Stellar Luminosity Calculator
A star's luminosity, the total power it radiates across all wavelengths, follows from the Stefan-Boltzmann law for a spherical black body: L = 4 pi R squared times sigma T to the fourth power. The steep dependence on temperature means even modest differences in surface temperature produce dramatic differences in brightness. Enter the star's radius (in solar radii, where 1 R_sun = 695,700 km) and effective surface temperature in Kelvin to find total luminosity in watts and in solar luminosities.
Stellar luminosity formula
L = 4 * π * R^2 * σ * T^4
Where R is the radius in meters, sigma = 5.670374419 x 10 to the -8th W m to the -2 K to the -4 (Stefan-Boltzmann constant, NIST 2018 CODATA), T is effective surface temperature in Kelvin, and L is luminosity in watts. 1 solar radius R_sun = 695,700,000 m. Solar luminosity L_sun = 3.828 x 10 to the 26th W (IAU 2015 nominal value).
Luminosity by spectral class
O class (30,000 K, 10 R_sun): ~100,000 L_sun. A class (10,000 K, 2 R_sun): ~20 L_sun. G class like the Sun (5,778 K, 1 R_sun): 1 L_sun. M dwarf (3,000 K, 0.3 R_sun): ~0.005 L_sun. Red supergiant (3,500 K, 1,000 R_sun): ~100,000 L_sun despite lower temperature because size dominates.
Stellar luminosity: frequently asked questions
What is stellar luminosity?
Stellar luminosity is the total energy output of a star per unit time, measured in watts. The Sun's luminosity is approximately 3.828 x 10 to the 26th watts, defined as 1 solar luminosity (L_sun). More massive, hotter, or larger stars are more luminous.
What formula is used to calculate stellar luminosity?
The Stefan-Boltzmann law for a spherical black body: L = 4 pi R squared sigma T to the fourth power, where R is the stellar radius, T is the effective surface temperature in Kelvin, and sigma = 5.670374419 x 10 to the -8th W m to the -2 K to the -4 is the Stefan-Boltzmann constant.
What is the Sun's effective temperature?
The Sun's effective temperature (the temperature of a black body that would produce the same luminosity) is approximately 5,778 K. Combined with the Sun's radius of 695,700 km, the formula gives the solar luminosity of 3.828 x 10 to the 26th watts.
Why does a small change in temperature produce a large change in luminosity?
Because luminosity scales as T to the fourth power. Doubling the temperature increases luminosity by 2 to the 4th = 16 times. This is why hot O-type stars are millions of times more luminous than cool M-type red dwarfs, even with similar sizes.
How does luminosity relate to absolute magnitude?
Absolute magnitude M is defined as M = M_sun - 2.5 log10(L/L_sun), where M_sun = 4.74 is the Sun's absolute visual magnitude. A star 100 times more luminous than the Sun has an absolute magnitude of 4.74 - 5 = -0.26.
Official sources
- NIST CODATA 2018 (Stefan-Boltzmann constant): physics.nist.gov.
- IAU 2015 nominal solar values: iau.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.