---
title: "Binocular Calculator: Exit Pupil & Field | Backyard Orbit"
description: "Exit pupil, twilight factor, relative brightness and true and apparent field for any binoculars, from degrees, feet at 1,000 yards or metres at 1,000 m."
url: https://backyardorbit.me/binocular-calculator/
---

# 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.

## 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".

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## 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](https://blogs.zeiss.com/sports-optics/hunting/en/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](https://doi.org/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](https://www.televue.com/engine/TV3b_page.asp?id=102), *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](https://eclipse.aas.org/eye-safety/optics-filters).