Double Point Calculator

Calculations at a double point. This is a cylinder with a matching cone attached on each end. The cones can have different or equal heights.
Enter the radius of the cylinder and cone base and three of the four heights respectively lengths. Choose the number of decimal places, then click Calculate.

	Radius (r):
	Cylinder height (a):
	Height first cone (b):
	Height second cone (c):
	Length double point (l):
	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, length 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 surface area of ​​this shape is the sum of the lateral surface areas of the constituent forms, one cylinder and two cones, while the volume is the sum of the corresponding three volumes. Such a double point is a solid of revolution formed by rotating a trapezoid around its longer parallel side. This side becomes the axis of rotation, which passes through the tips of the two cones of the double point. This solid is axially symmetric with respect to any plane containing the axis of rotation. If both cones have the same height, the solid is formed by rotating an isosceles trapezoid. In this case, an additional plane of symmetry exists, dividing the cylinder, the central section of the double point, into two equal halves. Under these conditions, this shape also exhibits point symmetry about its center, which is the intersection of the axis of rotation and the axis of symmetry passing perpendicularly through the cylinder.
The two tips can be considered geometric vertices. Furthermore, the solid has two equal edges in the form of circles and three curved surfaces. If a trapezoid is rotated around its shorter parallel side rather than the longer one, the resulting shape, which has a cylindrical convex hull and two concave vertices, possesses the same surface area as the double point. Its volume, however, is reduced by twice the volume of the two cones.

Calculation of volume and other dimensions: double point

Last updated on 07/23/2026. Author: Jürgen Kummer

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