Hollow Cylinder Volume
A hollow cylinder has an outer wall and an empty center — like a pipe, a drinking straw, or a roll of paper towels. Enter the outer radius (R), inner radius (r), and height (h) to calculate the volume of material between the two walls.
Hollow Cylinder Volume
Hollow Cylinder Formula
The volume of a hollow cylinder is the outer cylinder minus the inner cylinder:
V = π × h × (R² − r²)
where R is the outer radius, r is the inner radius, and h is the height (or length).
This formula gives the volume of the material itself — the metal in a pipe, the cardboard in a tube, the plastic in a straw. The empty space inside is not included.
Example: A pipe with R = 5 cm, r = 4 cm, h = 100 cm. V = π × 100 × (25 − 16) = 2,827.4 cm³.
Using Diameters Instead of Radii
If you have the outer diameter (D) and inner diameter (d), the formula becomes:
V = π × h × ((D/2)² − (d/2)²) = (π × h / 4) × (D² − d²)
Pipe specifications typically list outside diameter (OD) and inside diameter (ID), so this version is often more convenient.
Example: Schedule 40 steel pipe, 2-inch nominal. OD = 2.375 in, ID = 2.067 in, length = 120 in. V = (π × 120 / 4) × (5.64 − 4.27) = 94.25 × 1.37 = 129.1 in³.
Real-World Hollow Cylinders
Pipes and tubes are the most common hollow cylinders. Plumbers need the internal volume to calculate flow capacity. Engineers need the material volume to calculate weight and strength.
Other examples: toilet paper rolls, paper towel cores, cylindrical bushings, sleeves for bearings, concrete culverts, and the walls of cylindrical tanks.
For very thin walls (where R − r is much smaller than R), the volume can be approximated as V ≈ 2πRth, where t = R − r is the wall thickness. This is called the thin-wall approximation.