Telescope Magnification, FOV & Resolution Calculator

Understanding the telescope calculator — concept and principle

This calculator turns four numbers printed on a telescope and eyepiece into what you will actually see: magnification, true field, focal ratio, exit pupil, resolving power, faintest visible star and the highest useful magnification. Use it to choose eyepieces or compare telescopes.

Swap eyepieces to change power; aperture alone sets resolution and the 400× ceiling.

How it is calculated

Magnification = telescope focal length F ÷ eyepiece focal length f.
True field ≈ eyepiece apparent field ÷ magnification (degrees).
Focal ratio = F ÷ aperture D.
Exit pupil = D ÷ magnification (mm).
Dawes limit = 116 ÷ D(mm) arcseconds.
Limiting magnitude ≈ 2.7 + 5 log₁₀ D(mm), one common rule of thumb.
Maximum useful magnification ≈ 2 × D(mm).

The principle

The objective forms an image at its focal plane and the eyepiece magnifies it, so angles grow by F/f; dividing the eyepiece's fixed apparent angle by that factor gives the sky you see. Collected light leaves the eyepiece as a beam the width of the exit pupil; if it is wider than your pupil (about 7 mm when young and dark-adapted, less with age) light is wasted. Resolution is limited by diffraction: a larger aperture makes smaller star images, and William Dawes found empirically that equal double stars separated by 116/D arcseconds can just be split. Light grasp scales with aperture area, and each factor of 100 in brightness is 5 magnitudes, hence the 5 log D term.

Worked example

Inputs: D = 200 mm, F = 1200 mm, f = 25 mm, apparent field 52°.
Magnification = 1200 ÷ 25 = 48×.
True field = 52 ÷ 48 = 1.083333333° (65′), two full Moons wide.
Focal ratio = 1200 ÷ 200 = f/6.
Exit pupil = 200 ÷ 48 = 4.166666667 mm.
Dawes limit = 116 ÷ 200 = 0.58″.
Limiting magnitude = 2.7 + 5 × log₁₀ 200 = 2.7 + 11.505 = 14.20514998.
Maximum useful magnification = 2 × 200 = 400×.

Each point is the calculator re-run with only “Eyepiece focal length (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Eyepiece focal length (mm)	Magnification
6.25	192
12.5	96
18.8	64
25	48
31.2	38.4
37.5	32
50	24

How to read the result

Exit pupils of 4–7 mm suit wide views of nebulae and galaxies, 1–2 mm suit planets and the Moon, and below about 0.5 mm the image becomes dim and blurry. The theoretical maximum of 400× is rarely usable, because atmospheric turbulence (seeing) usually limits sharp views to far less.

Common mistakes

Judging a telescope by its magnification; aperture determines brightness and detail.
Using a Barlow lens without multiplying the telescope focal length by its factor.
Treating the limiting magnitude as guaranteed; light pollution can cut it by several magnitudes.

Keep in mind: True field from apparent field ÷ magnification is an approximation; the eyepiece field stop gives the exact value. Never point a telescope at the Sun without a certified solar filter over the front.

Frequently asked questions

What is the lowest useful magnification?

About D ÷ 7 (here roughly 29×), which makes the exit pupil equal to a 7 mm eye pupil. Lower power wastes light.

Is the Rayleigh criterion the same as the Dawes limit?

No. The Rayleigh criterion, 1.22 λ/D, is about 138/D(mm) arcseconds for green light, a stricter separation than Dawes' empirical 116/D.

Sources: W. R. Dawes, Catalogue of micrometrical measurements of double stars, Memoirs of the Royal Astronomical Society 35 (1867) · E. Hecht, Optics, 5th ed., Pearson, 2017 (telescopes and diffraction)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

Your numbers