Free · Mathematical relations and geometry

Solid and Hollow Cylinder Volume

Calculate solid or hollow cylinder volume, with radius, diameter, height and independent unit controls.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A solid cylinder of radius 3 and height 4 has volume 36π, approximately 113.097336 in the selected cubic unit.

V = πr²h; hollow V = π(R² − r²)h

Worked example

Enter these known values and leave the other values blank.

Cylinder type
1
Radius
3 cm
Height
4 cm
Diameter
6 cm
Volume
113.1 cm³

Assumptions and limitations

  • Height is perpendicular separation between the bases, including for an oblique cylinder.
  • A hollow cylinder has positive outer radius greater than its positive inner radius. The void is subtracted from the solid envelope.
  • Radius and diameter are linked, and positive inverse roots can recover a missing dimension.
  • Selected length and volume units convert independently.

Common questions

How can I solve for a missing quantity?

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

How should I interpret the worked example?

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

References

The cubic international mile uses the cube of the exact 1609.344-meter mile, replacing a rounded reciprocal factor. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor.

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