solid angular measure

Solid angular measure is a quantitative expression for the flare angle at the apex of a cone. It is the three-dimensional analog of plane angular measure .

The unit of solid angular measure in the International System of Units ( SI ) is the steradian (symbolized sr). There are 4 pi (approximately 12.5664) steradians in a complete sphere. A solid angle of 1 sr as defined at a point is such that the area of the subtended portion of a sphere centered at the point is equal to the square of the radius of the sphere.

Sometimes the angular degree (symbolized deg or °) is used to quantify solid angular measure. This is often the case in astronomy, when the angular radius of an apparently disk-shaped celestial object is to be defined. The angular degree is equivalent to 1/360 of a full circle. The Sun and the Moon, as seen from the Earth, both subtend solid angles represented by cones whose apexes are slanted approximately 0.25 degree to the cone axis. Thus, the Sun and the Moon can be said to have solid angular radii of about 0.25 degree.

Compare plane angular measure . Also see steradian , angular degree , SI , and Table of Physical Units .