Stefan-Boltzmann Calculator Formula
Understand the math behind the stefan-boltzmann calculator. Each variable explained with a worked example.
Formulas Used
Radiated Power
radiated_power = emissivity * 5.6704e-8 * area * pow(temperature, 4)Radiated Power (kW)
radiated_power_kw = emissivity * 5.6704e-8 * area * pow(temperature, 4) / 1000Variables
| Variable | Description | Default |
|---|---|---|
emissivity | Emissivity (0-1) | 1 |
area | Surface Area(m²) | 1 |
temperature | Temperature(K) | 1000 |
How It Works
Stefan-Boltzmann Law
Every object radiates thermal energy proportional to the fourth power of its temperature.
Formula
P = epsilon * sigma * A * T^4
where sigma = 5.6704 x 10^-8 W/(m²·K^4) is the Stefan-Boltzmann constant and epsilon is the emissivity (1 for a perfect black body).
Worked Example
A perfect black body (epsilon=1) at 1000 K with 1 m² surface area.
- 01P = epsilon * sigma * A * T^4
- 02P = 1 * 5.6704e-8 * 1 * 1000^4
- 03P = 5.6704e-8 * 1e12
- 04P = 56,704 W = 56.7 kW
Frequently Asked Questions
Why does radiation scale with T to the fourth power?
This comes from integrating the Planck radiation spectrum over all wavelengths. Small temperature increases cause large increases in radiated power.
What is emissivity?
A number between 0 and 1 describing how well a surface radiates compared to a perfect black body. Polished metals have low emissivity; dark rough surfaces have high emissivity.
How hot is the surface of the Sun?
About 5778 K. Using Stefan-Boltzmann with the Sun's radius gives its total luminosity of about 3.8 x 10^26 W.
Ready to run the numbers?
Open Stefan-Boltzmann Calculator