Telescope Focal Ratio Calculator

Background.

A 200 mm mirror with a focal length of 1,200 mm is an f/6 telescope: the focal ratio is focal length divided by aperture. Astrophotographers call a low focal ratio fast, and for nebulae, galaxies and the sky background that holds, because the same light is spread over a smaller image and each square millimetre of sensor fills up sooner. Halve the focal ratio and an extended target needs a quarter of the exposure.

Stars do not follow that rule. A star is a point, and the light it delivers depends on the area of the aperture alone; a lower focal ratio only squeezes the same photons onto fewer pixels. So a focal reducer that speeds up a nebula does nothing for the faintest star you can record, and the aperture is reported beside every result to keep that in view.

What a reducer or Barlow does change is the image scale, the number of arcseconds of sky that land on each camera pixel, and that decides whether stars are sampled finely enough to stay round and sharp. Enter the telescope, any reducer or Barlow, your camera's pixel size and your usual seeing, and you get the scale, the size of the diffraction disc, how many pixels span the star image the atmosphere actually delivers, and whether the camera is undersampled, well matched or oversampled. You can also work backwards to the focal length or aperture that gives a target focal ratio.

What is telescope focal ratio calculator?

Focal ratio, or f-number, is the focal length of a telescope's objective lens or primary mirror divided by its clear aperture, written f/6 for a ratio of 6. It is dimensionless, so a 1,200 mm focal length on a 200 mm aperture is f/6 in any unit. The effective focal ratio is the same quantity after a focal reducer (a factor below 1, commonly 0.63 or 0.8) or a Barlow lens or extender (a factor above 1) has changed the effective focal length; the aperture is untouched by either. Image scale turns the effective focal length into arcseconds of sky per millimetre of focal plane, and into arcseconds per pixel once the camera's pixel pitch is known.

How to use this calculator.

1. 01Under "Solve for", choose focal ratio to analyse a telescope you have, or focal length or aperture to find the size that reaches a target ratio, such as the focal length a 150 mm mirror needs to be f/8.
2. 02Enter the native focal length and clear aperture in millimetres as the maker lists them, before any accessory is added.
3. 03Set the reducer or Barlow factor: 1 for none, 0.63 or 0.8 for common reducers, 2 for a 2× Barlow. The real factor shifts with the spacing behind a reducer, so a measured value beats the nominal one.
4. 04Enter the camera's pixel size from its specification sheet (3.76 µm for the IMX571 and IMX533 sensors, roughly 3.7–6 µm for DSLRs, 6–9 µm for older CCDs) and your typical seeing as a star's full width at half maximum in arcseconds; 2″ is an ordinary night.
5. 05Leave the wavelength at 550 nm for broadband imaging or set your filter's wavelength for narrowband; it affects only the Airy disc. Then read the image scale and the sampling verdict together.

The formula.

The focal ratio is N = f ÷ D, focal length over aperture. A reducer or Barlow factor k makes the effective focal length f × k and the effective focal ratio N × k. Solving backwards, f = D × N for a target ratio, or D = f ÷ N.

Image scale comes from small-angle geometry: an object θ radians across forms an image f·θ long, so one millimetre of focal plane covers 1/f radians, which is 206,264.806 ÷ f arcseconds, the constant being 648,000/π, the number of arcseconds in a radian. Multiply by the pixel pitch in millimetres for arcseconds per pixel; with pitch in micrometres this reduces to the familiar shortcut 206.265 × pixel ÷ focal length.

The Airy disc, the diffraction image of a star measured to its first dark ring, is 2.44 × λ × N_eff across, twice Rayleigh's 1.22 coefficient. It assumes perfect optics and an unobstructed circular aperture; the secondary mirror of a reflector moves some light from the core into the rings. Pixels across the seeing disc are the seeing divided by the image scale, and the verdict calls fewer than 2 undersampled, following Shannon's sampling theorem, and more than 3 oversampled, a working convention rather than a theorem.

For extended objects the brightness of the image falls as 1 ÷ N², so the change in photographic stops is 2 log₂(N_native ÷ N_eff): positive with a reducer, negative with a Barlow, and exactly −2 with a 2× Barlow.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Tele Vue Optics, Inc., 'Telescope Formulas'. Manufacturer engineering note, verified by retrieval to state verbatim: Focal Ratio (f/#) = 'Objective focal length / objective diameter'. Open access. Retrieved 2026-07-29.
2. [2]Shannon, C.E. (1949). 'Communication in the presence of noise.' Proceedings of the IRE 37(1):10–21 (reprinted in Proceedings of the IEEE 86(2):447–457, 1998). Source of the two-samples-per-resolution-element floor used as the undersampling threshold. The three-sample upper bound used on this page is a practical convention and is labelled as such, not attributed to Shannon. Peer-reviewed; the IEEE reprint is paywalled and its landing page returns no content to automated retrieval, so this is shipped as a bibliographic reference rather than a link that reads as dead.
3. [3]Born, M. & Wolf, E. (1999). Principles of Optics, 7th (expanded) edition, §8.5.2, Cambridge University Press. The Airy pattern and the 1.22 coefficient that doubles to the 2.44 used for the disc diameter. Print / bibliographic reference; the publisher's page refuses automated retrieval, so no URL is shipped.
4. [4]Rayleigh, Lord (J. W. Strutt) (1879). 'Investigations in optics, with special reference to the spectroscope.' Philosophical Magazine, Series 5, 8(49), 261–274. Origin of the 1.22 coefficient. Print / bibliographic reference.