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Telescope Resolving Power Calculator

Enter your telescope's aperture in millimeters.

How it is calculated

You enter the diameter of the main lens or mirror, D, in millimetres. The tool returns two angular limits in arcseconds: Dawes = 116 ÷ D and Rayleigh = 138 ÷ D. Both fall as the aperture grows, so doubling the diameter halves the smallest separation you can split. The Dawes figure is an empirical rule from visual observation of equally bright double stars. The Rayleigh figure comes from the diffraction formula 1.22·λ ÷ D; the constant 138 corresponds to green light of about 550 nm, so no wavelength input is needed. Results are shown to three decimals. A zero or negative aperture gives no result. The numbers describe an ideal telescope under steady air; real seeing, optical quality, and the observer's eye usually make the practical limit worse.

Worked example

An 8-inch reflector has a 200 mm mirror. Dawes limit: 116 ÷ 200 = 0.58 arcseconds, shown as 0.580. Rayleigh limit: 138 ÷ 200 = 0.69 arcseconds, shown as 0.690. The result panel reads 0.580 arcsec for Dawes and 0.690 arcsec for Rayleigh. A double star with a separation near 0.6 arcseconds is therefore at the edge of what this aperture can split, while a pair 2 arcseconds apart is comfortably resolved on a steady night.

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Common mistakes

  • Typing the aperture in inches. The field expects millimetres, so an 8-inch telescope is about 203 mm; entering 8 gives 14.5 arcseconds.
  • Using the focal length instead of the aperture. Resolution depends on the diameter of the lens or mirror, not on how long the tube is.
  • Entering the diameter of the eyepiece or the finder. Only the main objective counts.
  • Expecting the calculated limit on every night. Atmospheric turbulence (seeing) often blurs the view to one or two arcseconds, which is worse than the limit for a mid-size telescope.
  • Mixing up the two limits. The Rayleigh number is always about 19 percent larger than the Dawes number, so quoting the wrong one changes the claim about which close pairs can be split.

About this calculator

A telescope's resolving power is the smallest angular separation at which it can still distinguish two close objects, such as a tight double star. The Rayleigh criterion (θ = 1.22·λ/D) gives the diffraction-limited theoretical minimum, while the empirical Dawes limit (116/D, with D in mm, giving arcseconds) is a slightly tighter rule of thumb derived from real observations of equal-brightness double stars.

Both scale inversely with aperture D — bigger apertures resolve finer detail. Amateur and professional astronomers use this calculator to compare telescopes and predict what detail — lunar craters, planetary cloud bands, close binary star pairs — a given aperture can actually reveal before buying or setting up equipment.

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Comments (1)

  • Editorial team

    These are ideal optical limits, and the atmosphere usually sets the real limit first. A 100 mm aperture gives a Dawes limit of 1.160 arcsec and a Rayleigh limit of 1.380 arcsec, while 200 mm halves both to 0.580 and 0.690. On a night of poor seeing a bigger mirror will not split closer pairs. What is the aperture of your scope, and which double star have you tried to split?

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