Angular Diameter Calculator
Angular diameter is how big an object appears in the sky, set by its true size and its distance. This calculator uses the exact trigonometric relation, so it stays accurate whether the object is a distant galaxy or a nearby crater rim, and reports the result in degrees, arcminutes and arcseconds at once. Enter the object's physical diameter and its distance in the same length unit (the ratio is what matters) to get its apparent size.
Angular diameter formula
angle (radians) = 2 * arctan(diameter / (2 * distance))
degrees = angle * 180 / pi
arcminutes = degrees * 60
arcseconds = degrees * 3,600
Diameter and distance must be in the same unit; only their ratio affects the angle. The exact arctangent form avoids the small error the simple linear approximation introduces for nearby objects.
Worked example
The Moon has a diameter of about 3,474.8 km at a mean distance of 384,400 km. The angle is 2 * arctan(3,474.8 / (2 * 384,400)) = 0.0090 radians, which is 0.52 degrees, 31.08 arcminutes, or 1,864.53 arcseconds: about half a degree, matching observation.
Angular diameter: frequently asked questions
What is angular diameter?
Angular diameter (also called apparent diameter) is the angle an object subtends as seen by an observer. It depends on both the object's true size and its distance: a small nearby object and a large distant one can look the same size. It is measured in degrees, arcminutes (1/60 of a degree) and arcseconds (1/3600 of a degree).
What is the formula for angular diameter?
The exact formula is angular diameter = 2 * arctan(physical diameter / (2 * distance)). For distant objects where the size is small compared to the distance, the small-angle approximation angular diameter (radians) = physical diameter / distance is accurate. This calculator uses the exact arctangent form so it stays correct even for nearby objects.
What is the angular diameter of the Moon and Sun?
Both the Moon and the Sun have an angular diameter of roughly half a degree (about 30 arcminutes) as seen from Earth, which is why total solar eclipses are possible: the Moon can almost exactly cover the Sun. The exact value varies slightly because the orbits are elliptical, so the distances change.
Sources
- Angular diameter is a direct trigonometric identity. Moon and lunar distance reference values: NASA Moon Fact Sheet.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.