How is telescope magnification calculated?

Magnification equals the telescope focal length divided by the eyepiece focal length. A 1200 mm telescope with a 10 mm eyepiece gives 120 times magnification. A shorter eyepiece gives more power.

What is exit pupil and why does it matter?

Exit pupil is the diameter of the beam of light leaving the eyepiece, equal to the aperture divided by the magnification. Around 2 mm is ideal for the Moon and planets, while 5 to 7 mm gives the brightest view of faint deep-sky objects.

What is the maximum useful magnification?

Roughly two times the aperture in millimetres, or about 50 times per inch. Pushing beyond this produces empty magnification, a larger but no sharper image, because the optics and the atmosphere run out of detail to enlarge.

How do I find the true field of view?

Divide the eyepiece apparent field of view (AFOV) by the magnification. A 68 degree eyepiece at 120 times shows a true field of about 0.57 degrees, slightly wider than the full Moon.

Why is there a minimum useful magnification?

Below about the aperture divided by seven, the exit pupil exceeds the roughly 7 mm of a dark-adapted human pupil, so light spills past the eye and aperture is wasted. The tool flags when you drop below that point.

Telescope Eyepiece Magnification Calculator

Match an eyepiece to a telescope correctly and you get a bright, sharp, well-framed view. This calculator turns the four numbers on your gear — two focal lengths, an aperture, and an apparent field of view — into magnification, exit pupil, focal ratio, and true field of view, with a sanity check on whether the power is useful.

How it works

The four standard relationships are:

magnification = telescope focal length / eyepiece focal length
exit pupil    = aperture / magnification
focal ratio   = focal length / aperture
true FOV      = apparent FOV (AFOV) / magnification

Useful magnification is bounded: the maximum is about two times the aperture in millimetres (empty magnification above that), and the minimum is the aperture divided by seven, where the exit pupil reaches the limit of a dark-adapted eye.

Example and tips

A 200 mm f/6 (1200 mm) telescope with a 10 mm, 68 degree eyepiece gives 120 times magnification, a 1.67 mm exit pupil, and a 0.57 degree true field — a good planetary combination. For sweeping the Milky Way, choose a longer eyepiece for a wider true field and a 5 to 7 mm exit pupil; for lunar and planetary detail, aim for a 1 to 2 mm exit pupil and stay under the maximum useful magnification.