Elongated Hemisphere Calculator

Calculations at an elongated hemisphere, a hemisphere with a matching cylinder attached to the flat side. This shape is a vertically halved or bisected capsule.
Enter the base radius (radius of hemisphere and cylinder) and the height of the cylinder and choose the number of decimal places. Then click Calculate.

	Base radius (r):
	Cylinder height (h):
	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.

Radius 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.

The elongated hemisphere is a solid of revolution. Its axis of rotation extends from the center of the hemisphere through the center of the base. It is mirror-symmetrical with respect to any plane containing this axis of rotation. This shape comprises three surfaces: a flat surface (the base), a lateral surface (that of the cylinder), and the surface of the hemisphere. There is an edge between the lateral surface and the base, but no edge between the lateral surface and the surface of the hemisphere.

If the elongated hemisphere is further bisected, the result is an elongated quarter-sphere, and so on. The slice plane of the elongated hemisphere is the elongated semicircle. When bisected, this becomes the elongated quarter circle. The elongated quarter circle is chiral. Thus, there exist two distinct versions of it that are mirror images of one another. This is not the case, however, for the elongated quarter-sphere, as it can be rotated in three-dimensional space, a possibility that is usually precluded for two-dimensional shapes.

Things in the shape of an elongated hemisphere are encountered relatively often in reality. Astronomical observatories often look like this. Also waste bins and bollards may be designed in this way. The flat end often rests on the ground. Or, as is the case with a bollard, the end may be embedded in the ground and therefore not visible at all. Indeed, a bollard presumably lacks a flat end entirely, meaning this geometric form applies solely to the visible portion.

Calculation of volume and other dimensions: elongated hemisphere

Last updated on 04/30/2026. Author: Jürgen Kummer

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