Stellar Luminosity (Stefan-Boltzmann)

L = 4\pi R^2 \sigma T^4

A star's luminosity depends on its surface area and temperature to the fourth power.

By Jožef Stefan, Ludwig Boltzmann

Space Sciences

1879 · Jožef Stefan

Why it matters: Connects observable stellar properties to physical parameters.

Discoverers: Jožef Stefan, Ludwig Boltzmann (1879)

What does it mean?

A star's luminosity depends on its surface area and temperature to the fourth power.

Connects observable stellar properties to physical parameters.

Symbol	Name	Unit	Meaning
$L$	Luminosity	W	Total power output
$R$	Radius	m	Stellar radius
$T$	Temperature	K	Effective temperature

Doubling T increases L by 16× (if R constant).

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Equation Universe

L = 4\pi R^2 \sigma T^4

Real-world impact

Energy infrastructure

Thermodynamic limits shape power and transport.

Photo: Unsplash — power plant

A star's luminosity depends on its surface area and temperature to the fourth power.

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