Telescope Focal Ratio Calculator

The focal ratio, or f-number, is the focal length divided by the aperture, both in millimetres. A 1200 mm scope with a 150 mm aperture is f/8. A short f-ratio gives a wide, bright field for deep-sky views, while a long f-ratio suits high power on planets and the Moon.

The Dawes limit estimates the finest detail a telescope can split, in arcseconds, as 116 divided by the aperture in millimetres. A 150 mm aperture gives about 0.773333 arcseconds. It was derived for separating close double stars, so a larger aperture resolves finer detail.

A common rule of thumb is about 2x the aperture in millimetres, so a 150 mm scope tops out near 300x. Push past that and the image grows dim and fuzzy without revealing more real detail, because you run out of resolving power and light.

Divide the telescope focal length by the eyepiece focal length. A 1200 mm scope with a 10 mm eyepiece gives 120x, and swapping to a 25 mm eyepiece drops it to 48x. Leave the eyepiece field blank if you only want the scope's fixed figures.

Exit pupil is the width of the light beam leaving the eyepiece, found by dividing the aperture by the magnification. A 150 mm scope at 120x gives a 1.25 mm exit pupil. Keep it under about 7 mm, the size of a dark-adapted pupil, so no gathered light is wasted.

Visually, brightness depends mainly on exit pupil, not f-ratio, because the eyepiece sets the magnification. F-ratio matters most for photography, where a faster (smaller) f-number records a given exposure quicker. For visual observing, treat f-ratio as a guide to field width and ease of focus.

All three fields are in millimetres and accept decimals, so 2032 mm and 203 mm for an eight-inch SCT work fine. Focal length and aperture are required and must be positive; the eyepiece is optional. Very large or small results are shown in scientific notation.

The formulas are the standard textbook relations and are exact for the inputs you give. Real-world resolution also depends on seeing, optical quality and collimation, and the maximum useful magnification is a rule of thumb rather than a hard limit, so treat the figures as solid planning estimates.

Yes. Every calculation runs in your browser with no network calls. The values you type are never uploaded, logged or stored, so you can experiment freely with different scopes and eyepieces.