Binocular calculator
Turn the numbers printed on your binoculars, such as 10×50 and 6.5°, into exit pupil, twilight factor, brightness and the size of the view, and see how common sizes compare for stargazing.
10×50: a 5.0 mm exit pupil, so your eye takes in all the light the 50 mm objectives gather, and a 6.5° view, 12.3 times the width of the full Moon.
Never look at or near the Sun through binoculars without solar filters made for them over both front lenses.
Common sizes compared
Light grasp is how much more light your eye receives than without binoculars; with a smaller pupil, big exit pupils lose part of their advantage.
| Size | Exit pupil | Twilight factor | Relative brightness | Light grasp, 7 mm pupil | Light grasp, 5 mm pupil |
|---|---|---|---|---|---|
| 7×35 | 5.0 mm | 15.7 | 25.0 | 25× | 49× |
| 7×50 | 7.1 mm | 18.7 | 51.0 | 49× | 49× |
| 8×42 | 5.3 mm | 18.3 | 27.6 | 36× | 64× |
| 10×42 | 4.2 mm | 20.5 | 17.6 | 36× | 71× |
| 10×50 | 5.0 mm | 22.4 | 25.0 | 51× | 100× |
| 12×50 | 4.2 mm | 24.5 | 17.4 | 51× | 100× |
| 15×70 | 4.7 mm | 32.4 | 21.8 | 100× | 196× |
| 20×80 | 4.0 mm | 40.0 | 16.0 | 131× | 256× |
| 25×100 | 4.0 mm | 50.0 | 16.0 | 204× | 400× |
What the numbers on binoculars mean
In 10×50, 10× is the magnification and 50 the diameter of each front lens in millimetres (about 2 inches). The exit pupil, 50 ÷ 10 = 5 mm, is the beam of light reaching your eye. If it is wider than your pupil, the extra light is wasted, so a 7×50 suits young dark-adapted eyes best.
Relative brightness is the exit pupil squared, and the twilight factor is the square root of magnification × aperture. ZEISS warns that the twilight factor alone can mislead: an 8×56 and a theoretical 56×8 share the same value. The true field is printed in degrees or as the width of the view at 1,000 yards or 1,000 metres; the calculator converts between them. The apparent field is how wide that view looks; Nikon now uses the ISO 14132-1 formula, which gives smaller numbers than the old "true field × magnification".
Questions
How do I convert feet at 1,000 yards to degrees?
The field is the angle that spans that width 3,000 feet away: 2 × arctan(feet ÷ 6,000). For example 341 ft at 1,000 yards is 6.5°. Metres at 1,000 metres work the same way with 2,000 in place of 6,000: 114 m is also about 6.5°.
Is a bigger exit pupil always better for stargazing?
Only up to the size of your own pupil. A 7×50's 7.1 mm exit pupil uses all of its light only if your pupil opens to 7 mm in the dark; if it opens to 5 mm, your eye uses just the central 35 mm of each lens, as with a 7×35.
Why do two binoculars with the same size show different fields?
Magnification and aperture do not fix the field: it depends on the eyepiece design. That is why the field is printed separately, and why you should enter it from your own binoculars rather than assume one for the size.
Sources
- Nikon Sport Optics catalogue (Nikon Vision, 2011), binocular basics and its note on apparent field: exit pupil = effective aperture ÷ magnification; relative brightness = exit pupil²; real field and field at 1,000 m; apparent field 2ω′ = 2 × arctan(Γ × tan ω) per ISO 14132-1:2002, which replaced real field × magnification.
- ZEISS, Twilight factor (2020): the square root of objective diameter × magnification, and why it can mislead.
- R. Lazar et al., Royal Society Open Science 11 (2024) 191613, doi:10.1098/rsos.191613: dark-adapted pupil size by age (8.13 mm − 0.408 mm per decade), used for the age estimates.
- Al Nagler, Choosing Your Telescope's Magnification, Sky & Telescope, May 1991: the 7 mm dark-adapted pupil commonly assumed.
- NASA Moon Fact Sheet: the full Moon's average diameter, 1896″, used for "Moon widths".
- American Astronomical Society, Solar Filters for Optics: Telescopes, Binoculars & Cameras.