Diffraction Limit Calculator
No optic, however perfect, can resolve detail finer than the diffraction limit set by the wave nature of light. The Rayleigh criterion gives that limit for a circular aperture: the smallest resolvable angle equals 1.22 times the wavelength divided by the aperture diameter. This calculator takes an aperture in millimetres and a wavelength in nanometres, returns the resolvable angle in radians and arcseconds, and reports the Airy disk angular radius, so you can judge a telescope, camera lens or microscope objective.
Rayleigh criterion formula
theta (radians) = 1.22 * wavelength / aperture diameter
(convert wavelength nm to m: * 1e-9; aperture mm to m: * 1e-3)
theta (arcseconds) = theta (radians) * 206265
theta (arcminutes) = theta (arcseconds) / 60
theta (degrees) = theta (radians) * 180 / pi
The 1.22 factor comes from the first zero of the Airy diffraction pattern of a circular aperture. The resolvable angle is inversely proportional to aperture, so larger apertures resolve finer detail at the same wavelength.
Optical resolution context
- The Rayleigh criterion sets the fundamental, defect-free resolution limit of an aperture.
- The 1.22 factor applies to circular apertures; a slit uses 1.0.
- One radian equals 206,265 arcseconds, a standard small-angle conversion.
- Visible light spans about 380 to 750 nm; 550 nm is near the eye's peak sensitivity.
- Resolution improves with larger aperture and shorter wavelength.
Diffraction limit: frequently asked questions
What is the Rayleigh diffraction limit?
The Rayleigh criterion gives the smallest angle two point sources can be separated and still resolved by a circular aperture: theta = 1.22 * wavelength / aperture diameter, with theta in radians. It defines the fundamental resolution limit set by the wave nature of light, independent of any optical defect.
Why the factor 1.22?
For a circular aperture, the first dark ring of the Airy diffraction pattern falls at an angle whose sine is 1.22 times the wavelength divided by the diameter. The 1.22 comes from the first zero of the Bessel function that describes circular-aperture diffraction. A slit, by contrast, uses a factor of 1.0.
What units does this use?
Enter aperture diameter in millimetres and wavelength in nanometres. The calculator converts both to metres, computes the angle in radians, then also reports it in arcseconds (radians times 206,265) so you can compare with telescope specifications, which are usually quoted in arcseconds.
How does aperture affect resolution?
Resolution improves (the resolvable angle gets smaller) as aperture increases, because theta is inversely proportional to diameter. Doubling the aperture halves the smallest resolvable angle. This is why large telescopes resolve finer detail than small ones at the same wavelength.
What wavelength should I use for visible light?
Visible light spans roughly 380 to 750 nanometres. A common reference for green light, near the peak of human eye sensitivity, is about 550 nanometres. Enter the wavelength of interest; shorter wavelengths give finer resolution for the same aperture.
Official sources
- NASA: Hubble Optics and Angular Resolution.
- National Institute of Standards and Technology: SI Units (radian, metre).
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.