HesapHanem

Telescope Magnification Calculator

Find the magnification and optics of your telescope and eyepiece.

How it is calculated

All three inputs are in millimetres: D the telescope's aperture, F its focal length and fe the eyepiece focal length. The tool computes Magnification = F / fe, Focal ratio = F / D (shown as f/number), Exit pupil = D / Magnification (mm) and Max useful magnification = 2 × D.

All inputs must be greater than zero. Magnification and the maximum are displayed as whole numbers, while the exit pupil is calculated from the unrounded magnification. The 2× per millimetre ceiling is a rule of thumb for the useful limit; atmospheric seeing and optical quality often set a lower practical limit. Barlow lenses or focal reducers change F and must be included by you.

Worked example

A telescope with a 200 mm aperture and 1200 mm focal length is used with a 25 mm eyepiece. Magnification = 1200 / 25 = 48×. Focal ratio = 1200 / 200 = f/6.00. Exit pupil = 200 / 48 ≈ 4.17 mm. Maximum useful magnification = 2 × 200 = 400×. A shorter eyepiece such as 10 mm would give 120× and a 1.67 mm exit pupil.

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Common mistakes

  • Entering the aperture in inches or the eyepiece in millimetres but the telescope in metres. All three fields must use millimetres.
  • Confusing eyepiece focal length with its apparent field of view. Only the focal length (such as 25 mm) is used here.
  • Using the stated focal ratio as the focal length. f/6 is a ratio; the focal length in mm (1200 here) is what the tool needs.
  • Forgetting Barlow lenses or reducers. If you use a 2× Barlow, double F yourself or double the resulting magnification.
  • Treating the maximum as a target. Pushing to the limit on a night of poor seeing gives a dim, soft image; a lower power often shows more.

About this calculator

This calculator finds a telescope's key optical numbers from its aperture and focal length together with an eyepiece's focal length: magnification = telescope focal length / eyepiece focal length, focal ratio (f/#) = focal length / aperture, and exit pupil = aperture / magnification. It also estimates the practical maximum useful magnification, roughly twice the aperture in millimetres.

Amateur astronomers and telescope shop staff use it to figure out which eyepieces suit a given telescope, avoid over-magnifying past the instrument's resolving power (which just produces a dim, blurry image), and match the exit pupil to their eye's dark-adapted pupil size for the brightest view.

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Comments (1)

  • Editorial team

    Compare the exit pupil with your own eye. A 200 mm aperture, 1,000 mm focal length and 25 mm eyepiece gives 40 times magnification, f/5.00 and a 5.00 mm exit pupil. If you add a Barlow lens, multiply the focal length by its factor before entering it. The 2x-per-millimetre limit of 400 is a guideline, and seeing conditions often cap it lower. What are you observing?

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