Telescope Angular Resolution Calculator
Calculate a telescope's angular resolution limit using the Rayleigh criterion and Dawes limit.
Find what you can resolve on the Moon, planets, and beyond.
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 ≈ 138.6 / 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.
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:
| Instrument | Aperture | Resolution |
|---|---|---|
| Human eye | ~7 mm | ~1 arcminute (60") |
| 60 mm refractor | 60 mm | 2.3" |
| 200 mm reflector | 200 mm | 0.69" |
| Hubble Space Telescope | 2,400 mm | 0.058" |
| Event Horizon Telescope | ~10,000 km baseline | 20 microarcseconds |
Why space matters: Earth’s atmosphere causes “seeing” — turbulence that blurs stellar images to typically 1–2 arcseconds. All ground-based telescopes are limited by seeing, not diffraction, unless adaptive optics is used. Only space telescopes and interferometers achieve their theoretical diffraction limit.
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