Telescope Angular Resolution Calculator

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

$D$ is the telescope’s aperture diameter, $\lambda$ the observing wavelength, and $\theta$ 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): $\theta$ ≈ 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

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 $\theta$ 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.

This diffraction limit is also the physical ceiling behind the “don’t exceed 2× your aperture in millimetres” rule amateur guides repeat: past that magnification you’re enlarging blur, not resolving anything this calculator’s $\theta$ doesn’t already say is impossible. The Telescope Magnification & Eyepiece Calculator applies that practical version directly to a telescope-and-eyepiece combo, with a verdict on whether a given setup is empty magnification.

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.