Hollow Cylinder Volume Calculator

What Is a Hollow Cylinder?

A hollow cylinder (also known as a cylindrical shell, circular tube, or pipe) is a three-dimensional geometric solid bounded by two concentric cylindrical surfaces sharing the same rotational axis and height. It consists of an outer cylinder of radius $R$ (or outer diameter $D$) from which a coaxial inner cylindrical core of radius $r$ (or inner diameter $d$) has been removed.

Hollow Cylinder Formulas

The geometry of a cylindrical shell involves several key formulas derived from basic cylinder dimensions:

1. Wall Thickness ($t$)

The wall thickness is the radial difference between the outer and inner radius:

$$t = R - r = \frac{D - d}{2}$$

2. Annular Cross-Sectional Area ($A_{cs}$)

The cross-sectional area perpendicular to the length of the cylinder is an annulus (a ring):

$$A_{cs} = \pi (R^2 - r^2) = \pi (R - r)(R + r) = \pi t (2r + t)$$

3. Hollow Cylinder (Shell) Volume ($V_H$)

The material volume of the solid shell is the cross-sectional area multiplied by the cylinder length or height $h$:

$$V_H = \pi (R^2 - r^2) h = \pi (t^2 + 2tr) h$$

Alternatively, this equals the difference between the total outer cylinder volume and the inner void volume:

$$V_H = V_{outer} - V_{inner} = \pi R^2 h - \pi r^2 h$$

4. Surface Area Formulas

• Outer Lateral Area: $A_{lat,out} = 2\pi R h$
• Inner Lateral Area: $A_{lat,in} = 2\pi r h$
• Total Lateral Area: $A_{lat} = 2\pi (R + r) h$
• Two End Rings (Caps): $A_{caps} = 2\pi (R^2 - r^2)$
• Total Surface Area: $A_{tot} = 2\pi (R + r) h + 2\pi (R^2 - r^2)$

5. Mass and Weight Calculation

The mass $m$ of the hollow cylinder depends on the material density $\rho$ and the solid shell volume $V_H$:

$$m = \rho \times V_H$$

Common Material Densities

For other 3D geometry calculations, check out our Cylinder Calculator, Pipe Volume Calculator, and Cross-Sectional Area Calculator.