Telescope Angular Resolution Calculator

Angular resolution is the smallest angular separation a telescope can distinguish as two separate objects.

Rayleigh criterion:

θ = 1.22 × λ / D (radians)

In arcseconds:

θ = 251.6 × λ(μm) / D(mm)

That constant is just 1.22 × 206,265 ÷ 1,000: the 206,265 converts radians to arcseconds, and the 1,000 accounts for wavelength being in micrometres while aperture is in millimetres.

For visible light (λ = 0.55 μm):

θ ≈ 138.4 / D(mm) arcseconds

Why aperture is the only thing that matters here. Magnification does not improve resolution. That surprises people, because the eyepiece is the part you swap. But diffraction happens at the aperture, and once two stars are blurred into one disc no amount of magnification separates them; you just get a bigger blur. This is the whole reason serious observers talk about aperture and barely mention magnification. Doubling the aperture halves the resolvable angle, and there is no other lever.

In practice the atmosphere usually wins anyway. Typical seeing blurs everything to 1 to 2 arcseconds, which is the diffraction limit of a 70 to 140 mm telescope. A 300 mm scope has a theoretical limit of 0.46 arcseconds but on an average night will show you no more detail than a 130 mm one. Larger apertures still gather more light, so they show fainter objects, and on the rare nights of steady air they deliver what the formula promises.

Dawes limit (empirical, from visual observation):

θ = 115.8 / D(mm) arcseconds

Where D is the objective (primary mirror or lens) aperture in millimeters. You will often see this quoted as 116/D, which is the same number rounded. Dawes derived it in the 1860s as 4.56 divided by the aperture in inches, and 4.56 × 25.4 is where 115.8 comes from. It sits slightly below the Rayleigh figure because a practised observer can detect a notched, elongated blob before the two discs are cleanly separated.

Physical resolution on the Moon (384,400 km away):

size_min = θ × d (in same angular/linear relation)

1 arcsecond at Moon distance = ~1.86 km on the surface.

Comparison of instruments (Rayleigh, green light at 550 nm):

The eye is the odd row there, and it is worth saying why. Its 7 mm pupil gives a diffraction limit near 20 arcseconds, but nobody has ever resolved anything that fine by eye. The retina’s cone spacing, not the pupil, sets the real limit at roughly an arcminute, which is what the Snellen 20/20 line measures. The eye is the one instrument on this list that throws away most of what its aperture could deliver.

Why space matters: Earth’s atmosphere causes “seeing”, the turbulence that blurs stellar images to typically 1 to 2 arcseconds.
All ground-based telescopes are limited by seeing rather than diffraction, unless adaptive optics is used. Only space telescopes and interferometers reach their theoretical diffraction limit.