Telescope Angular Resolution Calculator

Calculate a telescope's diffraction-limited angular resolution from its aperture and wavelength via the Rayleigh criterion θ = 1.22λ/D, compared against the empirical Dawes limit, in arcseconds, milliarcseconds, degrees, and radians — with a two-stars-resolving filmstrip and a resolution comparison scale.

Telescope angular resolution calculator

Light diffracts through any finite aperture, which alone limits how close together two point sources can be and still look distinct: θ = 1.22λ/D (Rayleigh criterion). This is an ideal, diffraction-only limit — real ground-based observations are very often limited far more by atmospheric seeing, optical quality, tracking, and detector sampling than by diffraction at all. See below for details.

Aperture diameter (D)

Wavelength (λ)

θ (Rayleigh) ≈ 1.384 ″

Dawes limit (empirical, visible light): ≈ 1.158 ″

Arcseconds1.384 ″

Milliarcseconds1384 mas

Arcminutes0.02307 ′

Degrees3.845 × 10⁻⁴ °

Radians6.71 × 10⁻⁶ rad

0.5× θ

not resolved

1× θ

just resolved

1.5× θ

resolved

2.5× θ

resolved

4× θ

resolved

Idealized overlapping-blob approximation of two point sources (not a true, ringed Airy pattern) at increasing separation, in multiples of this telescope's Rayleigh limit θ. Around 1× is the classic "just resolved" boundary.

Log scale — resolving power (smaller is better) spans more than four orders of magnitude from a single radio dish to a large visible-light telescope.

This is a theoretical ceiling, not a promise. Ground-based optical telescopes are routinely limited far more by atmospheric seeing (typically ~1″ at an average site, occasionally much worse) than by diffraction — a large amateur or even professional telescope's actual resolution can be worse than a much smaller instrument's diffraction limit on a bad night. Optical quality, mechanical tracking error, and how finely the detector samples the focal plane all set additional, independent limits.

Even a flawless telescope with a flawless mirror, pointed through a perfectly still atmosphere, can’t resolve two point sources arbitrarily close together. Light bends slightly as it passes through any finite opening — diffraction — and that alone sets a hard floor on resolving power that no amount of engineering below it can beat. That floor is what this calculator computes.

The Rayleigh criterion

\theta = 1.22\,\frac{\lambda}{D}

D is the telescope’s aperture diameter, λ the observing wavelength, and θ the smallest angular separation (in radians, here converted to arcseconds or whatever unit you prefer) at which two point sources are “just resolved” — precisely defined as the point where the first diffraction minimum of one source’s pattern lands exactly on the central peak of the other’s. A 100 mm telescope at 550 nm (green visible light): θ ≈ 1.38 arcseconds — the worked example this calculator opens with.

Bigger aperture means better (smaller) resolution; longer wavelength means worse resolution for the same aperture — which is part of why radio telescopes, working at wavelengths millions of times longer than visible light, need single dishes kilometers across (or interferometer arrays) just to match what a modest optical telescope does effortlessly.

The Dawes limit — an older, empirical alternative

\theta_{\rm Dawes} \approx \frac{116}{D(\text{mm})} \text{ arcsec} \approx \frac{4.56}{D(\text{inches})} \text{ arcsec}

William Dawes derived this in the 19th century from real observations of double stars, specifically in visible light — it isn’t a function of wavelength the way Rayleigh’s criterion is, and applying it outside visible-light point-source observations (radio, say) isn’t physically meaningful. It’s slightly more optimistic than Rayleigh (a smaller predicted limit for the same aperture), reflecting that a trained eye detecting some elongation in a double star’s image is an easier bar than the strict Rayleigh criterion.

This is a ceiling, not a promise

Both numbers above describe an idealized instrument limited by nothing but diffraction. Real observations, especially from the ground, are routinely limited far more by:

Atmospheric seeing — turbulent air blurs images to roughly 1 arcsecond at an average site, and often worse; this alone can swamp the diffraction limit of anything larger than a modest amateur telescope. It’s the entire reason adaptive optics and space telescopes exist.
Optical quality — a mirror or lens with real manufacturing imperfections won’t reach its theoretical diffraction limit at all.
Tracking and vibration — any wobble during an exposure blurs the image regardless of optics.
Detector sampling — a camera whose pixels are too large relative to θ can’t record detail the optics actually deliver (undersampling), while oversampling wastes light-gathering efficiency without adding real resolution.

A small, excellent instrument on a superb night can out-resolve a much larger one fighting bad seeing or poor optics. Diffraction sets the best case; everything else usually decides the real one.

Reading the visuals

The resolving filmstrip shows two idealized point sources at several multiples of this telescope’s Rayleigh limit apart — merged into one blob well inside it, distinctly separate well outside it, and passing through the classic “just resolved” boundary right around 1×.
The comparison scale places this telescope’s resolution on a log scale next to the human eye, a small amateur scope, Hubble, Keck, and a single radio dish — a sense of just how many orders of magnitude resolving power spans across real instruments.