Magnitude to Brightness Ratio Calculator
Convert between stellar magnitudes and brightness ratios.
Find out how many times brighter or dimmer one star is compared to another.
Photometric magnitude is the astronomical scale for measuring the brightness of stars and other celestial objects. The scale is logarithmic and inverted — smaller (and negative) numbers mean brighter objects.
The Pogson Formula:
m1 − m2 = −2.5 × log10(F1 / F2)
Where:
- m1, m2 = apparent magnitudes of two objects
- F1, F2 = flux (brightness received at the detector) of the two objects
Rearranged to find flux ratio:
F1 / F2 = 10^((m2 − m1) / 2.5)
Absolute Magnitude:
M = m − 5 × log10(d / 10)
Where d = distance in parsecs. This converts apparent magnitude to intrinsic luminosity.
Worked Example:
Two stars: Star A has magnitude 2.0, Star B has magnitude 5.0. How much brighter is A?
F_A / F_B = 10^((5.0 − 2.0) / 2.5) = 10^1.2 = 15.85×
Star A is almost 16 times brighter than Star B.
Brightness Reference:
| Object | Apparent Magnitude |
|---|---|
| Sun | −26.74 |
| Full Moon | −12.7 |
| Venus (brightest) | −4.89 |
| Sirius (brightest star) | −1.46 |
| North Star (Polaris) | +1.98 |
| Naked eye limit (dark sky) | +6.0 to +6.5 |
| Binoculars (10×50) | +9 to +10 |
| Hubble Space Telescope | +31.5 |
Magnitude System Rules:
- Each 1 magnitude difference = 2.512× brightness difference
- Each 5 magnitude difference = exactly 100× brightness difference
Practical Tips:
- Limiting magnitude for visual observing depends strongly on sky darkness — light pollution can reduce limit from 6.5 to 3.0
- Filters (V, B, R, I bands) isolate specific wavelengths — always state the filter when reporting magnitudes
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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