Essence of astronomy binoculars shopping

Shopping for astronomy binoculars can be complicated, and lots of terms are thrown around, such as magnification, diameter, weight, size, etc.

Is a 8x42 better than a 10x50? or a 20x60? What does that even mean?

Biology and Physics

In the dark, your eye's pupil will dilate up to 5 to 7 mm after about 20 minutes.

As a consequence, any binoculars / telescope image should match this size, and no more. This is called the Exit Pupil Diameter (EPD).

On the other hand, the magnification of a binocular is defined as the ratio of the size of the input diameter over the diameter of the exit pupil:

M=DEPDM = \frac{D}{\text{EPD}}

Diameter to magnification table

Given that EPD is fixed, we can define the best magnification factor for a given diameter.

This answers the following question: If I want to get 30 mm binoculars, what magnification factor should they have?

Diameter (mm) M (EPD = 5 mm) M (EPD = 7 mm)
10 2 1.4
20 4 2.8
30 6 4.3
40 8 5.7
50 10 6.2
60 12 8.6
70 14 10
80 16 11.4
90 18 12.9
100 20 14.3
110 22 15.7
120 24 17.1
130 26 18.6
140 28 20
150 30 21.4
160 32 22.9
170 34 24.3
180 36 25.7
190 38 27.1
200 40 28.6

Magnification to diameter table

Similarly, we can ask the reverse question: If I want to get binoculars with a 12x magnification factor, what diameter should they have?

For a given magnification factor, what is the best diameter?

Note: this tables also reads like what is sold online: 10x50, 8x40, etc.

M Diameter (EPD = 5 mm) Diameter (EPD = 7 mm)
2 10 14
5 25 35
8 40 56
10 50 70
12 60 84
15 75 105
20 100 140
25 125 175
30 150 210
35 175 245
40 200 280
50 250 350
60 300 420

Conclusion

Given those two tables, next time you want to buy a pair of binoculars, you can quickly check what to look for, and what not to.