LearnStars & evolutionNaked eye
The magnitude scale
A logarithmic, backwards brightness scale in which smaller numbers are brighter and five magnitudes is a factor of exactly 100.
Why it matters
Every brightness in astronomy is quoted this way. Reading it fluently is the difference between a catalogue being data and being noise.
Try it
Sirius
-1.46
Naked-eye limit, dark sky
+6.50
1,528×
Sirius delivers that many times more light than Naked-eye limit, dark sky — a difference of just 7.96 magnitudes.
The brightest star in the night sky.
The maths, in layers
1 · Intuition
The scale is Hipparchus's naked-eye ranking of 'first magnitude' to 'sixth', later pinned down so that the five-magnitude span he described is exactly a hundredfold in light.
2 · The equation
m₁ − m₂ = −2.5·log₁₀(b₁ / b₂)
- m
- apparent magnitude
- b
- apparent brightness
3 · Where it comes from
The 2.5 is not arbitrary: it is chosen so that 100^(1/5) = 2.512 is one magnitude. Absolute magnitude M is the same scale, defined as what the object would look like from 10 parsecs.
What people usually get wrong
Magnitude 2 is twice as bright as magnitude 4.
It is about 6.3 times brighter. Each whole magnitude is a factor of 2.512.