Is there a general equation expressing the area of a spherical quadrilateral using two polar angles, $\theta_1$ and $\theta_2$, an azimuth, $\phi$, and a radius, $r$?
I know this can be done by integration, but it seems like there should be an algebraic statement I could build in Excel.
http://wikisend.com/download/576780/Spherical quadrilateral.pdf