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Stellar Luminosity Calculator

Find a star's luminosity from its size and temperature.

How it is calculated

Luminosity follows the Stefan–Boltzmann law. Measured against the Sun the formula reduces to L / L☉ = R² × (T / 5772)⁴, where R is the star's radius in solar radii and T its surface temperature in kelvin; 5772 K is the Sun's effective temperature. Multiplying by L☉ = 3.828 × 10²⁶ W gives the power in watts. Because temperature is raised to the fourth power, a modest temperature change has a large effect, while radius counts squared. Both inputs must be greater than zero. The result assumes a spherical black-body star and ignores the real spectrum.

Worked example

A star with a radius of 2 solar radii and a surface temperature of 6000 K. R² = 4. T / 5772 = 1.0395 and its fourth power is about 1.1676. Relative luminosity = 4 × 1.1676 = 4.6705 L☉. In watts, 4.6705 × 3.828 × 10²⁶ = 1.7879e+27 W.

Try this example →

Common mistakes

  • Entering the radius in kilometres or metres instead of solar radii; 1 means the Sun's radius.
  • Using temperature in Celsius: the formula needs kelvin.
  • Forgetting the fourth power and assuming doubling the temperature doubles the output; it multiplies it by 16.
  • Mixing up luminosity (total power emitted) with apparent brightness seen from Earth, which also depends on distance.
  • Expecting precise values for real stars from rounded temperature and radius inputs.

About this calculator

A star's luminosity — its total power output — follows the Stefan-Boltzmann law: L = 4πR²σT⁴, where R is the star's radius, T is its surface (effective) temperature, and σ is the Stefan-Boltzmann constant. Since luminosity scales with the square of the radius but the fourth power of temperature, a modest increase in temperature has a much bigger effect on brightness than the same relative increase in size — this calculator typically expresses the result relative to the Sun's luminosity (L☉) for easy comparison.

Astronomers use this relationship to place stars on the Hertzsprung-Russell diagram, estimate distances to stars via the inverse-square law once luminosity is known, and classify stars by evolutionary stage — a red giant is luminous mainly because of its huge radius, while a blue main-sequence star is luminous mainly because of its high temperature. Enter a star's radius and surface temperature (relative to the Sun) to find its luminosity.

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