Free Stefan-Boltzmann Luminosity Calculator

Calculate a star's luminosity from its radius and surface temperature: L = 4 pi R^2 sigma T^4.

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Luminosity

384,367,872,304,942,960,000,000,000.000 W

In Solar Luminosities1.0041 L_sun

Luminosity vs Stellar Radius

View formula & how it works →

Stefan-Boltzmann Law

The total power radiated by a spherical blackbody:

L = 4π R² σ T⁴

  • σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴ (Stefan-Boltzmann constant)
  • R = stellar radius
  • T = surface (effective) temperature

    • Luminosity depends on radius squared and temperature to the fourth power.

    Example Calculation

    The Sun: R = 6.957e8 m, T = 5778 K.

    1. 01L = 4π R² σ T⁴
    2. 02R² = (6.957e8)² = 4.840e17
    3. 034π R² = 6.079e18 m²
    4. 04T⁴ = 5778⁴ = 1.115e15
    5. 05σ T⁴ = 5.670e-8 × 1.115e15 = 6.322e7
    6. 06L = 6.079e18 × 6.322e7 ≈ 3.843e26 W ≈ 1.00 L_sun

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