Ball Head Calculator

Calculations for a ball head, a spherical-head shape. Here, ball head refers to a sphere, which surpasses a hemisphere, from which a straight circular cylinder rises. More precisely, it is a spherical cap with a matching cylinder placed on its flat side.
Enter the radius of the sphere, as well as the radius and height of the cylinder. Choose the number of decimal places, then click Calculate.

	Sphere radius (r):
	Cylinder radius (q):
	Cylinder height (b):
	Segment gap angle (α):
	Total 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 heights 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.

Ball head is essentially the term for a type of joint, such as those used on tripods, that features precisely this shape. The cross-section of the ball head represents a two-dimensional head shape. The ball head itself is the solid of revolution formed by rotating this shape cut in half lengthwise. The angle of the segment gap, from the ball head's calculated values, is required to determine the head shape. In these formulas, as with the head shape itself, h_s represents the height of the circular segment. The formulas are derived from those for a spherical segment and a cylinder, or specifically from the height calculations for a circular segment and a rectangle.
At the transition point between the spherical segment and the cylinder, the shape features a concave, circular edge, matching the cylinder's other circular edge, which is convex.

Beyond tripod joints, this shape appears in various other applications. Single-neck spherical flasks look quite similar, though they typically feature a smooth transition between the spherical segment and the cylinder. Of course, such flasks are hollow rather than solid, meaning their interior roughly mirrors the shape of this ball head. Other types of couplings, such as trailer hitches and plug-in connectors, also frequently utilize this shape.

Calculation of volume and other dimensions: ball head

Last updated on 08/15/2026. Author: Jürgen Kummer

© Jumk.de Webprojects | Online Calculators





↑ up

---