A star’s power output depends very strongly on its temperature (T⁴) and on its surface area. Betelgeuse is cooler than the Sun but so enormous that it shines about 100,000 times brighter.
How to use the Luminosity Calculator
- Star radius R
- Surface temperature T
- Distance
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the star’s radius (in solar radii) and surface temperature, and its distance for the apparent magnitude.
Inputs explained
| Field | What to enter |
|---|---|
| Star radius R | Units: R☉, km, R⊕ |
| Surface temperature T | Units: K, °C, °F |
| Distance | Units: pc, ly, au |
What each result means
- Luminosity = 4×pi×[Star radius R]^2×5.670374419e-8×[Surface temperature T]^4
- Luminosity in solar units = [Luminosity]÷3.828e26
- Absolute bolometric magnitude = 4.74 – 2.5×log10([Luminosity]÷3.828e26)
- Apparent bolometric magnitude = 4.74 – 2.5×log10([Luminosity]÷3.828e26) + 5×log10([Distance]÷3.0856775814913673e17)
Example values
How the main result changes when Star radius R changes and everything else stays at the example values above:
| Star radius R (R☉) | Luminosity in solar units (L☉) |
|---|---|
| 0.5 | 0.25 |
| 0.75 | 0.5625 |
| 1 | 1 |
| 1.25 | 1.5625 |
| 1.5 | 2.25 |
| 2 | 4 |
Formula
L = 4πR²σT⁴, M = 4.74 − 2.5·log₁₀(L/L☉), m = M + 5·log₁₀(d / 10 pc)
Worked example
Inputs — Star radius R: 1 R☉; Surface temperature T: 5,772 K; Distance: 10 pc.
Results — Luminosity = 3.8280e26 W; Luminosity in solar units = 1 L☉; Absolute bolometric magnitude = 4.74; Apparent bolometric magnitude = 4.74.
Key terms
- Bolometric magnitude
- Magnitude over all wavelengths.
Frequently asked questions
What is the Sun's luminosity?
3.828 × 10²⁶ W.
Why does temperature matter so much?
Luminosity grows with T⁴ – doubling T gives 16 times the output.
What is absolute magnitude?
The apparent magnitude a star would have at 10 parsecs.
Lower or higher magnitude is brighter?
Lower – the scale is reversed.