Eyepiece calculator: magnification, exit pupil and true field

The formulas

All three come straight from the geometry of a telescope and eyepiece, and Tele Vue lists them together in its telescope formulas:

magnification = telescope focal length ÷ eyepiece focal length

exit pupil (mm) = aperture (mm) ÷ magnification = eyepiece focal length ÷ focal ratio

true field (°) ≈ apparent field (°) ÷ magnification, or = field stop (mm) ÷ telescope focal length (mm) × 57.3

A Barlow multiplies the telescope’s effective focal length, so it raises the magnification and shrinks the exit pupil and the true field by the same factor. The calculator applies the Barlow factor to all three.

The apparent-field method is a convenient approximation. The field stop is the ring inside the eyepiece that bounds the view; when the maker publishes its diameter, field stop ÷ focal length gives the true field directly and is the more reliable figure.

Worked examples

A Sky-Watcher Classic 200P Dobsonian (203 mm aperture, 1200 mm focal length, f/5.9 in the maker’s specifications) with eyepieces of 52° apparent field:

Eyepiece	Magnification	Exit pupil	True field (from 52°)
32 mm	37.5×	5.4 mm	1.39°
25 mm	48×	4.2 mm	1.08°
10 mm	120×	1.7 mm	0.43°
6 mm	200×	1.0 mm	0.26°

The same 25 mm eyepiece in a Skymax 127 Maksutov (1540 mm, f/12.1) gives 62× with a 2.1 mm exit pupil. Long focal ratios make high magnification easy and wide fields hard; short ones the opposite. As an illustration of the field stop method, an eyepiece with a 27 mm field stop on the 200P shows 27 ÷ 1200 × 57.3 = 1.29°.

The useful range of magnification

Upper end. Celestron’s guidance puts the highest useful magnification at 60× per inch of aperture, about 2.4× per millimetre; another common rule uses 2× per millimetre. For the 200P that is roughly 406–479×. Tele Vue lists the popular 50× per inch limit among its common telescope myths: small telescopes can go higher without showing more detail, while large ones, which suffer more from seeing, may top out at 20–30× per inch. The calculator shows the 2–2.4× range as a guide, not a ceiling.

Lower end. When the exit pupil is wider than your eye’s pupil, some of the light misses the eye and the telescope behaves as if it had a smaller aperture. The lowest useful magnification is therefore aperture ÷ your pupil diameter. Celestron’s 3.6× per inch corresponds to an exit pupil of about 7 mm. Tele Vue lists the 7 mm limit among its common telescope myths: with a refractor, larger exit pupils are usable when a wider field is needed, while a reflector’s low-power limit comes when the shadow of the secondary mirror in the exit pupil becomes obtrusive.

Your own pupil

Dark-adapted pupil size varies between people and shrinks with age. A 2024 study of pupil size across the lifespan (Lazar et al.) fitted a decline of about 0.41 mm per decade in darkness, from an intercept of 8.13 mm. Taking that fit at face value (our arithmetic, not a figure from the paper) gives roughly 7.3 mm at 20, 6.5 mm at 40, 5.7 mm at 60 and 4.9 mm at 80, with large differences between individuals. Enter your own value if you know it; for a 5.7 mm pupil, the 200P’s lowest useful magnification rises from 29× (7 mm) to 36×.

How the calculator describes the exit pupil

The note under the results groups exit pupils into ranges to help pick an eyepiece: wider than your pupil (wasted light), about 4–7 mm (low power, widest and brightest views), 1.5–4 mm (medium power), 0.5–1.5 mm (high power), and below 0.5 mm (the image dims and softens without showing more). These ranges are descriptive conventions, not limits from a single source. The exit pupil and magnification guide discusses them with the sources above.