I'm trying to calculate the angle Phi in the picture in the case where the droplet is the perfect sphere I have the correct formula but I'm not sure how they found it. and I want to know the formula is if the droplet isn't a perfect sphere (ellipsoid). the formula in the case if droplet is sphere is: $\phi=180^\circ-2\tan^{-1}\left(\frac{d/2}{h}\right)×\frac{180^\circ}{\pi}$
$$\varphi= \frac{\pi}{2}+2\tan^{-1}\left(\frac{h}{d/2}\right)$$
To convert into degrees multiply by $\dfrac{180}{\pi}.$
The factor $2$ in second part arises due to the angle at circle center being double that at top of droplet.