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Angular Resolution Calculator

Work out angular resolution instantly with clear inputs, formula shown and shareable results.

About Angular Resolution Calculator

Diffraction sets the limit on resolution: the Rayleigh criterion gives theta = 1.22 lambda/D. A 200 mm aperture at 550 nm resolves 0.69 arcseconds, which is about 3.4 mm at a kilometre. Larger apertures resolve finer detail, which is the fundamental reason telescopes keep getting bigger.

Formulas

Rayleigh criterion

theta = 1.22 lambda / D

Linear detail

detail = theta x distance

Worked example

With the default values below, Angular Resolution Calculator returns Angular Resolution of 0.6920. Change any input above and every figure here is recalculated in your browser.

Inputs used

Wavelengthminimum 0 nm
550 nm
Aperture diameterminimum 0 m
0.2 m
Distance to the targetminimum 0 m
1,000 m

Results

Angular Resolution
0.6920 arcsec
Same Resolution In Radians
3.3550 × 10⁻⁶
Smallest Detail At That Distance
3.355 mm
Resolution In Degrees
1.9223 × 10⁻⁴

Step by step

  1. 1Values used
  2. 2Rayleigh criterion
  3. 3Linear detail
  4. 4Angular Resolution= 0.6920 arcsec
  5. 5Same Resolution In Radians= 0.0000
  6. 6Smallest Detail At That Distance= 3.355 mm
  7. 7Resolution In Degrees= 0.0002

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why the factor 1.22?

It is the first zero of the Airy diffraction pattern from a circular aperture. A slit gives 1.0 instead.

Does magnification improve resolution?

No. Beyond the diffraction limit extra magnification only enlarges a blur - the empty magnification that cheap telescopes advertise.

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Angular Resolution Calculator – Calculate Angular Resolution