Angular Diameter Calculator
Calculate the angular size of any object in the sky — planets, galaxies, spacecraft — from its physical size and distance.
Angular diameter (also called angular size) is how large an object appears in the sky, measured as an angle rather than a physical distance.
Exact formula:
θ (radians) = 2 × arctan(d / 2D)
For small angles (when d « D), this simplifies to:
θ ≈ d / D (radians)
Converting to arcseconds:
θ (arcseconds) = 206265 × d / D
Where d is the physical diameter of the object and D is the distance to it. Both must be in the same units.
Reference objects in our sky:
- The Sun has an angular diameter of about 31–32 arcminutes
- The full Moon has an angular diameter of about 29–34 arcminutes (varies due to elliptical orbit)
- Jupiter at opposition: about 47 arcseconds
- Venus at closest approach: up to 64 arcseconds
Why it matters: Angular diameter determines how much detail a telescope can resolve. Even the largest stars appear as points of light through most telescopes — their angular diameter is smaller than the telescope’s resolution limit. The Sun and Moon appear nearly the same angular size, which is why total solar eclipses occur.
1 degree = 60 arcminutes = 3600 arcseconds