Calculate magnification, true field of view, and exit pupil for telescope-eyepiece combinations.
Enter a telescope's aperture and focal length, then an eyepiece's focal length and apparent field, and this tool returns the three numbers that shape every view: magnification, true field of view, and exit pupil. All three are the same two ratios rearranged, so changing one eyepiece moves all of them at once. The thing most beginners misread: a 2 mm exit pupil is not a defect - it is where planetary views are typically sharpest, while exit pupils wider than your dark-adapted eye just waste aperture.
A concrete input and expected output from the current implementation.
Input
Aperture 200 mm, telescope focal length 1000 mm, eyepiece 10 mm with a 50-degree apparent field
Expected output
Magnification 100x; true field of view 0.5 degrees (30 arcminutes); exit pupil 2.0 mm
1000 mm divided by 10 mm gives 100x; the 50-degree apparent field divided by 100x gives 0.5 degrees true field; and 200 mm of aperture divided by 100x gives a 2.0 mm exit pupil, which also matches eyepiece focal length divided by the f/5 ratio.
Magnification is the telescope's focal length divided by the eyepiece's focal length. Exit pupil is the aperture divided by that magnification - equivalently, eyepiece focal length divided by the telescope's f/ratio - and it is the diameter of the light beam your eye receives. True field of view is the eyepiece's apparent field divided by magnification. One eyepiece change moves all three together.
Two useful limits come from the exit pupil. Wider than your fully dilated pupil (about 7 mm, less with age) means some aperture is wasted: the image is no brighter, just larger. Narrower than about 0.5 mm means magnification exceeds what the optics and atmosphere can deliver - beyond roughly 2x per millimetre of aperture, image size grows but resolved detail does not.
About 2x per millimetre of aperture - a 200 mm scope tops out near 400x - and often less, because atmospheric seeing plus the telescope's collimation and optical quality set the real ceiling on any given night. Below that limit, more magnification enlarges the image; beyond it, the image gets larger but no sharper.
No. It means the eyepiece is longer than the telescope's minimum useful focal length, so part of the light cone is wider than your dark-adapted pupil and that aperture is wasted - the view is not dimmer, just not using the whole mirror or lens. Switch to a shorter eyepiece until the exit pupil sits between roughly 0.5 and 7 mm.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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