Solid angle a solid angle in steradians is the following ratio: where A is the spherical surface area and r is the radius of the considered sphere. Solid angles are often used in physics, in particular astrophysics. The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. The solid angle of a sphere measured from any point in its interior is 4 sr, and the solid angle subtended at the center of a cube by one
Solid angle of a planar triangle is equal to "", for the sum of the four internal solid angles of a tetrahedron as follows: where ranges over all six of the dihedral angles between any two planes that contain the tetrahedral faces OAB, OAC, OBC and ABC. A useful formula for calculating the solid angle subtended by the triangular surface ABC where formula_17 are the vector positions of the vertices A, B and C has been given by Oosterom and Strackee (although the result was known earlier by Euler and Lagrange): where denotes the scalar triple product of the three vectors; When