Stellar Luminosity Calculator (Stefan-Boltzmann)

Formula

How this is calculated

A star radiates roughly as a blackbody, so its luminosity (total power output in watts) depends only on its surface area and surface temperature. The surface area of a sphere of radius R is 4πR², and the Stefan-Boltzmann law states that each square metre of a blackbody radiates σT⁴ watts, where σ = 5.670×10⁻⁸ W·m⁻²·K⁻⁴ and T is the effective surface temperature in kelvin. Multiplying these gives L = 4πR²σT⁴.

Enter the radius R either in metres or in solar radii (1 Rsun = 6.957×10⁸ m); the calculator converts to metres internally. Enter the effective temperature T in kelvin. The result is given in watts and as a ratio to the Sun's luminosity, Lsun = 3.828×10²⁶ W, which is convenient for comparing stars. The defaults (1 Rsun, 5772 K) reproduce the Sun, returning L/Lsun ≈ 1.

Note the strong dependencies: luminosity scales with the square of radius and the fourth power of temperature, so a modest rise in temperature dramatically increases output. The model assumes an ideal spherical blackbody at a single effective temperature, ignoring limb darkening, spectral details, and non-spherical shapes. Negative inputs are rejected, and T must be in absolute kelvin (not Celsius).