Calculate true and apparent field of view for telescope-eyepiece combinations. Shows magnification, exit pupil, and limiting magnitude.
Give it a telescope aperture and focal length (or focal ratio) and an eyepiece focal length and apparent field, and it returns magnification, the true field of view on the sky, exit pupil, and a theoretical limiting magnitude. The figure printed on the eyepiece is the apparent field, the image size at your eye, not the sky: divide it by magnification, and a 100-degree eyepiece at 200x shows just 0.5 degrees, one full Moon. Most people are surprised how little sky high magnification actually allows.
A concrete input and expected output from the current implementation.
Input
Aperture 80 mm, focal length 400 mm (f/5). Eyepiece 25 mm, apparent field 50 deg.
Expected output
Magnification 16x. True field 3.1 deg. Exit pupil 5 mm. Limiting magnitude about 11.6 (with a 6 mm dark-adapted eye pupil and a 6.0 naked-eye limit).
Magnification is 400/25 = 16. The 50-degree apparent field is compressed onto the sky by that factor, giving 50/16 = 3.125 degrees. Exit pupil is 80/16 = 5 mm, matching eyepiece focal length divided by the f-ratio, 25/5. The limiting magnitude adds 5 x log10(80/6) = 5.6 to the naked-eye limit of 6.0.
Magnification is telescope focal length divided by eyepiece focal length, so a 400 mm scope with a 25 mm eyepiece magnifies 16x. True field is then the eyepiece apparent field divided by that magnification; apparent field is the eyepiece own spec, typically 40-100 degrees, while true field is what actually crosses the sky. Raising magnification shrinks the true field proportionally.
Exit pupil is aperture divided by magnification, the little disk of light leaving the eyepiece; it also equals eyepiece focal length divided by the telescope focal ratio. If it is wider than your dark-adapted pupil, part of the primary light misses your eye. Limiting magnitude adds 5 x log10(aperture divided by eye pupil) to the naked-eye limit near 6.0, assuming perfect optics and a dark sky.
The printed number is the apparent field, the angular size of the image at your eye, not the sky. The sky true field is that figure divided by magnification, so at 100x a 50-degree eyepiece shows 0.5 degrees, exactly one full Moon. Doubling the magnification halves the amount of sky you see; that trade-off is the whole game in eyepiece selection.
Rarely. The figure assumes perfect optics, a fully dark-adapted eye, transparent air, and no sky glow. Every glass-air surface costs a little light, and light pollution raises the sky background faster than the scope adds light. Expect to fall about a magnitude short in typical suburban skies, and treat the number as a way to compare scopes, not a promise.
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