Physics

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Angular Resolution Calculator.

Estimate diffraction-limited resolution with the Rayleigh criterion.

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Results update as you type.

resolutionRadians: 0.000007

resolutionRadians

0.000000
resolutionArcseconds: 1.384037

resolutionArcseconds

0.000000

Use Cases

Telescope Resolution Estimation

Determine the smallest angular detail a telescope can resolve based on its aperture and the wavelength of light observed.

Example: For a 0.1 m telescope observing at 500 nm, the angular resolution is about 6.1 × 10⁻⁶ radians.

Microscope Resolution Planning

Estimate the diffraction limit of a microscope objective to understand the minimum resolvable feature size.

Example: Using a 0.01 m aperture and 400 nm light, the resolution is approximately 4.88 × 10⁻⁵ radians.

Frequently Asked Questions

What is the Rayleigh criterion?
The Rayleigh criterion is a measure of the minimum angular separation at which two point sources of light can be distinguished. It states that resolution is limited by diffraction, with the angular resolution θ given by θ = 1.22 × (wavelength / aperture diameter).
How do I use the angular resolution calculator?
Enter the wavelength of light in meters and the aperture diameter in meters. The calculator will compute the angular resolution in radians using the Rayleigh criterion formula. Ensure both values are in meters for accurate results.
What units should I use for wavelength and aperture diameter?
Both wavelength and aperture diameter should be entered in meters. If you have values in other units (e.g., nanometers or millimeters), convert them to meters before entering them into the calculator.

Tips & Common Mistakes

Tips

  • Always convert wavelength and aperture diameter to meters before entering values to avoid errors.
  • Remember that the Rayleigh criterion assumes ideal conditions; real-world factors like aberrations can worsen resolution.
  • For visible light, typical wavelengths range from 400 to 700 nm (4e-7 to 7e-7 m).
  • Larger aperture diameters yield smaller angular resolutions, meaning better resolving power.

Common Mistakes to Avoid

  • Forgetting to convert units: entering wavelength in nanometers and aperture in meters will give incorrect results.
  • Using the formula incorrectly: the factor 1.22 is specific to circular apertures; do not omit it.
  • Assuming the result is in degrees: the calculator outputs radians; convert to degrees if needed (1 rad ≈ 57.3°).

Last updated: August 13, 2026