Volume of a Hollow Cylinder Calculator
Enter the outer and inner size as radii or diameters (pick the mode) plus the height, and get the wall volume of a tube or pipe, the bore volume, the ring cross-section, and the wall thickness.
Example: with Measurements are Radii (outer R, inner r) · Outer radius R (or diameter D) 5 · Inner radius r (or diameter d) 3 · Height / length (h) 10 → Wall (material) volume: 502.655 cubic units.
- Ring cross-section area50.265 square units
- Inner (bore) volume282.743 cubic units
- Wall thickness2 units
Computed by the calculator below using its default values. Change any input to see your own numbers.
V = π(R² − r²)h — outer cylinder minus the bore.
Outer minus inner
A hollow cylinder — a pipe, tube, sleeve, or ring — is just one cylinder with another removed from its core. So its material volume is the difference: V = πR²h − πr²h = π(R² − r²)h. The subtraction happens after squaring, which matters: a tube from R = 5 to r = 3 has cross-section π(25 − 9) = 16π, not π(5 − 3)² = 4π.
The bore volume πr²h is reported too, because it answers the other common question — how much fluid the tube carries — while the wall volume answers how much metal, concrete, or PVC you are buying.
Radius or diameter — pick honestly
Pipe and tubing specs are almost always quoted as diameters (OD and ID), while geometry homework speaks in radii. The mode switch halves diameters for you; entering diameters in radius mode inflates every volume by 4×. Wall thickness works out to R − r, which is (D − d)/2 — another factor-of-two trap when reading spec sheets.
How it’s calculated
V = π(R² − r²)h. Diameter mode halves both entries first. Ring cross-section = π(R² − r²); bore volume = πr²h; wall thickness = R − r. π is used at full double precision; display rounds to 3 decimals.
Assumes concentric, uniform walls; nominal pipe sizes often differ from true measured OD/ID, so measure when material cost matters.
Worked examples
| Outer R | Inner r | Height | Wall volume |
|---|---|---|---|
| 5 | 3 | 10 | 502.7 |
| 4 | 3 | 12 | 263.9 |
| 2 | 1.5 | 20 | 110.0 |
| 10 | 9 | 50 | 2,984.5 |
Computed with V = π(R² − r²)h; rounded to one decimal.
Common mistakes
- Entering diameters in radius mode — every volume comes out 4× too big.
- Subtracting before squaring: π(R − r)²h is wrong; square first, then subtract.
- Confusing wall thickness with the diameter difference — thickness is (D − d)/2, not D − d.
- Mixing units, like an inner size in millimeters against an outer size in centimeters.
Frequently asked questions
What is the volume formula for a hollow cylinder?
V = π(R² − r²)h, where R is the outer radius, r the inner radius, and h the height. It is simply the outer cylinder's volume minus the bore's.
Should I enter radius or diameter?
Either — just set the mode to match. Pipe specs (OD/ID) are diameters and get halved automatically; if you measured across the middle of the opening, that is a diameter too.
How do I turn the volume into weight?
Multiply the wall volume by the material's density in matching units — for example, cm³ × 7.85 g/cm³ for steel. Keep volume and density units consistent before multiplying.
What if the inner radius is zero?
Then there is no bore and the formula collapses to a solid cylinder, πR²h. The calculator accepts r = 0 and shows exactly that.