Telescope Resolution Calculator
What a telescope can resolve and how faint it can see from its aperture — the Rayleigh and Dawes limits, limiting magnitude, light grasp, and the useful range of magnification with a given eyepiece.
Aperture decides everything.
How the telescope resolution calculator works
Aperture decides everything. Resolution is set by diffraction — 1.22 times wavelength over diameter — so a 200 mm telescope splits stars 0.7 arcseconds apart at best; the atmosphere usually limits it to one or two. Light grasp goes with the area, so the same 200 mm gathers 800 times what a 7 mm pupil does and reaches magnitude 14.
Magnification is the least important number: it comes from focal length over eyepiece, and anything beyond about twice the aperture in millimetres just enlarges the blur.
Formula: θ_Rayleigh = 1.22 λ / D; Dawes = 116 / D_mm arcsec; m_lim ≈ 2.5 + 5 log₁₀ D_mm
Worked examples
| Inputs | Rayleigh resolution (arcseconds) | Note |
|---|---|---|
| A 200 mm f/6 with a 10 mm eyepiece | 0.692 | 120×, 0.69″ |
| Binocular-sized | 2.7681 | 10×, magnitude 11 |
| Over-driven | 0.692 | 480× is past the limit |
FAQFrequently asked questions
What limits a telescope's resolution?
Diffraction at the aperture: 1.22 λ / D radians. Bigger aperture, finer detail — but the atmosphere blurs everything to about 1 to 2 arcseconds on most nights, so beyond 250 mm the gain is mostly light, not detail.
What is the Dawes limit?
An empirical rule for splitting equal double stars: 116 / D arcseconds with D in millimetres. It is a little tighter than Rayleigh because the eye can see a notch before the full separation.
What is limiting magnitude?
The faintest star the telescope shows visually under a dark sky. It grows by five magnitudes for every tenfold in aperture, so 200 mm reaches about 14.
What magnification should I use?
Between aperture-in-mm over seven and twice the aperture in mm. Below that the exit pupil is larger than your eye and light is wasted; above it the image is dim and empty.
What is the exit pupil?
The width of the beam leaving the eyepiece — aperture over magnification. Match it to your eye: 5 to 7 mm for deep sky, 1 to 2 mm for planets, below 0.5 mm only on the steadiest nights.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- CSIRO Space and Astronomy — Australia's national science agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).