How this calculator works
An isolated point source forms a diffraction pattern rather than an infinitely small dot. The Rayleigh criterion places one central maximum on the first minimum of the other. This small-angle model assumes a clear circular aperture, monochromatic light and ideal optics. Atmospheric seeing, central obstructions and aberrations can reduce practical resolution.
Formula
θ = 1.22 λ/D in radians; D = 1.22 λ/θ. One radian is 206264.806247 arcseconds.
Worked example
At 500 nm, a 100 mm aperture has a Rayleigh limit of 0.0000061 rad, about 1.258 arcseconds. Halving the diameter doubles that angle.
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Frequently asked questions
Is a smaller angle better?
Yes. It means two sources can be closer together on the sky while remaining distinguishable.
Does magnification improve this limit?
Magnification enlarges the image but does not recover detail lost to diffraction.
Which aperture size should I enter?
Use the clear entrance aperture diameter, rather than the eyepiece diameter or focal length.