Angular Size Calculator
Find the apparent diameter of a spherical body from its diameter and centre distance.
Calculate locally
No account, API or uploaded inputs. All calculations run in this browser.
Worked example
A spherical body 100 km across at a centre distance of 100 km spans 60°. A Moon-like diameter of 3474.8 km at 384400 km spans approximately 0.518° (31.08 arcminutes).
Method and units
For a sphere, angular diameter θ = 2 asin(D/(2d)). D and d use kilometres; convert radians to degrees with 180/π. The observer must be outside the sphere: d > D/2. For small angles, θ in radians is approximately D/d.
What this result means
This model treats the target as a sphere. A flat object perpendicular to the line of sight uses 2 atan(D/(2d)), a different large-angle geometry. Irregular shape, perspective, atmospheric effects and changing lunar distance are omitted. The distance is supplied by you, not fetched live.