What this calculator does
Stefan-Boltzmann law works out total power radiated by a hot surface, from its temperature and emissivity. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaP = εσAT⁴, σ = 5.670374419×10⁻⁸ W/(m²·K⁴)
The inputs explained
| Field | What to enter |
|---|---|
| Emissivity (1 = ideal blackbody) | A number. Starts at 1. |
| Surface area (m²) | A number, measured in m². Starts at 1. |
| Temperature (K) | A number, measured in K. Starts at 300. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with emissivity (1 = ideal blackbody)
Every other input is held at the calculator’s starting values while emissivity (1 = ideal blackbody) varies. Select any row to load that scenario into the calculator.
How the answer changes with emissivity (1 = ideal blackbody)
| Emissivity (1 = ideal blackbody) | Radiated power | Blackbody radiant intensity (per m²) | Power at double the temperature |
|---|---|---|---|
| 0.5 | 229.650164 W | 459.3003279 W/m² | 3,674.402624 W (16x from T⁴) |
| 0.75 | 344.475246 W | 459.3003279 W/m² | 5,511.603935 W (16x from T⁴) |
| 1 | 459.3003279 W | 459.3003279 W/m² | 7,348.805247 W (16x from T⁴) |
| 1.5 | 688.9504919 W | 459.3003279 W/m² | 11,023.20787 W (16x from T⁴) |
| 2 | 918.6006559 W | 459.3003279 W/m² | 14,697.61049 W (16x from T⁴) |
| 3 | 1,377.900984 W | 459.3003279 W/m² | 22,046.41574 W (16x from T⁴) |