Cylindrical Segment Calculator

Name: Cylindrical Segment - Geometry Calculator
Author: Jürgen Kummer

Calculations at a right circular cylindrical segment. This is created when you cut a cylinder straight through from base to base. This creates two cylindrical segments. If they are the same size, they are half cylinders. If the cylindrical segments are of different sizes, the larger part extends beyond the center of the base, while the smaller part does not. These two seemingly different shapes are both called cylindrical segments, and the formulas for calculating them are the same.
Enter radius and length of the cylinder and height of the segment and choose the number of decimal places. Then click Calculate.

Formulas:

s = 2 \cdot \sqrt{2 \cdot r \cdot h - h^{2}}

b = r \cdot 2 \cdot \arccos (1 - \frac{h}{r})

L = l \cdot b

S = \frac{r}{2} \cdot b - \frac{s}{2} \cdot (r - h)

A = L + s \cdot l + 2 \cdot S

V = S \cdot l

Radius, length, width and height 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. The lateral surface is the curved part of the surface area.

One application in which this shape can be calculated is the capacity of a not fully filled cylindrical tank. Such tanks lie, when they should be transportable, on trucks, for example. Sometimes, however, such cylinders are not circular cylinders, but elliptic cylinders. The filled volume of these can be calculated by multiplying the area of an elliptical segment by the length (or height). The surface area of such an elliptical cylinder segment, however, cannot be calculated algebraically. If the cylindrical tank is upright, then the filled volume is of course also cylindrical, but with a lower height than that of the tank. If, on the other hand, the tank is inclined, then the filling has the shape of a cut cylinder, a cylindrical wedge, or a diagonally halved cylinder.

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