Stellar Luminosity Calculator
Temperature to the fourth power dominates everything.
Work out Stellar Luminosity. Temperature to the fourth power dominates everything. States the assumption instead of hiding it.
Luminosity
0.9999976 L☉
G — yellow, like the Sun · peaks at 502 nm
The Stefan-Boltzmann law: L = 4πR²σT⁴. Luminosity goes as the square of the radius and the fourth power of the temperature, and that fourth power dominates everything. A star twice as hot as the Sun at the same size is sixteen times as bright. That is why the hottest stars are so overwhelmingly luminous despite being rare, and why they burn out fast — an O-type star can shine a million times brighter than the Sun and exhaust its fuel in a few million years, while a red dwarf will still be going in a trillion. The peak wavelength comes from Wien's displacement law and is what sets a star's colour. The Sun peaks at about 500 nm, in the green, which is a reasonable clue as to why our eyes are most sensitive there.
How the Stellar Luminosity Calculator works
Stellar luminosity from radius and temperature by Stefan-Boltzmann, with absolute and apparent magnitude, peak wavelength and spectral class. The fourth power on temperature is what makes hot stars so overwhelmingly bright.
Also known as: how bright is a star · stefan boltzmann calculator · absolute vs apparent magnitude · star colour from temperature
Frequently asked questions
What is the Stefan-Boltzmann law?
L = 4πR²σT⁴. Luminosity goes as radius squared and temperature to the fourth, so temperature dominates — a star twice as hot at the same size is sixteen times brighter.
What is absolute magnitude?
How bright a star would appear at a standard distance of 10 parsecs. It removes distance from the comparison, so it measures actual output rather than appearance. Lower numbers mean brighter.
Why do hot stars live short lives?
Because luminosity rises far faster than mass does. An O-type star can shine a million times brighter than the Sun and burns through its fuel in a few million years, while a red dwarf will still be going in a trillion.
What is Wien's law?
Peak wavelength times temperature is a constant. It is why hotter objects glow blue and cooler ones red, and why the Sun at 5,772 K peaks at about 500 nm — in the green, near where our eyes are most sensitive.
What are spectral classes?
O, B, A, F, G, K, M in order of decreasing temperature, from about 30,000 K down to 3,000. The Sun is a G-type; M dwarfs are by far the commonest kind of star, and none is visible to the naked eye.
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