# Luminosity Calculator

URL: https://speedycalculator.com/calculators/physics/luminosity/
Last updated: 2026-10-30

> The luminosity calculator finds a star's luminosity from its radius and surface temperature (Stefan–Boltzmann law), its absolute magnitude, and its apparent magnitude at a given distance.

## Inputs

- Star radius R (R☉, km, R⊕)
- Surface temperature T (K, °C, °F)
- Distance (pc, ly, au)

## Results

- Luminosity
- Luminosity in solar units
- Absolute bolometric magnitude
- Apparent bolometric magnitude

## Formula

```
L = 4πR²σT⁴,  M = 4.74 − 2.5·log₁₀(L/L☉),  m = M + 5·log₁₀(d / 10 pc)
```

## Explanation

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

FieldWhat to enterStar radius RUnits: R☉, km, R⊕Surface temperature TUnits: K, °C, °FDistanceUnits: 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☉)0.50.250.750.5625111.251.56251.52.2524

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Astronomy 2e](https://openstax.org/details/books/astronomy-2e)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)