Stellar Luminosity Calculator
Enter a star's radius and effective temperature to find its luminosity from the Stefan-Boltzmann law, both in watts and as a multiple of the Sun.
How to use the luminosity calculator
- Enter the star's radius in metres, or start from the Sun preset.
- Enter the effective surface temperature in kelvin.
- Read the luminosity in watts and in solar luminosities.
Examples
Luminosity of the Sun
radius = 6.957e8 m, temperature = 5772 K
L = about 3.83e26 W (1 solar luminosity)
A hotter, larger star
radius = 1.3914e9 m, temperature = 10000 K
L = about 1.38e28 W (36 solar luminosities)
Frequently asked questions
What is luminosity?
Luminosity is the total power a star radiates into space across all wavelengths, measured in watts. It does not depend on how far away the star is.
What is the Stefan-Boltzmann luminosity formula?
L = 4 x pi x r^2 x sigma x T^4, where r is the radius, sigma is the Stefan-Boltzmann constant and T is the effective surface temperature in kelvin.
Why does temperature matter so much?
Luminosity scales with temperature to the fourth power, so doubling the temperature makes a star 16 times brighter for the same size.
What temperature should I use?
Use the effective temperature in kelvin, the blackbody temperature that reproduces the star's output. The Sun's is about 5772 K.
What is a solar luminosity?
One solar luminosity is the Sun's output, about 3.828e26 watts. Expressing results in solar units makes it easy to compare stars at a glance.
Related tools
Wavelength Frequency Calculator
Convert wavelength to frequency and back using c = f x lambda. Enter a wavelength or frequency in metres, nm, Hz, MHz or GHz and get the photon energy too.
Light Year Converter
Convert astronomical distances between light-years, AU, parsecs, kilometres, miles and metres. Fast, accurate unit conversion with worked examples. Free.
Escape Velocity Calculator
Calculate escape velocity from any planet, moon or star with v = sqrt(2GM/r). Pick Earth, Mars or Jupiter presets or enter mass and radius. Free tool.
555 Timer Calculator
Calculate 555 timer astable frequency, period, high and low times and duty cycle from R1, R2 and the timing capacitor. Free oscillator design helper.
Absolute Humidity Calculator
Calculate absolute humidity in grams of water vapor per cubic meter from air temperature and relative humidity. Fast, free and works in your browser.
Allele Frequency Calculator
Find allele frequencies from genotype counts. Enter the number of AA, Aa and aa individuals to get the A and a allele frequencies and allele totals.