Star Magnitude Calculator

Work out star magnitude instantly with clear inputs, formula shown and shareable results.

About Star Magnitude Calculator

The magnitude scale is logarithmic and inverted: five magnitudes is exactly a hundredfold brightness difference, so one magnitude is the fifth root of 100, about 2.512. A magnitude 1.25 star is 79.4 times brighter than a magnitude 6 star at the naked-eye limit. Smaller magnitudes mean brighter objects, a convention inherited from Hipparchus.

Formulas

Brightness ratio

ratio = 10^((m2 - m1) / 2.5)

Per magnitude

one magnitude = 100^0.2 = 2.512 times

Worked example

With the default values below, Star Magnitude Calculator returns Brightness Ratio of 79.433. Change any input above and every figure here is recalculated in your browser.

Inputs used

First magnitude: 1.25
Second magnitude: 6

Results

Brightness Ratio: 79.433 x
Magnitude Difference: 4.75
Brightness Factor Per Magnitude: 2.5119
Factor Across Five Magnitudes: 100

Step by step

1Values used
2Brightness ratio
3Per magnitude
4Brightness Ratio= 79.433 x
5Magnitude Difference= 4.75
6Brightness Factor Per Magnitude= 2.5119
7Factor Across Five Magnitudes= 100

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is the scale backwards?

Because Hipparchus ranked the brightest stars as first class and the faintest visible as sixth, and the numbering stuck when the scale was formalised.

What magnitude can the naked eye see?

About 6 under dark skies, 4 in suburbs and barely 2-3 in bright city centres.