Dawes Limit Calculator
The Dawes limit is the classic empirical benchmark for how close a double star a telescope can split into two distinct points. William Rutter Dawes found that the limiting separation in arcseconds equals about 116 divided by the aperture in millimeters for two equally bright stars. A larger aperture splits tighter pairs. This calculator returns the Dawes limit from your aperture, given in either millimeters or inches, and also reports the aperture in the other unit and the theoretical resolving angle in radians. The aperture is your own equipment value, so the result is exact for your telescope.
Dawes limit formula
Dawes (arcsec) = 116 / aperture in mm
equivalently = 4.56 / aperture in inches
inches = aperture mm / 25.4
radians = arcseconds / 206,265
The constant 116 arcsecond-millimeters is empirical, found from observing equal-brightness double stars near sixth magnitude. Larger apertures give smaller (better) limits.
Dawes limit notes
- It applies to two equally bright stars of about sixth magnitude.
- The Dawes limit is slightly tighter than the diffraction-based Rayleigh limit.
- Unequal or fainter pairs are harder to split than the Dawes figure suggests.
- Atmospheric seeing often prevents reaching the limit in practice.
- Good collimation and cooled optics are needed to approach it.
Dawes limit: frequently asked questions
What is the Dawes limit?
The Dawes limit is an empirical measure of the closest pair of equally bright stars a telescope can split. It equals 116 arcseconds divided by the aperture in millimeters, or 4.56 arcseconds divided by the aperture in inches. A larger aperture splits tighter pairs.
How does the Dawes limit differ from the Rayleigh limit?
Both describe resolving power, but the Dawes limit is an empirical rule found by William Rutter Dawes from observing double stars, while the Rayleigh criterion is derived from diffraction theory. The Dawes limit is slightly tighter (smaller angle) than the Rayleigh limit for the same aperture.
Why is the constant 116 arcseconds?
Dawes determined empirically that the resolving angle in arcseconds equals about 116 divided by the aperture in millimeters for two equal sixth-magnitude stars. It is a measured constant, not derived from first principles, which is why it is stated as a fixed number for this specific test case.
Does the Dawes limit apply to unequal or faint stars?
Strictly it applies to two equally bright stars of about sixth magnitude. Pairs that are unequal in brightness or much fainter are harder to split, so the practical limit is often a bit worse than the Dawes figure. It is still a useful benchmark.
Do atmosphere and optics affect the real limit?
Yes. Atmospheric seeing, optical quality, collimation, and thermal effects can prevent a telescope from reaching its Dawes limit. The figure here is the theoretical aperture-limited best case under steady, excellent conditions.
Official sources
- NASA Imagine the Universe: telescope resolving power.
- U.S. Naval Observatory: double star astrometry.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.