Stellar Luminosity Calculator
Enter a star's radius in metres and its effective surface temperature in kelvin, and the calculator applies the Stefan-Boltzmann law to return its total radiated power. Results appear both in watts and as a multiple of the Sun's output, so you can compare any star to our own at a glance. Four built-in presets fill the fields with real values for the Sun, Sirius A, Betelgeuse, and Proxima Centauri.
How to use the luminosity calculator
- Click a Preset button (Sun, Sirius A, Betelgeuse, or Proxima Cen) to load real values, or skip to enter your own.
- Type the star's Radius in metres, using scientific notation like 6.957e8 for large numbers.
- Type the effective Temperature in kelvin.
- Read the Luminosity in watts and the Solar luminosities figure beside it.
- Click Copy to grab both results as a single line of text.
Examples
The Sun
radius = 6.957e8 m, temperature = 5772 K
Luminosity = 3.82799e+26 W (0.999998 solar)
Sirius A, hotter and larger
radius = 1.1888e9 m, temperature = 9940 K
Luminosity = 9.83071e+27 W (25.6811 solar)
Proxima Centauri, a cool red dwarf
radius = 1.07e8 m, temperature = 3042 K
Luminosity = 6.98596e+23 W (0.001825 solar)
Frequently asked questions
What is luminosity?
Luminosity is the total power a star radiates in every direction across all wavelengths, measured in watts. Unlike apparent brightness, it does not depend on how far the star is from us; it is an intrinsic property of the star.
What formula does this use?
The Stefan-Boltzmann law for a spherical blackbody, L = 4 x pi x r^2 x sigma x T^4, where r is the radius in metres, sigma is 5.670374419e-8 W per m^2 per K^4, and T is the effective temperature in kelvin.
Why does temperature dominate the result?
Luminosity scales with temperature to the fourth power. Doubling the temperature multiplies the output by sixteen for the same radius, which is why hot blue stars vastly outshine cool red ones of similar size.
What temperature should I enter?
Use the effective temperature in kelvin, the temperature of a blackbody that would emit the same total power. The Sun's effective temperature is about 5772 K. Do not use core temperatures, which are millions of degrees.
What units does the radius need?
Metres. The Sun's radius is roughly 6.957e8 m. If you have a radius in solar radii or kilometres, convert it first, for example multiply solar radii by 6.957e8 to get metres.
What is a solar luminosity?
It is the Sun's total output, taken here as 3.828e26 watts. Dividing a star's luminosity by this value expresses the answer in solar units, which is the more common way astronomers compare stars.
Why does the Sun preset show 0.999998 rather than exactly 1?
The calculator computes the Sun's watts from its radius and temperature, then divides by the adopted solar luminosity constant. The tiny shortfall reflects rounding in those input values, not an error in the formula.
Does this account for limb darkening or non-blackbody spectra?
No. It treats the star as a perfect uniform blackbody sphere, which is the standard first approximation. Real stars deviate slightly because of limb darkening, spectral lines, and rotation, so treat the result as an idealised estimate.
Is my input sent anywhere?
No. The calculation runs entirely in your browser and nothing is uploaded, so the values you enter stay on your device.
Learn more
- The Stefan-Boltzmann law and how stars shine
What the L = 4 pi r squared sigma T to the fourth formula means, why radius and temperature drive luminosity, and how to read solar units.
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