page_title: Angular diameter
section_title: Formula
hierarchical_section_title: Angular diameter / Formula
caption_attribution_description: English: This diagram explains how the formula for calculating the Angular diameter is formulated.
context_page_description: The angular diameter, angular size, apparent diameter, or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is the angular aperture. The angular diameter can alternatively be thought of as the angle through which an eye or camera must rotate to look from one side of an apparent circle to the opposite side. Angular radius equals half of the angular diameter.
context_section_description: The angular diameter of a circle whose plane is perpendicular to the displacement vector between the point of view and the centre of said circle can be calculated using the formula
  in which  is the angular diameter, and  is the actual diameter of the object, and  is the distance to the object. When , we have , and the result obtained is in radians.
  For a spherical object whose actual diameter equals  and where  is the distance to the centre of the sphere, the angular diameter can be found by the formula
  The difference is due to the fact that the apparent edges of a sphere are its tangent points, which are closer to the observer than the centre of the sphere. For practical use, the distinction is only significant for spherical objects that are relatively close, since the small-angle approximation holds for :
   .
caption: Diagram for the formula of the angular diameter
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