Stefan-Boltzmann Calculator
Blackbody radiated watts from area and temp.
What it does
Hot faces shed power as light and heat by the fourth power of kelvin: small temp climbs mean large watt jumps. Emissivity, area, and the exact sigma constant scale that curve. This page runs one gray surface in watts from metric or imperial inputs.
The default is 1 m2 at 100 C with emissivity 0.9. Kelvin is 373, and power is 989 W. Imperial defaults convert the same plate to 10.76 ft2 at 212 F and match the same watts.
Emissivity is the judgment input. Black paint and skin sit near 0.9, rusted steel lower, and polished aluminum far below 0.1. Area is one side unless both faces radiate, which doubles it by hand.
Fourth power punishes guesswork. A 10% temp miss near 373 K moves watts about 46%, so measure surface temp rather than air temp.
How to use
- Pick metric or imperial first (metric default).
- Enter radiating area.
- Enter surface temp.
- Enter emissivity.
- Read watts first, then kelvin.
Formula
- A
- Surface area radiating.
- T
- Absolute temperature in kelvin.
- e
- Surface emissivity 0 to 1.
Sigma is exact by SI definition. Emissivity runs 0 to 1 (black near 1, polished metal far below). Fahrenheit converts to kelvin and ft2 to m2 at 0.092903 inside, so both modes agree.
Worked example
Example: hot plate 1 m2
1 m2 at 100 C, emissivity 0.9 (imperial 10.76 ft2 at 212 F).
- Kelvin: 100 + 273.15 = 373 K.
- Fourth: 373^4 = 1.94e10.
- Times sigma: 1.94e10 x 5.67e-8 = 1,099 W/m2.
- Times e and area: 1,099 x 0.9 x 1 = 989 W.
- Imperial 10.76 ft2 at 212 F gives the same 989 W.
- Tool shows 989 W both modes.
Reference table
| Temp | Kelvin | W/m2 |
|---|---|---|
| 0 C | 273 K | 316 |
| 100 C | 373 K | 1,099 |
| 500 C | 773 K | 20,241 |
| 1,000 C | 1,273 K | 148,911 |
| 1,500 C | 1,773 K | 560,244 |
Limits
- One gray surface. No view factors.
- No convection or conduction.
- Emissivity assumed constant with temp.
- Surroundings assumed cold.
Common mistakes
- Using C or F as T without kelvin.
- Squaring instead of fourth power.
- Reading area in ft2 as m2.
- Setting emissivity above 1.
- Counting one face twice.
Try it yourself
Quick checks. Answers sit tucked under each question.
0 K surface?
Zero watts at any area.
1 m2 black at 726 C (999 K)?
About 56,511 W.
Questions
Radiated power?
Emissivity times sigma times area times K^4. Here 989 W.
Kelvin?
C plus 273.15. Here 373 K.
What is that in imperial?
989 W for 10.76 ft2 at 212 F.
Sigma value?
5.670374419e-8 W per m2 per K4, exact by SI.
Total heat loss?
No. Convection and conduction sit outside radiation.
Enclosures?
No. View factors and surroundings sit outside one surface.