Stefan-Boltzmann radiation calculator
Radiated power goes as the fourth power of absolute temperature, which is why a hot object cools so quickly at first.
m2
Polished metal 0.05; oxidised steel 0.8; paint and most surfaces 0.9 to 0.95.
Net radiated power
17 858.258W
- Gross emitted power
- 18 235.148
- What a perfect blackbody would emit
- 20 261.275
- Net flux
- 17 858.258 W/m2
- Peak wavelength
- 3748.01 nm
Show the working
- Surface temperature = 500
- Surrounding temperature = 20
- Radiating area = 1
- Emissivity = 0.9
- tk = 500 + 273.15 = 773.15
- ak = 20 + 273.15 = 293.15
- Gross emitted power = 0.9 * sigmaSB * 1 * 773.15^4 = 18 235.1
- Net radiated power = 0.9 * sigmaSB * 1 * (773.15^4 - 293.15^4) = 17 858.3
- Net flux = 1 > 0 ? 17 858.3/1 : 0 = 17 858.3
- Peak wavelength = 2897771.955 / 773.15 = 3748.01
- What a perfect blackbody would emit = sigmaSB * 1 * 773.15^4 = 20 261.3
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- P = epsilon sigma A T^4
- net = epsilon sigma A (T^4 - T_ambient^4)
- Wien: peak wavelength = 2.897 771 955 x 10^-3 m K / T
The Stefan-Boltzmann constant is derived here from its definition 2 pi^5 k^4 / (15 h^3 c^2) rather than transcribed, so it cannot drift from the SI values it is built on.
The Sun peaks at 500 nm; a 500-degree hotplate peaks at 3750 nm, deep in the infrared.