Angular Diameter Calculator
Calculate the angular diameter of any astronomical object from its physical size and distance.
Returns results in degrees, arcminutes, and arcseconds.
How Angular Diameter Is Calculated
Angular diameter is how large an object appears in the sky, measured in degrees, arcminutes, or arcseconds — regardless of its actual physical size or distance.
Angular Diameter Formula:
δ = 2 × arctan(d / 2D)
For small angles (where d « D), this simplifies to:
δ (radians) ≈ d / D
Converting to arcseconds: δ (arcseconds) = (d / D) × 206,265
Where:
- δ = angular diameter
- d = actual physical diameter of the object
- D = distance from observer to object
Worked Example — The Moon:
- Diameter: 3,474 km
- Average distance: 384,400 km
- δ = (3,474 / 384,400) × 206,265 = 0.009036 × 206,265 = 1,863 arcseconds = 31.05 arcminutes ≈ 0.518°
The Sun has almost exactly the same angular diameter (~0.53°) — which is why solar eclipses are so spectacular.
Reference Angular Sizes:
- Moon: ~31 arcmin
- Sun: ~32 arcmin
- Jupiter (opposition): ~50 arcsec
- Venus (max): ~64 arcsec
- Alpha Centauri: ~0.007 arcsec (barely resolvable by Hubble)
- Human eye resolution limit: ~1 arcminute
Resolving Power:
Telescope resolving power (Rayleigh criterion): θ = 1.22 × λ / D where λ is wavelength and D is aperture diameter.