Telescope Exit Pupil & Useful Magnification Calculator

How it works

Magnification = telescope focal length ÷ eyepiece focal length; exit pupil = aperture ÷ magnification = eyepiece fl ÷ focal ratio; lowest useful power = aperture ÷ eye pupil; highest ≈ 2× aperture in mm

The exit pupil is the diameter of the beam of light leaving the eyepiece. If it is larger than your own pupil, the extra light simply misses your eye and the telescope behaves like a smaller one — the reason very low powers gain nothing. If it is smaller than about 0.5 mm the image is dim, floaters in your eye intrude and no new detail appears, because the telescope’s resolution has already been magnified past what the eye can use; that sets the “highest useful” power of roughly twice the aperture in millimetres. Between those limits, 2–4 mm gives the brightest views of faint nebulae and galaxies against a dark sky, while 1 mm and below suits the Moon, planets and double stars where brightness is plentiful and resolution is everything. Since exit pupil equals eyepiece focal length divided by focal ratio, an f/6 scope makes any eyepiece produce a pupil one-sixth its focal length — a quick way to choose eyepieces for any telescope.

Worked example

A 25 mm eyepiece in a 200 mm f/6 (1,200 mm) reflector gives 48× and a 4.2 mm exit pupil — a bright wide field. The useful range for a 6.5 mm pupil runs from 31× (39 mm eyepiece) to 400× (3 mm); planets are best around 200–300× with a 4–6 mm eyepiece.

Frequently asked questions