A general method to compute solid angle is developed that is based on Ishlinskii’s theorem, which specifies the relationship between the attitude transformation of an axis that completely slews about a conical region and the solid angle of the enclosed region. After an axis slews about a conical region and returns to its initial orientation, it will have rotated by an angle precisely equal to the enclosed solid angle. The rotation is the magnitude of the Euler rotation vector of the attitude transformation produced by the slewing motion. Therefore, the solid angle can be computed by first computing the attitude transformation of an axis that slews about the solid angle region and then computing the solid angle from the attitude transformation. This general method to compute the solid angle involves approximating the solid angle region’s perimeter as seen from the source, with a discrete set of points on the unit sphere, which join a set of great circle arcs that approximate the perimeter of the region. Pivot Parameter methodology uses the defining set of points to compute the attitude transformation of the axis due to its slewing motion about the enclosed solid angle region. The solid angle is the magnitude of the resulting Euler rotation vector representing the transformation. The method was demonstrated by comparing results to published results involving the solid angles of a circular disk radiation detector with respect to point, line and disk shaped radiation sources. The proposed general method can be applied to any detector-source geometric configuration.