Compare Brightness (Apparent Magnitude) Values

Calculator for the comparison of the brightness of two celestial objects given in mag. This measure is used in astronomy for stars and planets and is based on ancient traditions. The smaller the value, the brighter is the object. In 1850, the magnitude scale was defined in a way, so that the first magnitude (1,0 mag) is a hundred times brighter than the sixth (6,0 mag). Five magnitudes have a difference of 100 times, so from one step to the other, the difference is ⁵√ 100 times = 2.51188643150958. The base of the logarithm is the multiplicative inverse of that value, because the brightness decreases with increasing values.
Please enter two values, the third will be calculated.

Example: Sirius, the brightest star in the sky, except for the Sun, has with its -1.46 mag almost 24 times the brightness of Polaris with it 1.97 mag. The Sun with its brightness of -26.74 magnitudes is almost 13 billion times as bright as Sirius. Those are the apparent magnitudes which are caused by the different distances from Earth. For the absolute magnitude, if all those stars had the same distance, Polaris would be the brightest of these three, next would be Sirius.

The human eye can adapt to different brightness levels and therefore perceive brightnesses over extremely wide ranges. The factor of 13 billion for the brightness ratio between the sun and Sirius becomes even greater if, instead of the brightest star in the sky, you choose one that's just visible. Of course, you shouldn't look at the sun with the naked eye, and certainly not with telescopes that aren't specifically designed for that purpose. If you accidentally do, you'll immediately look away reflexively. Suppressing this reflex can cause serious eye damage.
So let's compare the full moon at -12.74 mag with a star that's just visible at 5 mag. Here, the ratio is 12.6 million, the full moon is brighter by this factor.

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First value (a):
Second value (b):
Ratio a to b: