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Dawes' Limit Calculator

Find a telescope's resolving power.

Result

0.77″

How it is calculated

The tool computes R = 116 / D, where D is the diameter of the telescope's aperture (the objective lens or primary mirror) in millimetres and R is the smallest separation of two equally bright stars that can be split, in arcseconds (″). The result is rounded to two decimals.

The aperture must be in millimetres and greater than zero; with 0 or an empty field there is no result. Only the aperture matters: focal length, eyepiece and magnification do not enter the formula. The value is a theoretical limit for a steady sky and a good optical system, so real results depend on seeing and the observer.

Worked example

A 150 mm (6 inch) reflector has an aperture of 150 mm. Divide 116 by 150: 116 / 150 = 0.7733. Rounded to two decimals, the limit is 0.77″. A double star closer than about three quarters of an arcsecond will look like a single point in this telescope under ideal conditions.

Try this example →

Common mistakes

  • Entering the aperture in inches or centimetres; the constant 116 only fits millimetres, so a 6 inch scope must be typed as 150, not 6.
  • Using the focal length (for example 750 mm) instead of the aperture diameter.
  • Expecting a higher magnification to beat the limit; more magnification enlarges the blur but does not add resolution.
  • Assuming the limit applies to unequal pairs: Dawes' limit is for two stars of similar, moderate brightness, and a faint companion next to a bright star is much harder to split.
  • Forgetting that atmospheric seeing often limits the view to one arcsecond or worse, so the theoretical value is rarely reached from the ground.

About this calculator

This calculator finds a telescope's theoretical resolving power using Dawes' limit, 116/D arcseconds where D is the aperture diameter in millimetres (or 4.56/D with D in inches). Formulated by the astronomer William Rutter Dawes in 1867 from his own extensive observations of close double stars, it's an empirical companion to the diffraction-based Rayleigh criterion, giving the closest angular separation at which a telescope of a given aperture can still show two point sources of light — like a double star — as distinct rather than blurred together.

Amateur astronomers use it to judge how much detail a telescope can realistically resolve before buying one, double-star observers use it to check whether a given instrument can split a specific known pair, and telescope manufacturers reference it when specifying an instrument's performance. Enter the aperture diameter to get the theoretical resolving power in arcseconds.

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