# Angular diameter

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 (of a lens). 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 the angular diameter.

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 ${\displaystyle \delta }$ is the angular diameter, and ${\displaystyle d}$ and ${\displaystyle D}$ are the actual diameter of and the distance to the object. When ${\displaystyle D\gg d}$, we have ${\displaystyle \delta \approx d/D}$, and the result obtained is in radians.

For a spherical object whose actual diameter equals ${\displaystyle d_{\mathrm {act} },}$ and where ${\displaystyle D}$ 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 ${\displaystyle x\ll 1}$:

Estimates of angular diameter may be obtained by holding the hand at right angles to a fully extended arm, as shown in the figure.

## Related Topics

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag msub invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag math invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag semantics invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mrow invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mstyle invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mi invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mo invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag mn invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389

Warning: DOMDocument::loadHTML(): Tag annotation invalid in Entity, line: 1 in /home/ashver/webapps/infospaze/index.php on line 389