About this tool
The Angular Size Calculator is a free, in-browser astronomy tool that relates an object's true physical size, its distance, and the apparent angle it subtends in the sky. It uses the exact relation θ = 2·arctan(size / (2·distance)); for the small angles common in astronomy this matches the handy approximation θ(arcsec) ≈ 206,265 × size / distance. Leave any one of the three quantities blank and the calculator solves for it.
All of the trigonometry runs locally in your browser, so the values you type are never uploaded or stored. The physical size and distance must be entered in the same length unit — metres, kilometres, light-years, whatever you like — because only their ratio matters; the apparent angle can be entered or read out in degrees, arcminutes, or arcseconds.
The angular result is always reported in all three angular units at once (1° = 60′ = 3,600″), which makes it easy to check, for example, that the Moon and the Sun both subtend roughly half a degree from Earth, or to work out how large a planet or galaxy appears through a telescope. The small-angle form is accurate to better than 1% for angles under about 10°.