Telescope Focal Ratio & Image Scale Calculator

How it works

Focal ratio = focal length × Barlow/reducer ÷ aperture; image scale (″/px) = 206.265 × pixel size (µm) × binning ÷ focal length (mm); sampling = seeing FWHM ÷ image scale (aim for 2–3.5); FOV (°) = sensor size ÷ focal length × 57.3; exposure ∝ f-ratio²; Dawes limit = 116 ÷ aperture (mm) arc-seconds, Rayleigh = 138 ÷ aperture; Airy disk = 2.44 × λ × f-ratio; planetary f-ratio ≈ 3.6–5 × pixel size (µm); limiting magnitude ≈ 7.7 + 5 log₁₀(aperture in cm); magnification = focal length ÷ eyepiece

The focal ratio is focal length over aperture and it governs two different things. For extended objects — nebulae, galaxies, the sky background — the exposure needed for a given surface brightness scales with the square of the f-ratio, so f/4 gathers light on the sensor four times faster than f/8, which is why imagers prize fast scopes and reducers. For resolution what matters is image scale: how many arc-seconds each pixel covers, set by pixel size, binning and focal length. Stars blurred by the atmosphere to 2–3 arc-seconds should span about two to three and a half pixels — under-sampling loses detail, over-sampling spreads the light thin and forces longer exposures. Match the scale to your typical seeing, not to the diffraction limit, which in most backyards is far finer than the air allows; then the sensor size sets the field of view. Pick a camera preset or type your own pixel and sensor size, try 2×2 binning, and compare every common Barlow and reducer in the table. Planetary imaging is the exception: with very short exposures that freeze the seeing, the target is the diffraction limit, which for green light means a focal ratio of about 3.6 to 5 times the pixel size in microns. The page also gives the Dawes and Rayleigh limits, the Airy disk size, an approximate visual limiting magnitude and light grasp, and what a chosen eyepiece shows.

Worked example

A 200 mm f/5 Newtonian (1,000 mm) with 3.76 µm pixels: image scale 0.78″/px, so 2.5″ seeing spans 3.2 pixels — well sampled. An APS-C sensor (23.5 × 15.7 mm) covers 1.35° × 0.90°, and exposures run at the f/5 baseline; a 0.75× reducer would make it f/3.75 with 1.03″/px and 56% of the exposure time. Binned 2×2, the same camera gives 1.55″/px (1.6 px per star — under-sampled). For Jupiter with a 2.9 µm planetary camera, aim for about f/10.5–f/14.5, a 2×–3× Barlow on this scope. A 25 mm eyepiece gives 40× with a 1.3° true field and a 5 mm exit pupil.

Sources: Astronomy Tools — CCD suitability and image scale · Astronomy Tools — Dawes, Rayleigh and limiting magnitude

Frequently asked questions