#1 Free Angular Resolution Calculator 2025

How to Use This Calculator

This calculator determines the angular resolution of an optical instrument (like a telescope or an eye) based on the Rayleigh Criterion. Angular resolution is the smallest angle between two point sources that can still be distinguished as separate.

• Enter the wavelength of light (λ) you are observing. Choose appropriate units (nm, µm, mm).
• Enter the diameter (D) of the instrument's aperture (e.g., telescope mirror, lens, or eye pupil). Choose appropriate units (mm, cm, m, inches).
• Click the "Calculate Angular Resolution" button.
• The results, including the resolution in radians, degrees, arcminutes, arcseconds, and a step-by-step solution, will be displayed below.

Theory: Angular Resolution & Rayleigh Criterion

Due to the wave nature of light, when it passes through an aperture (like a lens or opening), it diffracts (spreads out). This diffraction limits the ability of an optical instrument to distinguish between two closely spaced objects. The smallest angular separation at which two point objects can just be resolved is known as the angular resolution or the diffraction limit.

The Rayleigh Criterion provides a common estimate for this limit. It states that two images are just resolvable when the center of the diffraction pattern of one image is directly over the first minimum of the diffraction pattern of the other. For a circular aperture, this leads to the formula:

θ ≈ 1.22 × (λ / D)

• A smaller θ value means better (finer) angular resolution.
• To improve angular resolution (get a smaller θ):
  • Use a shorter wavelength (λ) of light.
  • Use a larger aperture diameter (D).
• This formula assumes a diffraction-limited system, where resolution is only constrained by diffraction and not by optical aberrations or atmospheric turbulence.

Formulas Used

• 1. Angular Resolution (θ in radians):

  θrad = 1.22 × (λ / D)

  • θrad = Angular resolution in radians
  • 1.22 = Constant derived from the Rayleigh criterion for circular apertures
  • λ (lambda) = Wavelength of light in meters (m)
  • D = Diameter of the aperture in meters (m)
• 2. Conversions:
  • θ_deg = θ_rad × (180 / π)
  • θ_arcmin = θ_deg × 60
  • θ_arcsec = θ_arcmin × 60

Calculate Angular Resolution

Calculation Results

• Radians: rad
• Degrees: °
• Arcminutes: '
• Arcseconds: "