What is a blackbody?
An idealised object that absorbs all incident radiation (ε = 1) and emits maximum thermal radiation at every wavelength.
Stefan-Boltzmann Radiated Power Calculator
P = εσAT⁴
Calculate radiated power using the Stefan-Boltzmann law. P = εσAT⁴ — thermal radiation from any object.
Calculate
Enter values above to calculate
How it calculates
1
σ = 5.670 × 10⁻⁸ W/(m²·K⁴) (Stefan-Boltzmann constant)
2
P = ε × σ × A × T⁴
3
Result in watts
Formula
P = εσAT⁴
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| P | Radiated power | W |
| ε | Emissivity (0=perfect reflector, 1=blackbody) | — |
| σ | Stefan-Boltzmann constant = 5.670×10⁻⁸ | W/(m²·K⁴) |
| A | Surface area | m² |
| T | Absolute temperature | K |
How to Use This Calculator
This stefan-boltzmann radiated power calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula P = εσAT⁴ is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A 1 m² blackbody (ε=1) at 300 K. Find radiated power.
Step 1: P = 1 × 5.67×10⁻⁸ × 1 × 300⁴
Step 2: P = 5.67×10⁻⁸ × 8.1×10⁹
Answer: P ≈ 459 W
Common Mistakes
- Temperature must be in kelvin — never Celsius or Fahrenheit
- Power scales as T⁴ — doubling temperature gives 16× more radiation
- ε = 1 is a perfect blackbody; real surfaces have ε < 1
Related
Frequently Asked Questions
Does this apply to humans?
Yes — the human body (ε ≈ 0.97, T ≈ 310 K, A ≈ 1.7 m²) radiates about P ≈ 500 W of infrared radiation.