Telescope Resolving Power Calculator
A telescope cannot show detail finer than diffraction allows. The Rayleigh criterion sets the theoretical limit: the smallest angle two stars can have and still be seen as separate equals 1.22 times the observing wavelength divided by the aperture diameter. A bigger aperture resolves finer detail, and shorter wavelengths help too. This calculator returns the resolving angle in radians, arcseconds, and degrees from the aperture and wavelength you enter. The wavelength is a user-editable input so you can match visual, hydrogen-alpha, or any other observing band.
Rayleigh criterion formula
theta (radians) = 1.22 * wavelength / aperture
wavelength and aperture in the same length unit
arcseconds = theta * 206,265
degrees = theta * 180 / pi
inches = aperture mm / 25.4
The factor 1.22 comes from the first dark ring of the circular-aperture diffraction (Airy) pattern. Smaller angles mean finer resolution, so larger apertures and shorter wavelengths resolve more detail.
Resolution notes
- This is the theoretical diffraction limit, not the real seeing-limited resolution.
- Ground-based seeing often limits resolution to about 1 arcsecond without adaptive optics.
- The eye is most sensitive near 550 nm, the default wavelength.
- Doubling the aperture halves the resolving angle.
- Use consistent length units for wavelength and aperture inside the formula.
Telescope resolution: frequently asked questions
What is a telescope's resolving power?
Resolving power is the smallest angular separation between two points that a telescope can show as separate. It is set by diffraction: a larger aperture resolves finer detail. The Rayleigh criterion gives the limiting angle as 1.22 times the wavelength divided by the aperture diameter.
What wavelength should I use?
For visual observing, green light near 550 nanometers is the standard reference because the eye is most sensitive there. Wavelength is a user-editable input, so you can use any value, for example 656 nm for hydrogen-alpha or shorter wavelengths for blue light, which give finer resolution.
How is the Rayleigh angle converted to arcseconds?
The Rayleigh criterion gives an angle in radians. Multiply by 206,265 to convert radians to arcseconds, the unit astronomers use for small angles on the sky. This calculator reports both radians and arcseconds.
Why does a bigger telescope resolve more detail?
Diffraction spreads light from a point source into a small disk whose size is inversely proportional to the aperture. A larger aperture produces a smaller diffraction disk, so two close stars stay separated rather than blurring together. This is why observatory telescopes have very large mirrors.
Does the atmosphere limit real resolution?
Yes. Ground-based telescopes are often limited by atmospheric seeing to about 1 arcsecond regardless of aperture, unless they use adaptive optics or are in space. The Rayleigh figure here is the theoretical diffraction limit, the best the optics could do in ideal conditions.
Official sources
- NASA Imagine the Universe: telescopes and diffraction.
- NASA Science: how telescopes work.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.