# Stefan-Boltzmann Constant

on . Posted in Classical Mechanics

The Stefan-Boltzmann constant, denoted by σ (sigma), is a fundamental physical constant that plays a crucial role in the study of blackbody radiation and thermodynamics.  It quantifies the total energy radiated per unit surface area of a blackbody per unit time and per unit temperature difference to the fourth power.  A blackbody is an idealized object that absorbs and emits all incoming radiation at all wavelengths.

### This constant is fundamental in various areas of physics and astronomy

• Blackbody radiation  -  It is used to describe the power radiated by a blackbody at a given temperature and to calculate the intensity of radiation at different wavelengths.
• Astrophysics  -  The Stefan-Boltzmann law is used to estimate the luminosity of stars and other celestial objects based on their temperatures.  It plays a crucial role in understanding the energy output of stars and their life cycles.
• Climate science  -  The Stefan-Boltzmann law is used in climate models to estimate the radiative heat transfer between the Earth's surface and the atmosphere, contributing to our understanding of Earth's energy budget and climate change.

## Stefan-Boltzmann Constant formula

$$\large{ \sigma = \frac{ 2\; \pi^5 \; k_b^4 }{ 15 \; h^3 \; c^2 } }$$
Symbol English Metric
$$\large{ \sigma }$$  (Greek symbol sigma) = Stefan-Boltzmann constant $$\large{\frac{Btu}{ft^2\;hr\; R^4}}$$  $$\large{ \frac{W}{m^2-K^4} }$$
$$\large{ k_b }$$ = Boltzmann constant $$\large{ \frac{lbm-ft^2}{sec^2} }$$  $$\large{ \frac{kJ}{molecule-K} }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ h }$$ = Planck constant $$\large{ \frac{lbf-ft}{sec} }$$  $$\large{ J-s }$$
$$\large{ c }$$ = speed of light in vacuum $$\large{ \frac{ft}{sec} }$$  $$\large{ \frac{m}{s} }$$

## Stefan-Boltzmann Constant

$$\large{ \sigma = 1.713441 \;x\; 10^{-9} \frac{Btu}{ft^2 \; hr \; R^4}}$$

$$\large{ \sigma = 5.670374419 \;x\;10^{-8} \;\frac{W}{m^2 \; K^4} }$$ Tags: Temperature Constant