Stellar Luminosity Calculator
Find a star's luminosity from radius and temperature.
Results update as you type.
How it works
A star's luminosity is the total power it radiates, and this calculator finds it from the star's size and temperature using the Stefan-Boltzmann law. You enter the star's radius in meters and its surface temperature in kelvin, and it returns the luminosity in watts and in solar luminosities, where one solar luminosity is the Sun's output. The law states that luminosity equals the star's surface area, four pi times the radius squared, multiplied by the Stefan-Boltzmann constant and the temperature raised to the fourth power. Two relationships stand out: luminosity grows with the square of the radius, so a bigger star is much brighter, and it grows with the fourth power of temperature, so a modest rise in surface temperature produces a dramatic increase in energy output. This is why hot, large stars can be tens of thousands of times more luminous than the Sun, while cool dwarfs are far fainter. Expressing the result in solar luminosities makes it easy to compare a star to the Sun. Luminosity is a fundamental stellar property that, combined with distance, gives a star's apparent brightness, and combined with temperature places it on the Hertzsprung-Russell diagram that organizes stellar evolution. Both the radius and temperature must be positive. Enter the radius and surface temperature to compute the star's luminosity.
L = 4πR²σT⁴
The Stefan-Boltzmann law gives a star's luminosity as its surface area, four pi times the radius squared, multiplied by the Stefan-Boltzmann constant and the fourth power of its surface temperature. Because luminosity scales with temperature to the fourth power, small temperature differences produce large changes in energy output.
Source:Astrophysics (Stefan-Boltzmann law)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter star radius and surface temperature.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Luminosity updates instantly as you type — no button to press.
Frequently asked questions
What is stellar luminosity?
Stellar luminosity is the total amount of energy a star radiates per second across all wavelengths, essentially its true power output. It differs from apparent brightness, which also depends on distance. Luminosity is an intrinsic property of the star, determined by its size and surface temperature through the Stefan-Boltzmann law.
What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law states that the power radiated by a hot object per unit surface area is proportional to the fourth power of its absolute temperature. For a star, multiplying by its total surface area gives luminosity equal to four pi times the radius squared, times the Stefan-Boltzmann constant, times temperature to the fourth power.
Why does temperature have such a large effect?
Because luminosity depends on temperature raised to the fourth power, small changes in surface temperature cause large changes in energy output. Doubling a star's temperature increases its luminosity sixteenfold for the same size. This strong dependence is why hot blue stars are enormously more luminous than cooler red stars of similar size.
What is a solar luminosity?
A solar luminosity is the luminosity of the Sun, about 3.83 times ten to the 26 watts, used as a convenient unit for comparing stars. Expressing a star's luminosity in solar luminosities immediately tells you how many times brighter or fainter it is than the Sun, which is easier to grasp than a huge number in watts.
How does luminosity relate to a star's life?
Luminosity, together with surface temperature, determines a star's position on the Hertzsprung-Russell diagram, which maps stellar types and evolutionary stages. More massive stars are far more luminous and burn through their fuel quickly, living short lives, while low-luminosity stars can shine steadily for billions or trillions of years. Luminosity is thus central to understanding stellar evolution.