Geometry desk
Cylinder Volume Calculator
Calculate a cylinder's volume from radius and height.
Cylinder Volume Calculator: Estimate the space in a circular cylinder from its base radius and height. The result is a volume for the ideal shape, suitable for comparing cylindrical containers or solid rods when the circular cross-section stays constant along their length. Runs 100% locally in your browser with zero server file uploads.
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- Calculators
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Volume
282.74 cm³
Volume = π × radius² × height- The cylinder has a circular base and straight sides.
- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Volume = π × radius² × height
A worked example with sample values:
| Inputs | |
|---|---|
| Radius | 3 cm |
| Height | 10 cm |
| Results | |
|---|---|
| Volume | 282.74 cm³ |
A stack of equal circular slices
Volume V = π × r² × h, where r is base radius and h is the perpendicular distance between the circular ends. Each slice has the same area πr². Stacking these slices over the height multiplies that area by h, just as stacking identical rectangular sheets fills a box. The radius is measured across the base from its centre, not along the curved wall.
With radius 3 cm and height 10 cm, base area is π × 3² = 9π cm². Multiplying by 10 cm gives V = 90π = 282.743338… cm³. The displayed Volume = 282.74 cm³. Using diameter 6 cm in the radius field would make this result four times too large.
OpenStax explains constant-cross-section volumes (https://openstax.org/books/calculus-volume-2/pages/2-2-determining-volumes-by-slicing) as base area multiplied by height. This calculator does not report the cylinder's surface area.
Capacity in cubic units and litres
A centimetre multiplied by a square centimetre yields a cubic centimetre. Since 1 litre is 1,000 cm³, the example occupies about 0.282743 litres. For a cylinder measured in metres, the output is m³ and multiplying by 1,000 converts it to litres. Changing the selected unit only changes labels, so convert each input yourself. If radius is 30 mm and height is 10 cm, use either 3 cm and 10 cm or 30 mm and 100 mm; the second calculation reports a thousand times as many cubic millimetres.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
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Frequently asked questions
Should cylinder volume use the inside or outside radius?
Use the inside radius for internal capacity and outside radius for the full external shape. Wall thickness is not subtracted automatically. For a cylindrical tube's material volume, subtract an inner-cylinder calculation from an outer-cylinder calculation with the same length.
How can I calculate cylinder height from a target volume?
Use h = V ÷ (πr²). A volume of 90π cm³ with radius 3 cm requires height 10 cm. Convert the volume to cubic units matching the radius before dividing; litres and centimetres cannot be substituted together without conversion.
Will doubling the cylinder radius double its capacity?
Keeping height fixed, it quadruples capacity because the circular base area uses r². Doubling height alone doubles volume. Doubling both radius and height multiplies the volume by eight.
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