Telescope Magnification Calculator

Background.

Slide a 10 mm eyepiece into a telescope with a focal length of 1,200 mm and Jupiter looks 120 times wider than it does to the naked eye. Swap in a 25 mm eyepiece and the same telescope gives 48×. Magnification belongs to the pairing rather than to the tube: it is the telescope's focal length divided by the eyepiece's, and changing either one changes the view.

That division is the easy part. Whether a given power is worth using depends on two more numbers that come from the same inputs. The exit pupil, the width of the beam of light leaving the eyepiece, equals the aperture divided by the magnification, and it decides how bright the view is and whether your eye can take in all the light the telescope gathers. The useful range of powers runs from a lower bound set by your own pupil to an upper bound set by a rule of thumb, 2× per millimetre of aperture unless you change it. For the default 200 mm f/6 reflector that range is 28.6× to 400×.

The sum also runs backwards. Enter the power you want and you get the eyepiece focal length that delivers it, with any Barlow lens you own built in, so you can see whether a new eyepiece would duplicate one already in the case or ask for more than the sky will allow before you spend money on it.

What is telescope magnification calculator?

Telescope magnification is angular. It is the ratio of the angle an object spans as seen through the eyepiece to the angle it spans to the unaided eye, so at 120× the Moon, half a degree across without the telescope, overflows the field of many eyepieces. A telescope used by eye is afocal: light arrives from a distant object and leaves the eyepiece as a parallel beam for a relaxed eye, so there is no image on a screen whose size could be measured, only angles. Within that model the magnification is exactly the objective's focal length divided by the eyepiece's. The exit pupil is the image of the objective formed by the eyepiece, the small bright disc you can see floating behind the eye lens when the telescope points at a bright sky. Its diameter is the aperture divided by the magnification.

How to use this calculator.

1. 01Under Solve for, choose Magnification from an eyepiece to check an eyepiece you have, or Eyepiece needed for a target power to plan a purchase.
2. 02Enter the telescope focal length in millimetres from the tube label or manual. If only the focal ratio is printed, multiply it by the aperture: a 200 mm f/6 mirror has a 1,200 mm focal length.
3. 03Enter the aperture, the clear diameter of the main lens or mirror, in millimetres. A telescope sold as an 8-inch has an aperture of 8 × 25.4 = 203.2 mm.
4. 04Enter the eyepiece focal length engraved on its barrel, or the magnification you want. Set Barlow / focal extender to its stated factor, or to 1 if you are not using one.
5. 05Adjust Your dark-adapted pupil to suit your age: about 7 mm suits most young adults, and many people in their sixties reach only about 5 mm. Leave the upper-limit convention at 2 unless you want a stricter ceiling, such as 1 for a large telescope under unsteady air.
6. 06Read the magnification together with the exit pupil and the verdict. The exit pupil says more about how the view will look than the magnification does.

The formula.

With a Barlow of factor B, M = (f_tel × B) ⁄ f_eye, where f_tel is the telescope's focal length and f_eye the eyepiece's, both in millimetres. Solving for the eyepiece instead gives f_eye = (f_tel × B) ⁄ M. The exit pupil is d_exit = D ⁄ M, with D the aperture; written another way it is the eyepiece focal length divided by the focal ratio the eyepiece actually sees, f_tel × B ⁄ D. The focal ratio reported is that of the telescope alone, f_tel ⁄ D. Magnification per inch of aperture is M × 25.4 ⁄ D, using the inch of exactly 25.4 mm.

The main relation comes straight from geometry. A ray from a star at angle θ off the axis crosses the objective's focal plane at a height of f_tel × tan θ. The eyepiece shares that focal plane and sends the ray out parallel at a new angle θ′, where the same height equals f_eye × tan θ′. Dividing one by the other, tan θ′ ⁄ tan θ = f_tel ⁄ f_eye. Within the thin-lens, paraxial model this is exact rather than a small-angle approximation.

The two bounds are of different kinds. The lower one, M_min = D ⁄ p with p your dark-adapted pupil, is physics: below that power the exit pupil is wider than your pupil and the iris blocks the outer part of the beam. The upper one, M_max = k × D, is a convention, and at the default k of 2 per millimetre it is simply another way of saying stop at an exit pupil of 0.5 mm. A rough justification exists. By the Rayleigh criterion an aperture of D millimetres resolves about 138 ⁄ D arcseconds in green light, and at 1× per millimetre that detail is already enlarged to about 2.3 arcminutes, above the roughly one arcminute a normal eye can separate; doubling the power again makes the image larger without revealing anything new.

Brightness follows the exit pupil. For an extended object such as a planet's disc or a nebula, the surface brightness you see scales with the square of the exit pupil, as long as the exit pupil is no wider than your own, so halving it leaves a quarter of the brightness. The model stops applying when the telescope is focused on something close, when a camera sits at prime focus with no eyepiece, or when you want the true field of view, which depends on the eyepiece's field stop and has its own calculator.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Tele Vue Optics, Inc., 'Telescope Formulas / Common Telescope Myths'. Manufacturer engineering note. Verified by retrieval to state: Magnification = 'Objective focal length / Eyepiece focal length' and 'Objective diameter / Exit pupil'; Exit Pupil = 'Objective diameter / Magnification' and 'Eyepiece focal length / (Objective f/#)'; Focal Ratio = 'Objective focal length / objective diameter'. Independent of the optics textbooks below, open access. Retrieved 2026-07-29.
2. [2]Hecht, E. (2017). Optics, 5th edition, §5.7.3 'Telescopes', Pearson Education. Derivation of the angular magnification MP = f_objective / f_eyepiece for the afocal refracting telescope, and of the exit pupil as the image of the aperture stop. Print / bibliographic reference — no authoritative free full text exists, so no URL is offered rather than linking a scan of uncertain provenance.
3. [3]Winn, B., Whitaker, D., Elliott, D.B. & Phillips, N.J. (1994). 'Factors affecting light-adapted pupil size in normal human subjects.' Investigative Ophthalmology & Visual Science 35(3):1132–1137. Shows that pupil diameter falls with age, which is why the dark-adapted pupil is an editable input rather than a fixed 7 mm. It measured light-adapted pupils, so it does not give a dark-adapted decline rate. Abstract open access; full text paywalled. Retrieved 2026-07-29.
4. [4]National Institute of Standards and Technology, Special Publication 811 (2008 edition), Appendix B.8 'Factors for Units Listed Alphabetically': inch (in) → metre (m), factor 2.54 E-02, printed in boldface, which the table's own legend defines as exact. That is 25.4 mm exactly, following the 1959 international yard and pound agreement. Used for the magnification-per-inch output. Open access. Retrieved 2026-07-29.
5. [5]ISO 14132-1:2015, 'Optics and photonics — Vocabulary for telescopic systems — Part 1: General terms and alphabetical indexes of terms'. Standardises the definitions of magnification and exit pupil for telescopic systems used here. Paywalled standard; listed as a bibliographic reference for the terminology, not as free full text.
6. [6]Born, M. & Wolf, E. (1999). Principles of Optics, 7th (expanded) edition, §4.8 and §8.6, Cambridge University Press. Paraxial treatment of afocal systems and of the pupils of an optical instrument. Print / bibliographic reference.