Calculations at a spherical cap (spherical dome). A spherical cap ist an evenly cut off part of a sphere. The remaining part is also a spherical cap. The calotte is the curved part of the cap. Enter radius of the sphere and height of the spherical cap and choose the number of decimal places. Then click Calculate.

A calotte is the upper side of the segment without the closing circle area.

Formulas:
a = √ h * ( 2 * r - h )
A = π * ( 2 * r * h + a² )
A_{C} = 2 * π * r * h
V = h² * π / 3 * ( 3 * r - h )

pi:
π = 3.141592653589793...

Radiuses and height have the same unit (e.g. meter), the areas 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}.

The spherical cap is the three-dimensional equivalent of the circular segment. It is axially symmetrical to any plane perpendicular to the height line and rotationally symmetrical to any angle around the same line. Its surface is also called the lateral surface, although this term is more common for bodies such as cylinders. A special case of the spherical cap is the hemisphere, which is created when the sphere is divided in the middle into two equal-sized segments. A spherical cap including the cone towards the center is called a spherical sector. If a smaller spherical cap is removed from above a spherical cap, a spherical segment is created. Two identical spherical caps with a height that is smaller than the radius and which are joined together on their flat sides form a double calotte. If the calottes have different heights but the same radius as the spherical caps, then such a joining creates a lens, which in this case is missing the middle cylinder. A cylinder from which spherical caps are removed from its sides forms a concave lens. If a spherical shell is cut through both spheres, the result is a spherical shell cap.