Apparent magnitudes of some familiar objects

For the apparent brightness, we usually use the apparent magnitude, conventionally written as m.

Suppose we have two stars with apparent magnitudes m1 and m2. We can calculate the ratio of their brightnesses b1 and b2 by the formula:

m1 - m2 = -2.5 log (b1 / b2)

Let's compare Sirius, the brightest star visible in the night sky, to the Sun.

(-1.5) - (-26.8) = -2.5 log bSirius / bSun

log bSirius / bSun = -10.1

bSirius / bSun = 10-10.1 = 7.9 x 10-11

bSirius / bSun = 1/13,200,000,000.

Sirius appears 13,200,000,000 times fainter than the Sun.

But Sirius is actually more luminous than the Sun. It is just much more distant.