Luminosity Calculator Formula
Understand the math behind the luminosity calculator. Each variable explained with a worked example.
Formulas Used
Luminosity
luminosity = 4 * pi * pow(distance, 2) * fluxIn Solar Luminosities
luminosity_solar = 4 * pi * pow(distance, 2) * flux / 3.828e26Variables
| Variable | Description | Default |
|---|---|---|
flux | Observed Flux(W/m²) | 1361 |
distance | Distance(m) | 149600000000 |
How It Works
Luminosity from Flux and Distance
Luminosity is the total power output of a star. If we measure the flux (power per unit area) at a known distance:
L = 4π d² F
The Sun's luminosity is 3.828 × 10²⁶ W, and its flux at 1 AU is about 1361 W/m² (the solar constant).
Worked Example
The Sun: flux = 1361 W/m² at 1 AU (1.496e11 m).
flux = 1361distance = 149600000000
- 01L = 4π d² F
- 02d² = (1.496e11)² = 2.238e22
- 034π d² = 2.812e23 m²
- 04L = 2.812e23 × 1361 = 3.827e26 W ≈ 1.0 L_sun
Frequently Asked Questions
What is the solar luminosity?
3.828 × 10²⁶ watts. It is a standard unit for expressing other stars' luminosities.
How does luminosity differ from brightness?
Luminosity is an intrinsic property (total power). Brightness (flux) is what we measure, and it diminishes with distance.
What is the range of stellar luminosities?
From about 10⁻⁴ L_sun for the faintest red dwarfs to over 10⁶ L_sun for the most luminous supergiants.
Ready to run the numbers?
Open Luminosity Calculator