Luminosity Calculator Formula

Understand the math behind the luminosity calculator. Each variable explained with a worked example.

Use the Luminosity Calculator

Formulas Used

Luminosity

luminosity = 4 * pi * pow(distance, 2) * flux

In Solar Luminosities

luminosity_solar = 4 * pi * pow(distance, 2) * flux / 3.828e26

Variables

VariableDescriptionDefault
fluxObserved Flux(W/m²)1361
distanceDistance(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
  1. 01L = 4π d² F
  2. 02d² = (1.496e11)² = 2.238e22
  3. 034π d² = 2.812e23 m²
  4. 04L = 2.812e23 × 1361 = 3.827e26 W ≈ 1.0 L_sun

Ready to run the numbers?

Open Luminosity Calculator