Sharp Bent Cylinder Calculator

Calculations at a sharp bent right circular cylinder. This is made of two cut cylinders with equal radius and difference between long and short height. They are connected with each other at their elliptic surfaces. The smaller the difference between long and short height relative to the radius is, the larger is the bend angle, this is between 0 and 180 degrees.
Enter the radius and three of the four heights and choose the number of decimal places. Then click Calculate. The angle is calculated and displayed in degrees, here you can convert angle units.

	Cylinder radius (r):
	First short height (h1):
	First long height (h2):
	Second short height (i1):
	Second long height (i2):
	Bend diameter (x):
	Bend angle (α):
	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 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.

A bend angle α of 90 degrees is achieved when the difference between the long and short heights equals twice the radius, for example, (h₂-h₁)=2r. Such cylinders bent at a right angle are sometimes encountered, such as in railings with round handrails that turn a corner. However, a sharp bend is often undesirable, for instance, in pipes carrying fluids, where it would create an obstruction. An alternative to a sharp bend for changing direction is a torus sector with the corresponding angle.
Bent cylinders are often actually bent cylindrical shells, where the two arms consist of cut cylindrical shells. Such a bent hollow cylinder can be visualized as a bent cylinder with a correspondingly smaller bent cylinder removed from its interior.

A bent cylinder is mirror-symmetrical about the plane that bisects both visible circular faces. If the outer and inner heights are equal, it possesses an additional plane of symmetry running along the elliptical faces of the cylinder segments, perpendicular to the other plane of symmetry.

Calculation of volume and other dimensions: sharp bent cylinder

Last updated on 07/11/2026. Author: Jürgen Kummer

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