How to Calculate Stellar Radii

••• stars on sky image by Marek Kosmal from

Except for our Sun, stars are too far away to measure their radii. To work around this restriction, scientists have developed a system of inferring their radius by using their luminosity and surface temperature. The surface temperature is measured by the star's color. This luminosity can be measured with special equipment and adjusted for distance. Luminosity measurements are usually given in comparison to our Sun's luminosity, such that the units used are L-sun. The resulting diameter is called the stellar radii.

    Measure or reference the luminosity of the star and its surface temperature. As an example, Betelgeuse, which forms the left-shoulder of the constellation Orion, has a luminosity of 38,000 L-sun and a surface temperature of 3,400 Kelvin (K).

    Convert the luminosity from L-sun to watts by multiplying by 3.8 x 10^26. This figure is scientific notation to avoid using an excessive and confusing series of zeros. The notation "^26" means "to the power of 26." In the example, Betelgeuse would have a luminosity of 1.4 x 10^31 watts, i.e., 38,000 * 3.8 x 10^26.

    Write out the stellar radii formula: Stellar Radii = squareroot [Luminosity / (4 * pi * Stefan-Boltzmann Constant * (Temperature^4))] "Pi" is a constant, measured at 3.14. The "Stefan-Boltzmann Constant" is measured at 5.7 x 10^-8.

    Plug your values into the formula to solve for stellar radii: Stellar Radii = square root [(1.4 x 10^31) / (4 * 3.14 * (5.7 x 10^-8) * (3,400^4))] Stellar Radii = 3.8 x 10^11 meters This equates to about 360 billion meters across.


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