Girard's Spherical Excess Formula

Let a Spherical Triangle $\Delta$ have angles $A$, $B$, and $C$. Then the Spherical Excess is given by

$$\Delta=A+B+C-\pi.$$

See also Angular Defect, L'Huilier's Theorem, Spherical Excess

References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 94-95, 1969.