What is the Stefan-Boltzmann law?

The Stefan-Boltzmann law states that a blackbody radiates energy proportional to the fourth power of its temperature. For a star of radius R and temperature T, luminosity L = 4πR²σT⁴, where σ = 5.670374 × 10⁻⁸ W m⁻² K⁻⁴.

What is a solar luminosity (L☉)?

One solar luminosity (L☉) equals 3.828 × 10²⁶ watts — the total power radiated by the Sun. It is the standard unit for expressing stellar luminosity in astrophysics.

Why does temperature matter more than radius?

Luminosity scales with T⁴ but only with R². Doubling a star's temperature increases luminosity 16-fold, while doubling the radius only increases it 4-fold. That is why hot blue stars are far more luminous than cool red giants of similar size.

What is absolute magnitude and how is it related to luminosity?

Absolute magnitude (M) is a logarithmic scale of intrinsic brightness. The calculator derives M using M = M☉ − 2.5 × log₁₀(L / L☉), where M☉ = 4.83. A lower (more negative) number means a brighter star.

Does this assume stars are perfect blackbodies?

Yes. The formula treats stars as ideal blackbodies, which is a standard and accurate approximation for main-sequence and giant stars. Real stellar spectra deviate slightly, but the error is typically less than a few percent for most star types.

What radius and temperature does the Sun have?

The Sun has a radius of 1 R☉ (695,700 km) and an effective surface temperature of about 5,778 K, giving a luminosity of 1 L☉ by definition.

Stellar Luminosity Calculator

Name: Stellar Luminosity Calculator
Availability: InStock
Author: Nham Vu

Enter a star's radius and surface temperature to calculate its luminosity in watts and as a multiple of the Sun's luminosity.

Star Parameters

Stellar Radius

1 R☉ = 695,700 km

Surface Temperature (K)

Sun ≈ 5,778 K | Blue supergiants up to ~50,000 K

Preset Stars

Enter star parameters and click Calculate

Results will show luminosity in watts, solar units, and absolute magnitude.

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Summary

Enter a star's radius and surface temperature to calculate its luminosity in watts and as a multiple of the Sun's luminosity.

How it works

Enter the star's radius in solar radii (R☉) or kilometers.
Enter the star's surface temperature in Kelvin.
The calculator applies the Stefan-Boltzmann law: L = 4πR²σT⁴.
Results appear instantly in watts, solar luminosities, and absolute magnitude.
Use the preset star buttons to explore well-known stars.

Use cases

Astronomy students learning the Stefan-Boltzmann law.
Compare the energy output of different stellar classes.
Estimate a star's luminosity from observational data.
Understand why giant stars vastly outshine dwarf stars.
Explore how temperature dominates luminosity via the T⁴ relationship.
Calculate luminosity for fictional stars in science fiction world-building.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu