Stellar Luminosity Converter
Instantly convert stellar luminosity with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
L = 4*pi*R^2*sigma*T^4; M_abs = 4.83 - 2.5*log10(L/L_sun)
Luminosity in watts equals the input solar luminosities times 3.828e26. Absolute magnitude is calculated from M = 4.83 - 2.5*log10(L). The Stefan-Boltzmann law L = 4*pi*R^2*sigma*T^4 connects luminosity, radius, and temperature, allowing calculation of any unknown quantity from the other two.
Worked Examples
Example 1: Sirius Luminosity Conversion
Problem:Sirius has a luminosity of 25.4 solar luminosities. Convert to watts and absolute magnitude.
Solution:Watts = 25.4 x 3.828e26 = 9.72e27 W\nAbsolute Mag = 4.83 - 2.5 x log10(25.4)\nAbsolute Mag = 4.83 - 2.5 x 1.405 = 1.32
Result:Sirius: 9.72e27 watts, absolute magnitude +1.32
Example 2: Betelgeuse Radius from Luminosity
Problem:Betelgeuse has luminosity of 126,000 L_sun and surface temperature 3,500 K. Find its radius.
Solution:L = 4*pi*R^2*sigma*T^4\nR = sqrt(L / (4*pi*sigma*T^4))\nR = sqrt(4.826e31 / (4*pi*5.67e-8*3500^4))\nR = 6.97e10 m = 1,002 solar radii
Result:Betelgeuse radius is about 1,002 solar radii
Frequently Asked Questions
What is stellar luminosity and how is it measured?
Stellar luminosity is the total amount of electromagnetic energy a star emits per unit time, measured in watts or in solar luminosities. The Sun's luminosity is 3.828 x 10^26 watts. Astronomers determine luminosity by measuring a star's apparent brightness (how bright it appears from Earth) and its distance (from parallax or other methods). Using the inverse-square law, the true luminosity equals the apparent brightness times 4*pi*distance^2. Luminosity is one of the most fundamental properties of a star.
What is absolute magnitude and how does it relate to luminosity?
Absolute magnitude is a logarithmic measure of a star's intrinsic brightness, defined as the apparent magnitude the star would have if placed at exactly 10 parsecs (32.6 light years) from the observer. The Sun has an absolute magnitude of +4.83. Each decrease of 1 magnitude corresponds to a brightness increase of about 2.512 times. The relationship to luminosity is M = 4.83 - 2.5*log10(L/L_sun). Sirius has an absolute magnitude of +1.42 (about 25 times the Sun's luminosity), while Betelgeuse has about -5.85 (roughly 126,000 solar luminosities).
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy