What Is a Hollow Cylinder?
A hollow cylinder — also called a tube, pipe or cylindrical shell — is a solid bounded by two concentric circular cylinders of the same height. It has an outer radius R, an inner radius r (the bore), and a height h. This calculator finds the volume of material that makes up the wall of such a shape, which is exactly the outer cylinder volume minus the inner cavity volume.
How to Use This Calculator
Enter the outer radius, the inner radius and the height in any consistent unit of length (for example, all in centimeters). The calculator returns the hollow volume in the corresponding cubic units, along with the full outer cylinder volume, the inner bore volume, and the wall thickness. Make sure the inner radius is smaller than the outer radius — if they are equal, the volume is zero.
The Formula Explained
The volume of a full cylinder is \(\pi \cdot \text{radius}^{2} \cdot \text{height}\). For a hollow cylinder you subtract the inner cylinder from the outer one:
$$V = \pi \cdot h \cdot R^{2} - \pi \cdot h \cdot r^{2} = \pi \cdot h \cdot \left( R^{2} - r^{2} \right)$$The term \((R^{2} - r^{2})\) captures the cross-sectional area of the ring (annulus), and multiplying by the height extrudes that ring into a 3-D shell.
Worked Example
Suppose a pipe has an outer radius of 5 cm, an inner radius of 3 cm and a height of 10 cm. Then:
$$V = \pi \times 10 \times \left( 5^{2} - 3^{2} \right) = \pi \times 10 \times (25 - 9) = \pi \times 10 \times 16 = 160\pi \approx 502.65 \text{ cm}^{3}.$$FAQ
What units does it use? Any unit of length works as long as all three inputs use the same unit; the result is in those units cubed.
Can I use diameter instead of radius? No — divide each diameter by 2 first to get the radius, then enter the radii.
What if R equals r? The wall has zero thickness, so the volume is zero. The inner radius must be less than the outer radius for a real hollow cylinder.
