How to calculate the area covered by any spherical rectangle? Is there any analytic or generalized formula to calculate area covered by any rectangle having length $l$ & width $b$ each as a great circle arc on a spherical surface with a radius $R$? i.e. How to find the area $A$ of rectangle in terms of length $l$, width $b$ and radius $R$
($A=f(l, b,R)$)?

Note: Spherical rectangle is a quadrilateral having equal opposite sides but non-parallel & all the interior angles are equal in magnitude & each one is greater than $90^\circ$.


The solid angle subtended by any spherical rectangle with length $l$ & width $b$ each as a great circle arc on a spherical surface of radius $R$ is given by following generalized formula as follows
$$\omega=4\sin^{-1}\left(\tan \left(\frac{l}{2R}\right)\tan \left(\frac{b}{2R}\right)\right)$$
hence the area ($A$) of spherical rectangle will be given as follows
$$A=\omega R^2$$
$$\boxed{\color{blue}{A=4R^2\sin^{-1}\left(\tan \left(\frac{l}{2R}\right)\tan \left(\frac{b}{2R}\right)\right)}}$$
