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Angular Resolution Calculator

Find a telescope's angular resolution.

Result

1.3840″

How it is calculated

The Rayleigh criterion gives the smallest angle at which two point sources can still be told apart:

θ (rad) = 1.22 × λ / D and θ (arcseconds) = θ (rad) × 206265

λ is the wavelength in nanometres and D is the aperture diameter in millimetres; the tool converts both to metres internally. The answer is printed in arcseconds with four decimals. Both values must be above zero. This is the diffraction limit of a perfect circular aperture: real telescopes can be limited more by the atmosphere (seeing), optical quality or a central obstruction, so it is a best case.

Worked example

Green light at 550 nm through a 100 mm aperture.

  1. λ = 550 × 10-9 m and D = 0.1 m
  2. θ = 1.22 × 550e-9 / 0.1 = 6.71 × 10-6 rad
  3. In arcseconds: 6.71e-6 × 206265 ≈ 1.3840″

Two stars closer than about 1.38 arcseconds would blur together in the ideal case.

Try this example →

Common mistakes

  • Entering the wavelength in micrometres or metres: the field is nanometres, so visible light is roughly 400 to 700, not 0.55.
  • Entering the aperture in centimetres or inches: the field is millimetres, so a 4-inch telescope is about 102.
  • Expecting the focal length to matter: only the aperture diameter and the wavelength set the limit.
  • Treating the result as what you will see: atmospheric turbulence often blurs images worse than this limit for larger apertures.

About this calculator

This calculator applies the Rayleigh criterion, θ = 1.22·λ/D, to find the smallest angular separation a telescope (or any circular-aperture optical instrument) can resolve between two point sources, where λ is the light's wavelength and D is the aperture diameter — the 1.22 constant comes from the position of the first dark ring in the Airy diffraction pattern produced by a circular opening. A larger aperture or shorter wavelength gives finer resolution, which is why large observatory mirrors can separate close double stars that small telescopes blur together.

Amateur and professional astronomers evaluating what a telescope can realistically show, optical engineers designing camera lenses or microscopes, and physics students studying diffraction-limited optics use this. Enter the wavelength of light and the aperture diameter to get the angular resolution.

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