Magnification is simply the telescope focal length divided by the eyepiece focal length, but the useful numbers around it matter more: the exit pupil tells you whether the view will be bright or dim, the true field tells you how much sky fits in the eyepiece, and the classic per-millimetre limits tell you when more power stops showing more detail. This calculator works all of them out as you type. Enter either the focal length or the focal ratio; the other is filled in for you and labelled as derived.

Calculator

The calculator needs JavaScript. The formulas and guidance below still work without it: magnification is focal length divided by eyepiece focal length, and exit pupil is aperture divided by magnification.

How the numbers are calculated

All results come from standard geometric optics, as given in Sidgwick's Amateur Astronomer's Handbook and on the Tele Vue telescope formulas page. Magnification is the telescope focal length (multiplied by any Barlow or reducer factor) divided by the eyepiece focal length. The focal ratio is focal length divided by aperture. The exit pupil, the diameter of the light beam leaving the eyepiece, is aperture divided by magnification, which is the same as eyepiece focal length divided by the effective focal ratio. A Barlow multiplies the effective focal length and focal ratio by its factor; a focal reducer does the same with a factor below 1.

True field of view is estimated with the common approximation: apparent field of view divided by magnification. Because eyepiece distortion inflates the quoted apparent field, this approximation is typically good to a few percent for 50 degree eyepieces and can be off by 5 to 10 percent or more for very wide 80 to 100 degree designs (telescope-optics.net discusses why). When you need the exact figure, use the field stop method instead: true field in degrees equals 57.3 times the eyepiece field stop diameter divided by the telescope focal length.

Useful magnification limits, honestly

The lowest useful magnification here is aperture in millimetres divided by 7, the power at which the exit pupil matches a typical 7 mm fully dark-adapted young eye pupil. Below it, the exit pupil is wider than your eye's pupil and some of the light the telescope collected simply misses your eye; in an obstructed reflector the secondary mirror's shadow can also become visible. Many adapted eyes, especially past middle age, open only to 5 or 6 mm, so treat 7 mm as a generous upper bound rather than a target.

The highest useful magnification shown is the traditional rule of thumb of 2x per millimetre of aperture (50x per inch). It is a rule of thumb, not physics: it marks the point where the exit pupil shrinks to about 0.5 mm and the image becomes dim, floaters intrude, and no further detail appears. In practice the atmosphere decides. On most nights seeing limits any telescope, whatever its aperture, to roughly 250 to 350x, while small refractors on the Moon and double stars can occasionally profit from more than the rule suggests. Suiter's Star Testing Astronomical Telescopes and Sidgwick both treat these limits as guidance shaped by conditions, and this tool labels them the same way.

Accuracy and limits

The arithmetic is exact for the numbers you enter, and everything is computed in your browser as you type; nothing you enter leaves this page. Real-world values differ slightly: manufacturers round focal lengths, a Barlow's true factor changes with its spacing from the eyepiece, and quoted apparent fields are often optimistic. Magnification is shown to one decimal place below 100x and to the nearest whole number above; exit pupils are shown to 0.01 mm; the derived focal length or focal ratio field is rounded for display, but results always use the exact values you entered. Inputs are accepted for apertures of 30 to 1000 mm, focal lengths of 100 to 10000 mm, eyepieces of 2 to 60 mm, apparent fields of 30 to 120 degrees, and Barlow or reducer factors of 0.3 to 5.

Sources

• J. B. Sidgwick, Amateur Astronomer's Handbook (Dover reprint), sections on magnification and exit pupil.
• H. R. Suiter, Star Testing Astronomical Telescopes, on practical magnification limits.
• Tele Vue: telescope formulas and magnification myths, including the field stop method for true field.
• telescope-optics.net: eyepiece functions, on exit pupil and why apparent field over magnification is only an approximation.
• Sky & Telescope: choosing your telescope's magnification, on per-object magnification ranges and seeing limits.