How do astronomers calculate a star’s luminosity?

Astronomers calculate a star’s luminosity—the total amount of energy it emits per unit of time—by accounting for both its observed brightness and its distance from Earth.12

Because a star's apparent brightness decreases with distance according to the inverse square law, astronomers must first determine the distance ($r$) to the star to convert its measured intensity ($I$) into its true radiated power ($L$). This relationship is expressed by the formula:34
$$I=\frac{L}{4\pi d^2}$$

To compare the true luminosities of different stars, astronomers often use absolute magnitude, which represents the brightness a star would have at a standard distance of 10 parsecs. Because stars emit radiation across various wavelengths, astronomers may also calculate bolometric magnitude, which accounts for the total energy output across the entire electromagnetic spectrum, often requiring corrections for atmospheric absorption or energy emitted in non-visible wavelengths like ultraviolet or infrared.25

Once luminosity and temperature are determined, they can be plotted on a Hertzsprung-Russell diagram, which helps astronomers classify stars and understand their evolutionary stages.62