Telescope Resolution Calculator (Dawes & Rayleigh)

Background.

An arcsecond is about the width of a one-euro coin seen from five kilometres. Double-star observers chase pairs a fraction of that apart, and whether a telescope can show them as two points is decided almost entirely by the diameter of its main lens or mirror.

Light passing through a circular opening cannot focus to a true point. Diffraction spreads every star into a small bright disc ringed by fainter circles, the Airy pattern, and the disc shrinks as the aperture grows. Two stars closer together than about one disc radius merge into a single blob. Lord Rayleigh put a number on this in 1879: two equal points count as resolved when the peak of one sits on the first dark ring of the other, at an angle of 1.22 λ ⁄ D radians.

A rival figure comes from the telescope eyepiece rather than the equations. William Rutter Dawes, working through years of double-star measurements, found in 1867 that he could separate roughly equal pairs at 4.56 arcseconds divided by the aperture in inches. That is about 16 % tighter than Rayleigh, because a practised eye notices a notch or an elongation in a blended image before two clean peaks appear. The calculator gives both, and works each backwards to tell you the aperture a given pair would need.

Neither figure allows for the air. Turbulence blurs every star into a seeing disc that on an ordinary suburban night spans 2 to 4 arcseconds, and once the telescope's own limit is finer than that, extra aperture buys brightness, not sharpness. So the last number reported is the aperture at which your night's seeing overtakes the optics.

What is telescope resolution calculator?

Resolving power is the smallest angle between two point sources at which a telescope still shows them as separate, measured in arcseconds (1⁄3600 of a degree). It depends on aperture and wavelength only. Focal length and eyepieces change how large and comfortable the image is, never how much detail it contains, which is why pushing a small refractor to very high magnification produces a bigger blur rather than new detail. The Airy disc is the central bright spot of a star's diffraction pattern; its diameter out to the first dark ring is exactly twice the Rayleigh angle.

How to use this calculator.

1. 01Enter the clear aperture in millimetres, the diameter of the objective lens or primary mirror rather than the tube. An 8-inch mirror is 203 mm; many makers round to 200.
2. 02Enter the focal length. It changes nothing about resolution and is used only to work out the focal ratio and the physical size of the Airy disc on a sensor.
3. 03Leave the wavelength at 550 nm for visual observing, or type the centre wavelength of a filter you image through; red and near-infrared filters coarsen the Rayleigh limit in proportion.
4. 04Enter the separation of the double star you want to split, in arcseconds, as listed in a double-star catalogue or observing guide.
5. 05Enter the seeing you expect: about 2 arcseconds for an ordinary night, 1 or less for a steady one at a good site. Then read the verdict alongside the aperture at which seeing takes over.

The formula.

Rayleigh's limit is θ = 1.22 λ ⁄ D in radians, multiplied by 206,264.806 (648000 ⁄ π) to give arcseconds. The 1.22 comes from the first zero of the Bessel function that describes the Airy pattern, 3.8317 ⁄ π = 1.21967; using the published 1.22 makes the result 0.027 % larger, far less than the uncertainty in a nominal aperture. With 550 nm substituted, the whole expression collapses to the observer's shorthand 138.4 ⁄ D(mm).

Dawes' limit is 4.56″ ⁄ D(inches). Converting with the exact 25.4 mm inch gives 115.824 ⁄ D(mm); handbooks that print 116 are 0.15 % out. Dawes contains no wavelength, so filters cannot move it. Set the two expressions equal and the aperture cancels, leaving a wavelength of about 460 nm: Dawes' rule behaves like a Rayleigh criterion in blue light. Neither man stated that number; it falls out of the two coefficients.

The Airy disc's angular diameter is 2.44 λ ⁄ D, twice the Rayleigh angle, and its physical diameter in the focal plane is 2.44 λ N, where N is the focal ratio. That second form explains why imagers care about f-number rather than aperture when matching pixels to the optics. The required-aperture outputs invert each criterion for your target separation, and the seeing crossover is the aperture whose Rayleigh limit equals the seeing you entered.

All of this assumes a perfect, unobstructed circular aperture in still air. Central obstructions, imperfect mirrors, poor collimation and an unequal pair all make real performance worse, and the atmosphere usually dominates the lot.

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: Dawes Limit (Resolving Power) = '4.56 arc seconds / Objective diameter in inches', and Focal Ratio = 'Objective focal length / objective diameter'. This is the independent second authority used to check the Dawes coefficient. Open access. Retrieved 2026-07-29.
2. [2]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 resolution criterion implemented here. Print / bibliographic reference — no authoritative free full text is offered rather than linking a scan of uncertain provenance.
3. [3]Dawes, W. R. (1867). 'Catalogue of Micrometrical Measurements of Double Stars.' Monthly Notices of the Royal Astronomical Society 27. Origin of the empirical 4.56″ separating-power rule. Secondary sources cite this 1867 catalogue at both p. 158 and p. 217; both are recorded here rather than one chosen silently. Print / bibliographic reference; the ADS record is JavaScript-rendered and the article scan refuses automated retrieval, so no URL is shipped rather than one that reads as dead.
4. [4]Born, M. & Wolf, E. (1999). Principles of Optics, 7th (expanded) edition, §8.5.2 (the Airy pattern; first zero of 2J₁(v)/v at v = 3.8317) and §8.6.2 (resolving power of image-forming systems), Cambridge University Press. Source of the exact 1.2196699 coefficient that 1.22 rounds. Print / bibliographic reference; the publisher's page refuses automated retrieval, so no URL is shipped.
5. [5]National Institute of Standards and Technology, Special Publication 811 (2008 ed.), Appendix B.8 'Factors for Units Listed Alphabetically': inch (in) → metre, 2.54 E-02, printed in boldface, which the table's legend defines as exact. Used for the 4.56″/inch → 115.824″/mm conversion. Open access. Retrieved 2026-07-29.