The Magnitude Scale Explained: Star Brightness
Why do brighter stars have smaller magnitudes? Learn the logarithmic magnitude scale, the 100× rule for 5 magnitudes and how to compare brightness.
The idea behind it
The magnitude scale runs backward: smaller numbers mean brighter objects. It is logarithmic, so a difference of five magnitudes corresponds to a factor of one hundred in brightness.
The relationship to remember
10^(0.4 × (6 − 1)) = 100. Object A delivers 100 times the flux of object B in the same band.
Make your own discovery
Swap the two magnitudes. The brightness ratio becomes its reciprocal.
Open the Stellar Magnitude & Brightness Calculator ↗Key formulas
| Quantity | Formula | Note or example |
|---|---|---|
| Brightness ratio | F_A / F_B = 10^(0.4 × (m_B − m_A)) | Same photometric band |
| Magnitude difference | m_B − m_A = 2.5 log₁₀(F_A / F_B) | |
| One magnitude | ≈ 2.512× in brightness | The fifth root of 100 |
Worked examples
Each row uses one of this lab’s presets and the same model as the interactive tool.
| Example | Flux A / Flux B | Magnitude difference | Brighter object |
|---|---|---|---|
| Five magnitudes | 100× | 5 mag | Object A |
| Equal brightness | 1× | 0 mag | Equal |
| One magnitude | 2.51× | 1 mag | Object A |
What this model leaves out
Both magnitudes must refer to the same photometric band. This compares received flux, not intrinsic luminosity. Symbol sizes use a compressed scale.
Check your understanding
Can a magnitude be negative?
Yes. Very bright objects have negative apparent magnitudes. Zero is a reference level, not a lower limit.
What is absolute magnitude?
It is the apparent magnitude an object would have at a distance of ten parsecs, with extinction accounted for.
How much brighter is one magnitude?
About 2.512 times — the fifth root of 100 — so five magnitudes is exactly a factor of 100.
Continue with the formula reference or test yourself in space practice.