Calculations at a stylized drop. This is made of a spherical cap with a height larger than the radius and smaller than twice the radius, r < hs < 2r, on which a fitting cone is attached. Its slice plane is a drop shape. The cone base angle is the tangent angle at the point where the spherical cap ends. This is equal to the angle between the legs and the base of the isosceles triangle, which is the cross section of the upper cone.
Enter radius and height of the spherical cap. Choose the number of decimal places, then click Calculate. The angle is calculated and displayed in degrees, here you can convert angle units.
Formulas:
a = √ h * ( 2 * r - h )
α = 180° - arccos( 1 - h / r)
s = 2 * a / sin(180°-2*α) * sin(α)
A = [ 2 * r * h + a * s ] * π
V = [ h² * ( 3 * r - h ) + a² * √ s² - a² ] * π/3
pi:
π = 3.141592653589793...
Radiuses, height and slant height have the same unit (e.g. meter), surfaces have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
This stylized drop is a common but simplified three-dimensional graphic representation that has little in common with a real physical drop. A water drop looks most like this when it detaches from a surface that is free at the bottom, to which it was previously attached due to the surface tension of the water. This happens when more water is added to what is already there, as is the case with rain, for example. Even at this moment of detachment, the drop does not have a tip, but is narrower towards the top. During the fall, the water drop is round, i.e. a sphere. If it falls for a longer period of time, as is normal with raindrops, and if the rain is a little heavier, which leads to a drop size of just over two millimeters, the drops are flattened by air resistance and take on the shape of a lens, their underside can also become concave, i.e. bent inwards.