# Calculating angle from sphere

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: $$\phi=180^\circ-2\tan^{-1}\left(\frac{d/2}{h}\right)×\frac{180^\circ}{\pi}$$ New contributor
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• Then you don't have enough information. You need to know something like the ratio of the semiaxes. Sep 14 at 22:49
• @Khalil.h Normally as per new guidelines we do not reply directly. However your question has an error of sign that needs to be pointed out. Sep 15 at 0:06

$$\varphi= \frac{\pi}{2}+2\tan^{-1}\left(\frac{h}{d/2}\right)$$
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. 