known area and emissivity.
- Compare emitted and net radiation when a surrounding temperature is available.

## How it works

- Enter the surface emissivity ε, where 1 represents an ideal blackbody.
- Enter the surface temperature and select K, °C, or °F; Celsius and Fahrenheit values are converted to Kelvin.
- Enter the radiating area and select m² or cm².
- Optionally enter the surrounding temperature to calculate net radiation, then choose the number of decimal places.

## Use cases

- Thermal engineering estimates for radiative heat transfer.
- Comparing blackbody and grey-body radiation at different temperatures.
- Checking radiation losses from heated surfaces, panels, or other radiating areas.

## Frequently asked questions

### What does this calculator calculate?

It calculates blackbody emissive power E_b, total radiated power Q_rad, and optional net radiative exchange Q_net.

### What is the Stefan-Boltzmann law used here?

The calculator uses E_b = σT⁴, Q_rad = εσAT⁴, and, when T₀ is provided, Q_net = εσA(T⁴ − T₀⁴).

### Can I enter temperature in Celsius or Fahrenheit?

Yes. Select °C or °F, and the calculator converts the absolute temperature to Kelvin before calculating.

### What emissivity should I enter for a blackbody?

Enter ε = 1 for an ideal blackbody. Grey surfaces use an emissivity greater than 0 and no greater than 1.

### What happens if I leave the surrounding temperature blank?

The calculator returns blackbody emissive power and total radiated power, while net radiation is not calculated.

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