Stellar Magnitude & Brightness Ratio Calculator

How it works

Brightness ratio = 10^(0.4 × Δm) = 2.512^Δm; combined magnitude = −2.5 log₁₀(10^(−0.4 m₁) + 10^(−0.4 m₂)); absolute magnitude M = m − 5 log₁₀(d/10 pc); L/L☉ = 10^(0.4 × (4.83 − M))

The magnitude scale is logarithmic and backwards: brighter objects have smaller (even negative) numbers, and by Pogson’s definition five magnitudes is exactly a factor of 100 in brightness, so each magnitude is a factor of 2.512. That makes ratios easy — a magnitude-1 star is 100 times brighter than a magnitude-6 star at the limit of naked-eye vision — and it means magnitudes cannot be added directly: two equal stars together are 0.75 mag brighter than one, not twice the number. Apparent magnitude depends on distance; absolute magnitude places every object at 10 parsecs so that intrinsic luminosities compare, and the difference between the two, the distance modulus, is how astronomers measure distances once they know a star’s true brightness.

Worked example

Magnitude 1.0 versus 6.0: a difference of 5 is exactly 100× in brightness, and seen together they would register as magnitude 0.99. A magnitude-1.0 star 100 parsecs away has an absolute magnitude of −4.0 — about 3,400 times the Sun’s luminosity.

Frequently asked questions