Hollow Cylinder Volume CalculatorFree online math calculator — instant results, no sign-up
Calculate the material volume of a cylindrical tube.
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About the Hollow Cylinder Volume Calculator
The Hollow Cylinder Volume Calculator calculates the volume of material in a cylindrical tube by subtracting its hollow interior from its outer cylinder. Enter the outer radius, inner radius, and length to find the volume of the tube wall, excluding the empty space inside.
- Outer radius
- The distance from the tube’s central axis to its outside surface, entered in a length unit such as centimeters or inches; the default is 5.
- Inner radius
- The distance from the tube’s central axis to its inside surface, entered in the same length unit as the outer radius; the default is 3.
- Length
- The distance along the tube’s axis from one end to the other, entered in the same length unit as both radii; the default is 10.
Formula and method
V = π(R² − r²)L = π(5² − 3²) × 10 = 160π ≈ 502.6548245744
- VVolume of material in the tube, measured in cubic units.
- ROuter radius of the tube.
- rInner radius of the hollow space.
- LLength of the tube along its axis.
- πPi, the constant equal to a circle’s circumference divided by its diameter.
Subtract the inner circular area, πr², from the outer circular area, πR², to find the material cross-sectional area. Multiply that area by the tube’s length. With the default inputs, the squared-radius difference is 25 − 9 = 16, so the material volume is 16π × 10 = 160π, displayed as 502.6548245744 cubic units.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Outer radius5
- Inner radius3
- Length10
Results
- Result502.6548245744
How to use the Hollow Cylinder Volume Calculator
- 1Choose a single length unit for all three measurements, converting any measurements that use a different unit.
- 2Enter the outer radius, using 5 for the default example; if you measured the outside diameter, divide it by two first.
- 3Enter the inner radius, using 3 for the default example, and check that it does not exceed the outer radius.
- 4Enter the axial length, using 10 for the default example, and run the calculation.
- 5Read the Result as the volume of tube material: 502.6548245744 cubic units for the default inputs.
Reading your result
The Result row reports the material volume, not the capacity of the hollow interior or the total volume enclosed by the outside surface. With outer radius 5, inner radius 3, and length 10, Result = 502.6548245744. If the inputs are in centimeters, this is cubic centimeters; if they are in inches, it is cubic inches.
Limitations
The calculation assumes a straight tube with concentric circular inner and outer surfaces and constant radii throughout its length. It excludes end caps, fittings, grooves, and other departures from that shape. Use nonnegative dimensions with the inner radius no greater than the outer radius; a physical tube with positive material volume requires a positive length and an outer radius larger than its inner radius. Displayed decimal places do not imply that the measurements are equally precise.
Common questions
Does this calculate how much liquid the tube can hold?+
No. It calculates the material in the tube wall. The geometric volume of the hollow interior is πr²L, which is 90π cubic units for inner radius 3 and length 10; holding liquid also requires suitable closures.
Can I enter outside and inside diameters instead of radii?+
Divide each diameter by two before entering it. Both radius fields measure from the central axis to a surface, not all the way across the tube.
How can I use wall thickness to find the inner radius?+
For a uniform concentric tube, inner radius equals outer radius minus wall thickness. The default radii of 5 and 3 correspond to a wall thickness of 2 length units.
What happens if the inner radius of the tube is zero or equals the outer radius?+
An inner radius of zero removes the hollow space, so the formula becomes the solid-cylinder volume πR²L. Equal inner and outer radii give zero material volume because the wall has zero thickness.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.