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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.

Sources

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.

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Comments (1)

  • Editorial team

    Amateur observers often quote Dawes' limit instead, about 116 divided by the aperture in millimetres, in arcseconds. For 100 mm that is 1.16 arcseconds against the 1.38 this tool gives for green light, so the Rayleigh value is the more conservative of the two. Both are ideal-optics limits. What aperture are you working with, and is the target a close double star?

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