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?

## 1. 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:

$$M = \frac{D}{EPD}$$

## 2. 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

## 3. 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

## 4. 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.