Luminosity Calculator
Enter a star's radius and surface temperature to calculate its luminosity using the Stefan-Boltzmann law. The result comes back in solar luminosities, watts, and absolute magnitude. Add a distance and you also get apparent magnitude, so you can see how bright the star looks from Earth. All inputs support multiple units, and you can swap between Kelvin, Celsius, solar radii, and kilometres without changing your numbers.
Formula
Worked example
Betelgeuse has a radius of about 887 solar radii and an effective temperature of 3,600 K. Surface area: 4 x pi x (887 x 6.957e8)^2 = 1.702e24 m^2. Luminosity: 5.670e-8 x 1.702e24 x 3600^4 = 4.83e29 W. In solar units: 4.83e29 / 3.828e26 = 126,000 L_sun. Absolute magnitude: 4.74 - 2.5 x log10(126000) = -5.5.
What is stellar luminosity?
Luminosity is the total power a star radiates across all wavelengths per unit of time, expressed in watts or as a multiple of the Sun's luminosity (one solar luminosity, L☉, equals 3.828 x 10^26 W). It is an intrinsic property of the star, independent of how far away it is. Luminosity must not be confused with apparent brightness, which is how bright a star looks from Earth and depends heavily on distance. A dim red dwarf nearby can outshine a supergiant that is thousands of light-years away.
Stefan-Boltzmann law and the luminosity formula
Stellar luminosity is computed from the Stefan-Boltzmann law: L = sigma x 4 pi R^2 x T^4, where sigma = 5.670 x 10^-8 W m^-2 K^-4 is the Stefan-Boltzmann constant, R is the star's radius in metres, and T is its effective surface temperature in Kelvin. The 4^4 dependence on temperature is the key insight: doubling the temperature increases luminosity by a factor of 16, while doubling the radius only quadruples it. This is why hot blue supergiants outshine much larger but cooler red supergiants, even when the red star has a bigger radius.
Absolute and apparent magnitude
Astronomers measure brightness on a logarithmic scale called magnitude where lower numbers mean brighter objects. Absolute magnitude (M) is the brightness a star would have if placed exactly 10 parsecs (32.6 light-years) from Earth, and it is linked to luminosity by M = 4.74 - 2.5 x log10(L/L☉). Apparent magnitude (m) is what an observer on Earth actually measures and depends on distance: m = M + 5 x log10(d/10 pc). At 10 pc the two are identical. Sirius, the brightest star in the night sky, has an apparent magnitude of -1.46 but an absolute magnitude of only +1.4, meaning it would be unremarkable from 10 parsecs away. Rigel, by contrast, has an absolute magnitude of -7, making it intrinsically one of the most luminous stars in the galaxy.
How the stellar classification system relates to luminosity
Stars are classified by spectral type (O, B, A, F, G, K, M from hottest to coolest) and luminosity class (I supergiant, III giant, V main sequence, and others). Main-sequence O stars can be a million times as luminous as the Sun, while M dwarfs at the cool end may be ten thousand times less luminous. The Hertzsprung-Russell diagram plots luminosity against temperature and shows that most stars fall on a diagonal band called the main sequence, where luminosity scales roughly as the fifth power of mass for sun-like stars. Giants and supergiants sit above the main sequence because their greatly inflated radii raise total luminosity even at relatively cool surface temperatures.
Well-known stars at a glance
| Star | Type | Radius (R☉) | Temp (K) | Luminosity (L☉) |
|---|---|---|---|---|
| Sun | G2 V | 1.00 | 5,778 | 1 |
| Proxima Centauri | M5.5 Ve | 0.154 | 3,042 | 0.0017 |
| Sirius A | A1 V | 1.711 | 9,940 | 25.4 |
| Vega | A0 Va | 2.362 | 9,602 | 40.1 |
| Pollux | K0 IIIb | 9.06 | 4,586 | 32 |
| Arcturus | K0 III | 25.4 | 4,286 | 170 |
| Rigel | B8 Ia | 78.9 | 12,100 | 120,000 |
| Betelgeuse | M2 Iab | 887 | 3,600 | 126,000 |
Selected stars with their spectral type, radius, effective temperature, and luminosity relative to the Sun. Values are approximate and taken from published astronomical catalogs.
Frequently asked questions
What is the difference between luminosity and brightness?
Luminosity is the total power a star radiates and is an intrinsic property that does not change with distance. Brightness, or flux, is the power received per unit area at the observer and falls off as the inverse square of distance. A star can be highly luminous but appear faint because it is very far away, and a dim star nearby can appear bright. Absolute magnitude captures intrinsic luminosity; apparent magnitude captures observed brightness.
Why does temperature affect luminosity so strongly?
The Stefan-Boltzmann law raises temperature to the fourth power (T^4). That means doubling a star's surface temperature multiplies its energy output per unit area by 16. Because luminosity is the energy output per unit area times the surface area, a hot but small star can easily outshine a large but cool one. This is why hot blue-white O-type stars are the most luminous objects in the galaxy despite having comparable or smaller radii than some red supergiants.
What is absolute magnitude and how is it different from apparent magnitude?
Absolute magnitude is the brightness a star would have if placed exactly 10 parsecs (about 32.6 light-years) from the observer. It is a standardised measure of intrinsic luminosity. Apparent magnitude is the brightness we actually observe, which depends on both the star's true luminosity and how far away it is. The two are linked by the distance modulus: m - M = 5 log10(d / 10 pc). At exactly 10 pc the two magnitudes are equal.
How do I convert solar luminosities to watts?
Multiply by the IAU nominal solar luminosity: 1 L☉ = 3.828 x 10^26 W. For example, Sirius A at 25.4 L☉ has a power output of about 25.4 x 3.828 x 10^26 = 9.7 x 10^27 W. This calculator shows both units automatically.
Can I use this calculator for planets or other objects?
The Stefan-Boltzmann formula applies to any spherical blackbody radiator, so you can use it for brown dwarfs, white dwarfs, or even theoretical objects with a defined radius and temperature. Planets, however, reflect sunlight rather than generating their own and are not well approximated as blackbodies in this way. For reflected-light brightness, a different approach using albedo and solar flux is needed.
What is the Sun's luminosity and how does it compare to other stars?
The Sun's luminosity is the reference point: 1 L☉ = 3.828 x 10^26 W. Among main-sequence stars, the Sun sits near the middle. Red dwarfs like Proxima Centauri can be 500 to 10,000 times less luminous, while a massive O-type star can exceed 1,000,000 L☉. Supergiants like Betelgeuse and Rigel each produce roughly 100,000 to 300,000 L☉.