Exit pupil calculator

Worked example: 8x42

An 8x42 binocular has an exit pupil of 5.3 mm. Nikon uses this very size in its guide: 42 divided by 8 gives 5.3.

The twilight factor for 8x42 is 18.3, a figure Celestron prints for the same size. Nikon squares the exit pupil to get a relative brightness of 28.1 for 8x42.

The chart holds 75 binoculars of this size, with a median view of 393 ft and a median weight of 24.2 oz. See the 8x42 binoculars for every model.

How the figures are worked out

Nikon defines exit pupil as the effective diameter of the objective lens divided by the magnification. Swarovski Optik and ZEISS give the same formula, and the RSPB calls it a rough indicator of low-light performance.

A 7x50 works out to 7.1 mm, and Nikon's 8x20 example gives 2.5 mm. A larger exit pupil gives a brighter view in dim light, according to Nikon.

The twilight factor is the square root of the magnification times the objective diameter, as Celestron and Swarovski Optik print it. For 10x42 that is 20.5.

Relative brightness is the exit pupil squared, the method Nikon and Celestron both use. Nikon notes that brightness can differ even when two exit pupils are equal.

ZEISS says every 8x42 has the same twilight factor whatever its quality, and that an 8x56 and a 56x8 would score alike at 21.2. It treats the figure as a limited guide and points to exit pupil instead.

What your eye can use

Nikon states the human pupil opens about 2 mm in daylight and 7 mm in the dark. Any exit pupil above about 2 mm looks bright enough in daylight, Nikon adds.

ZEISS puts the daytime pupil at 2 to 3 mm. It says children's pupils can open to more than 8 mm, while they seldom exceed 4 mm in old age. Swarovski Optik also gives 8 mm for children, with flexibility falling as we age.

Practical Sailor, citing NIH data, reports a mean night pupil of 7.33 mm for ages 20 to 29 and 5.58 mm for ages 60 to 69. It says the average 50-year-old has a pupil of 5 to 6 mm, so an exit pupil of 7.1 mm may be wider than an older eye can use.

Exit pupil by size in the chart

Each row below uses the exit pupil and twilight factor worked out from the size, with the median view and weight of the models in the chart. The size chart lists every size.

What to do with the result

For dawn, ZEISS advises an exit pupil of at least 4 mm, and says anything under 4 mm is unsuitable as light fades. The 8x32 sits right at 4 mm, and the 10x42 and 12x50 reach 4.2 mm.

ZEISS also notes that a 7x42 gives a larger exit pupil than a 10x42, so a brighter image at dawn and a larger field of view. Compare both in 8x42 against 10x42 before you choose.

For bright days, a 2.5 mm exit pupil such as the 10x25 is above the 2 mm Nikon gives for the eye in daylight. Light, small binoculars suit that use, and the compact binoculars list shows the models.

If dusk matters most, start from the binoculars for hunting. The twilight factor and exit pupil in the results also pair with the field of view calculator and the best binoculars compared.