How fine a detail can my telescope show, and how faint a star?
A telescope’s aperture sets two limits that no eyepiece can change: how close two stars can be and still look like two, and how faint a star can be and still be seen. This telescope resolution calculator gives the Dawes limit and the Rayleigh criterion in arcseconds, the light grasp compared with your eye, and an approximate limiting magnitude.
Everything is calculated in your browser from the aperture alone, with the formulas shown so you can check the numbers.
How to use the Telescope Resolution & Limiting Magnitude Calculator
- Enter the aperture, the diameter of the lens or mirror, in millimetres.
- Leave the wavelength at 550 nm (green) unless you are working in another colour.
- Adjust the naked-eye limit and pupil if you want formula B tuned to your sky and eyes.
- Read the resolution, light grasp and limiting magnitudes, or find your aperture in the table.
Telescope Resolution & Limiting Magnitude Calculator features
Two resolution limits
Dawes (empirical, for equal double stars) and Rayleigh (diffraction theory), both in arcseconds.
Wavelength input
The Rayleigh limit scales with colour; 550 nm gives 138.4 ÷ D.
Light grasp
How many times more light than a 7 mm pupil the aperture collects, and the gain in magnitudes.
Two limiting-magnitude formulas
Shown side by side, each labelled as approximate.
Formulas and a worked example
Dawes limit = 116 ÷ D arcseconds, with D in millimetres (4.56 ÷ D for inches). Rayleigh = 1.22 λ ÷ D radians, which at 550 nm is 138.4 ÷ D arcseconds, usually rounded to 138. Light grasp = (D ÷ pupil)².
Example: a 102 mm telescope resolves 116 ÷ 102 = 1.14″ by Dawes and 138.4 ÷ 102 = 1.36″ by Rayleigh. Its light grasp over a 7 mm pupil is (102 ÷ 7)² ≈ 212 times, about 5.8 magnitudes.
Which limiting magnitude formula?
Published limiting-magnitude formulas differ because they make different assumptions. Formula A, 2.7 + 5 log₁₀ D (D in mm, equal to 7.7 + 5 log₁₀ D in cm), depends on aperture only and is the one quoted by many hobby calculators. Formula B, naked-eye limit + 5 log₁₀ (D ÷ pupil), starts from your own sky and eye, so it is lower under average conditions. Neither includes light lost in the optics, magnification, sky glow or the observer, so treat both as approximate; your sky usually matters more than the telescope.
Limits
- Dawes assumes two equally bright, moderately bright stars; unequal pairs are harder.
- Atmospheric seeing often limits ground-based views to 1–2″, whatever the aperture.
- Central obstructions (as in reflectors and catadioptrics) move light from the core of a star into its rings, slightly lowering contrast on close pairs.
- Use the magnification calculator to pick an eyepiece that shows the detail and the exit pupil calculator to check brightness.
Telescope Resolution & Limiting Magnitude Calculator FAQ
What is the Dawes limit?
An empirical resolution limit found by W. R. Dawes: 116 ÷ aperture in mm arcseconds for two equally bright stars of about 6th magnitude.
What is the difference between Dawes and Rayleigh?
Rayleigh comes from diffraction theory and is slightly wider (138 ÷ D). Dawes is based on observation and is a little tighter (116 ÷ D).
How do I calculate the limiting magnitude of a telescope?
A common approximation is 2.7 + 5 × log₁₀ of the aperture in mm. Another adds 5 × log₁₀ (aperture ÷ pupil) to your naked-eye limit. Both are approximate.
Does a bigger telescope always see more detail?
Only if the air is steady and the optics are good; seeing usually caps the detail at about 1–2 arcseconds.
Can I use this for binoculars or a camera lens?
Yes, for the diffraction limit of any circular aperture. Real binoculars and lenses are limited more by their optics and by hand shake than by diffraction.
Why does the wavelength matter?
Diffraction blur grows with wavelength, so red light resolves less finely than blue through the same aperture.