Example 1
A = 1 m², T = 300 K, blank ε -> P ≈ 459 W.
Stefan-Boltzmann law calculator
Enter area and temperature in kelvin. You can leave emissivity blank; then we treat a black body, ε = 1. One square meter at 300 K is about 459 W.
Heat at ΔT: Q = cmΔT. Density: ρ = m/V. Electrical power: P = U·I.
Result
Area A (m²), Temperature T (K) and Emissivity ε (blank = 1). The result shows up here.
How it works
Radiated power grows with the fourth power of temperature: P = ε σ A T⁴. The constant is σ = 5.670374419e-8 W/(m²·K⁴). At A = 1 m², T = 300 K and blank ε the calculator uses ε = 1 and you get about 459 W. That is a black body. You can leave emissivity blank; then that is exactly how we compute.
Temperature must be in kelvin. 27 °C is about 300 K, not 27. A twenty-seven in the T field sits near absolute zero and yields a fraction of a watt from a meter. 100 °C is 373 K: 0.01 m² with blank ε is about 11 W.
A gray body has ε between 0 and 1. Skin is often about 0.97. At A = 1.8 m² and T = 310 K you get about 914 W of emission. The room radiates back, so the net is much smaller. This formula does not subtract the background.
Doubling T does not double P. From 300 K to 600 K, T⁴ grows sixteen times: 459 W becomes about 7350 W on the same meter. Area enters linearly: two meters at 300 K is about 918 W.
Watts from T⁴ are radiation. Watts from U·I are current in a wire. The unit is shared. The inputs are not. Heat Q = c m ΔT says how many joules enter a mass when temperature changes, not how many watts leave a surface.
Type A and T. Leave ε blank if you want a black body, or type 0.97 when the problem says so. Then Calculate. 1 m² and 300 K with blank ε should come back near 459 W.
How to use
- Type area A in m², for example 1, or 1.8 when you model a person.
- Type T in kelvin. Convert 27 °C to 300. 100 °C is 373.
- You can leave emissivity blank; then we treat a black body, ε = 1. Or type 0.97.
- Click Calculate. 1 m², 300 K and blank ε give about 459 W.
- For power from volts and amperes, open P = U·I. For heat of a mass, open Q = c m ΔT.
Formula
P = ε σ A T⁴
σ = 5.670374419·10⁻⁸ W/(m²·K⁴). A > 0, T > 0, ε > 0. Blank ε = 1.
Letters in P = εσAT⁴
Power grows with T to the fourth: P = ε σ A T⁴. One square meter at 300 K and blank ε (meaning 1) is about 459 W.
- P
- Radiated power in watts. A = 1 m², T = 300 K and ε = 1 give about 459 W.
- ε
- Emissivity. A blank field means a black body, ε = 1, and then you get those 459 W.
- σ
- The Stefan-Boltzmann constant 5.670374419×10⁻⁸ W/(m²·K⁴), built in; you do not type it.
- A
- Area in m². At T = 300 K each extra square meter adds another ~459 W when ε = 1.
- T
- Temperature in kelvin. 27 °C is about 300 K; typed 27 sits near absolute zero and crushes P.
Real-life examples
Example 2
A = 1.8 m², T = 310 K, ε = 0.97 -> P ≈ 914 W.
Example 3
A = 0.01 m², T = 373 K, blank ε -> P ≈ 11.0 W.
Example 4
A = 10 m², T = 293 K, blank ε -> P ≈ 4178 W.
Example 5
A = 0.00001 m², T = 2500 K, blank ε -> P ≈ 2.21e4 W.
Example 6
A = 1 m², T = 255 K, blank ε -> P ≈ 240 W.
Example 7
A = 0.5 m², T = 1000 K, ε = 0.8 -> P ≈ 2.27e4 W.
Example 8
A = 1 m², T = 5800 K, blank ε -> P ≈ 6.42e7 W.
Ways to use this calculator
- You leave ε blank and check 459 W from a meter at 300 K.
- You type 1.8 m², 310 K and 0.97 to see the scale of body emission, without subtracting the room.
Frequently asked questions
How many watts at A = 1 m², T = 300 K and blank ε?
P ≈ 459 W, because blank ε means 1. At T = 600 K on the same meter it is about 7350 W, sixteen times more.
Can I type 27 °C as 27?
No. 27 °C is about 300 K. A bare 27 in kelvin is almost absolute zero and yields a fraction of a watt.
Why leave ε blank?
You can leave emissivity blank; then we treat a black body. That is a deliberate shortcut, ε = 1, not missing data.
How much at A = 1.8 m², T = 310 K and ε = 0.97?
P ≈ 914 W of emission. The room shines back, so the net is smaller. The formula does not subtract the background.
How much at 0.01 m², 373 K and blank ε?
About 11 W. 373 K is 100 °C, and T⁴ makes a small area still radiate.
How are these watts different from P = U·I?
Here temperature and area. There volts and amperes. Shared unit, different question.
Does ε = 0.5 cut 459 W in half?
Yes, at the same A and T. 0.5 × 459 ≈ 230 W. Typed ε must be positive.
Where do I compute joules to warm a mass?
On Q = c m ΔT. Energy in the body there, power from a surface here.
Can A be 2 m² at 300 K?
Yes. Two meters with blank ε give about 918 W, a clean check that A is linear.
Does a comma in 1.8 work?
Yes. 1,8 and 1.8 mean the same area [m²]. Power scales with that A.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.