Spherical Ring Calculator

Calculations at a spherical ring. A spherical ring, as used here, refers to a sphere with a cylindrical drill hole through its center. The shape that is removed in this process is a sphere cylinder intersection.
Enter at sphere radius and at cylinder radius and height two of the three values and choose the number of decimal places. Then click Calculate.

	Sphere radius (r):			Spherical Ring Slice plane: annulus
	Cylinder radius (a):
	Cylinder height (h):
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Radiuses and height have the same unit (e.g. meter), the area has 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.

Spherical rings are familiar, for example, in the form of beads on a necklace, or as napkin rings. The cylindrical hole, created by a circular drill bit, allows spheres to be threaded or for objects to be inserted through it. If the hole is large enough, it also prevents the sphere from rolling, as long as it does not roll along the plane of the largest diameter.

A spherical ring is a toroid with a circular segment as its base. More generally, this is a solid of revolution.
The symmetry properties of the spherical ring extend beyond those of a general toroid. So it is, like the toroid, rotationally symmetric and also has infinitely many axes of symmetry through the axis of rotation and a line along a radius, perpendicular to the plane of the radii. It is also axially symmetric with respect to this plane of the radii. Therefore, it is also point-symmetric with respect to its center, where all planes of symmetry intersect.

Last updated on 03/31/2026. Author: Jürgen Kummer

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