Cylindrical Shell Volume Calculator
From an outer radius, an inner radius, and a height, get the volume, the cross-sectional area, and the wall thickness — the numbers that describe any pipe or tube.
Three inputs, three answers
Enter the outer radius, inner radius, and height and the calculator returns the wall volume (π·h·(R²−r²)), the ring-shaped cross-section area, and the wall thickness at once.
Outer radius must exceed inner
A hollow cylinder only exists when the outer radius is larger than the inner radius. The inputs are unit-agnostic, so keep all three in the same length unit.
What is a cylindrical shell volume calculator?
Two radii and a height in, full tube out
A cylindrical shell volume calculator turns three measurements — the outer radius, the inner radius, and the height — into the numbers that describe a hollow cylinder: how much solid material it contains (volume), the area of its ring-shaped end face (cross-section area), and how thick its wall is (wall thickness). A cylindrical shell is the shape of a pipe, a tube, a washer, a sleeve bearing, or a roll of tape: a solid wall wrapped around a hollow bore. The wall volume is what you bill, weigh, or order material for, so those three measurements are all you need for plumbing, machining, and packaging.
Enter the outer radius, inner radius, and height in any length unit to get the wall volume, cross-section area, and wall thickness instantly.
Three short formulas, all built from the two radii, the height, and the constant π (about 3.14159).
volume = π × (R² − r²) × hThe end face is an annulus — a ring between two circles — whose area is the big circle minus the small one: π × (R² − r²). The wall volume is that ring area multiplied by the height. The wall thickness is simply the gap between the two radii, R − r — the same as subtracting the bore diameter from the outer diameter and halving it.
Suppose you have a pipe with an outer radius of 5, an inner radius of 3, and a height of 10.
Cross-section area
π × (5² − 3²) = π × (25 − 9) = π × 16 = 50.265482 square units — the ring-shaped end face.
Volume
50.265482 × 10 = 502.654825 cubic units — the wall material.
Wall thickness
5 − 3 = 2 units — how thick the wall is.
The three outputs answer three different everyday questions. The volume (about 502.654825 cubic units for R = 5, r = 3, h = 10) is the amount of solid material in the wall — what you weigh, cost, or order for a pipe, sleeve, or tube. It is the volume of the full outer cylinder minus the empty bore, so it always undercuts a solid cylinder of the same outer radius. The cross-section area (about 50.265482 square units) is the ring-shaped end face; it sets how much material each slice carries and how strong the tube is under load, and it stays constant along the height. The wall thickness (2 here) is the gap between the radii — a quick check that the pipe is sturdy enough, and the figure most often quoted on a spec sheet. A useful intuition: because the area depends on R² − r², the volume is dominated by the outer radius, so widening a thin-walled tube slightly adds far more material than you might expect.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Concentric circular walls and consistent units
These formulas assume a perfect hollow cylinder — two concentric circular walls of constant thickness running straight along the height — and require the outer radius to be larger than the inner radius. A tube with an off-centre bore, an oval or tapered wall, threaded ends, or a fitting will differ from the computed value. The radii and height are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: radii and a height in centimetres give a volume in cubic centimetres and a cross-section in square centimetres, never a mix.