The problem of this article concerns the evaluation of the solid angle of an elliptical cone of any shape. It is not easy to get a mathematical formula for the solid angle that is convenient for computer calculation. It is necessary to use a third kind of complete elliptic integral, a method inconvenient for the computer. Then, usually, we have to evaluate by a numerical integration. But it is very difficult to get a value with high precision especially for compressed cones. The author has succeeded in getting a convenient series expansion formula by considering the difference between the circumscribed rectangular cone and the elliptical cone. He has succeeded also in writing a computer program to obtain the solid angle of any type of elliptical cone with any required precision better than 10⁻¹² absolute error using the series expansion formula and numerical integration.