What this calculator does
A hollow cylinder, sometimes called a tube or pipe, is a cylinder with a cylindrical hole running through its centre. The volume of a hollow cylinder is the outer cylinder’s volume minus the volume of the hole: V = π(R² − r²)h, where R is the outer radius, r is the inner radius and h is the height or length.
This comes up whenever the material itself, not the space inside, is what needs measuring: how much metal is in a length of pipe, how much concrete fills a cylindrical shell, or how much plastic makes up a tube. It differs from a plain cylinder calculation only by subtracting the hollow core, but skipping that subtraction overstates the material volume considerably once the wall gets thin.
The formula
Square the outer radius, square the inner radius, subtract the two, multiply by pi and by the height. That gives the volume of material in the wall of the tube. The calculator also reports the wall thickness (R minus r) and the total surface area, which adds the outer curved surface, the inner curved surface, and the two flat ring-shaped ends.
| Term | Meaning |
|---|---|
| R | Outer radius: the radius measured to the outside edge of the tube. |
| r | Inner radius: the radius measured to the inside edge of the hole. |
| h | Height or length of the cylinder, measured along its axis. |
| Wall thickness | R − r, the width of material between the inner and outer surface. |
The inputs explained
| Field | What to enter |
|---|---|
| Outer radius (cm) | The outer radius of the tube, from the centre to the outside surface. |
| Inner radius (cm) | The inner radius of the hole, from the centre to the inside surface. Must be smaller than the outer radius. |
| Height (length) (cm) | The length of the tube or pipe, measured along its axis. |
When to use it
Estimating material for a length of pipe
Steel, PVC or concrete pipe is sold and priced by the material it actually contains, which is the hollow cylinder volume, not the volume of the outer cylinder as if it were solid.
Checking a casting or mould
A cylindrical shell casting, such as a bushing or sleeve, uses this same formula to work out how much material fills the mould once the core that forms the hole is accounted for.
Comparing wall thickness options
For a fixed outer size, a thicker wall (smaller inner radius) uses proportionally more material; this calculator makes that trade-off concrete rather than a guess.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How volume changes with wall thickness at a fixed outer size
The same 10 cm outer radius and 30 cm height, with the inner radius (and so the wall thickness) varied.
| Inner radius | Volume of material (hollow cylinder) | Wall thickness |
|---|---|---|
| 1 cm | 9,330.53 | 9.000 |
| 3 cm | 8,576.55 | 7.000 |
| 5 cm | 7,068.58 | 5.000 |
| 7 cm | 4,806.64 | 3.000 |
| 9 cm | 1,790.71 | 1.000 |
How volume scales with length at a fixed cross-section
A fixed 3 cm wall (outer radius 10 cm, inner radius 7 cm), stretched across a range of lengths.
| Height (length) | Volume of material (hollow cylinder) | Wall thickness |
|---|---|---|
| 10 cm | 1,602.21 | 3.000 |
| 20 cm | 3,204.42 | 3.000 |
| 30 cm | 4,806.64 | 3.000 |
| 50 cm | 8,011.06 | 3.000 |
| 100 cm | 16,022.12 | 3.000 |
Questions
What is the difference between a hollow cylinder and a plain cylinder calculation?
A plain cylinder calculation treats the shape as solid: V = πr²h. A hollow cylinder subtracts the volume of the inner hole from the outer cylinder’s volume, giving V = π(R² − r²)h. Using the solid formula on a tube overstates the material by the volume of the hole.
What if I only know the diameters, not the radii?
Divide each diameter by two to get the radius before entering it. The outer diameter divided by two gives R, and the inner diameter divided by two gives r.
Can the inner radius equal the outer radius?
No. That would describe a shape with no material at all (zero wall thickness), so the calculator requires the inner radius to be strictly smaller than the outer radius.
How does wall thickness affect the surface area shown?
The total surface area includes the outer curved surface, the inner curved surface, and the two flat ring-shaped ends. A thinner wall reduces the ring-shaped end areas but the curved surfaces stay governed by R and r individually, so surface area and volume do not shrink at the same rate as the wall thins.
For a plain solid cylinder with no hole through the middle, see the cylinder calculator. For a cone-shaped solid instead, see the cone calculator.