Hollow Cylinder Volume

Hollow Cylinder Volume is a calculator for finding the volume of cylindrical objects that have an empty center — like pipes, tubes, drinking straws, rolls of paper, bushings, and cylindrical shells. This tool exists because hollow cylinders require a different formula than solid ones, and confusing the two leads to significant errors.

Unlike a solid cylinder where V = πr²h, a hollow cylinder's volume is the material between the outer wall and the inner cavity: V = πh(R² − r²). This calculator accepts the outer radius (R), inner radius (r), and height (h) to compute the material volume accurately.

This is essential for plumbers calculating pipe material, engineers determining shaft weight, manufacturers costing cylindrical components, and anyone working with tubes, rings, or cylindrical shells.

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.

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.