Luminosity Calculator
Enter a star's radius and surface temperature to get its luminosity in watts and in solar luminosities — and see why brightness climbs with the fourth power of temperature.
Watts and solar luminosities
Enter the radius and the surface temperature and the calculator returns the luminosity (4πR²σT⁴) in watts and in solar luminosities (L☉) together.
Use SI units
Radius in metres and temperature in kelvin give luminosity in watts — add 273.15 to a Celsius reading to get kelvin before you start.
What is luminosity?
The total power a star radiates
This luminosity calculator turns two measurements of a star — its radius in metres and its surface temperature in kelvin — into its luminosity, the total power it radiates as light across all directions and wavelengths. Luminosity is an intrinsic property: unlike apparent brightness, it does not depend on how far away the star is. The calculator models the star as an ideal blackbody sphere and reports the answer both in watts and in solar luminosities (L☉), so you can see at a glance how a star compares with the Sun. It is the number behind a star's place on the Hertzsprung-Russell diagram, its energy budget, and how it outshines or dims relative to its neighbours.
Enter a radius in metres and a surface temperature in kelvin to get the luminosity in watts and in solar luminosities instantly.
The luminosity is the surface area of the star (4πR²) multiplied by the Stefan-Boltzmann constant σ and by the absolute temperature raised to the fourth power.
L = 4π × R² × σ × T⁴Here σ is the Stefan-Boltzmann constant, 5.670374419 × 10⁻⁸ W/(m²·K⁴), a fixed constant of nature. Take the Sun: square its radius of 6.957 × 10⁸ m, multiply by 4π to get the surface area, multiply by σ, and multiply by 5772 raised to the fourth power. The result is about 3.83 × 10²⁶ W — which, divided by the nominal solar luminosity L☉ = 3.828 × 10²⁶ W, comes to 1.0 solar luminosity. Because the temperature is raised to the fourth power, it dominates the result: a small rise in surface temperature produces a large rise in luminosity.
The formula is the standard way to estimate stellar luminosity, but a couple of practical points are worth keeping in mind.
Ideal blackbody, effective temperature, absolute units
This calculator models the star as an ideal blackbody sphere with emissivity ε = 1 and uses the effective surface temperature. Real stars deviate slightly, and the radius and temperature you enter must be measured values. The temperature must be absolute, in kelvin, or T⁴ is meaningless — convert Celsius by adding 273.15. The result is the star's total output, not its apparent brightness, which also depends on distance.