Pressure in A Contact Area Between Two Spheres Formula

Equation for calculate pressure in a contact area between two spheres is,

$p_r=p_{\mathrm{<mn>0</mn>}}\sqrt{1-\frac{r^2}{a^2}}$

where,
p_r = Pressure in the Contact Area
p₀ = The maximum contact pressure
r = Distance from the center of the circle
a = The radius of the circle contact area