Cylinder Volume: Formula, Units, and Examples

To calculate a cylinder’s volume, multiply the area of its circular base by its height: V = πr²h. Enter the radius and height in the same unit to get the volume in cubic units; this calculator also shows the base area.

Formula

The volume of a cylinder is the area of its circular base multiplied by its perpendicular height:

V = πr²h

• V is volume, in cubic units such as cubic centimetres (cm³), cubic metres (m³), cubic inches (in³), or cubic feet (ft³).
• r is the radius of the circular base, in a length unit.
• h is the cylinder’s height, measured perpendicular to its circular bases, in the same length unit as the radius.
• π (pi) is approximately 3.14159.

The calculator’s first result is volume, rounded to two decimal places. Its second result is the area of one circular base, A = πr², in square units. The formula works because a cylinder has the same circular cross-section all along its height: stacking those cross-sections gives base area times height.

Worked Example

Using the calculator’s default radius of 3 cm and height of 10 cm:

1. Square the radius: 3² = 9 cm².
2. Find the base area: A = π × 9 = 28.2743… cm², or 28.27 cm² to two decimal places.
3. Multiply by the height: V = 28.2743… × 10 = 282.7433… cm³.
4. Round the volume to two decimal places: 282.74 cm³.

The exact volume is 90π cm³. Keeping π unrounded until the final step avoids unnecessary rounding error.

How to Measure the Cylinder

Measure the radius from the centre of a circular end to its edge. If you can measure only the full width across the circle, that measurement is the diameter, d, and the radius is half of it: r = d/2. Do not enter the diameter as though it were the radius; doing so makes the calculated volume four times too large because the radius is squared.

Measure the cylinder’s height as the straight, perpendicular distance between its two circular ends. For a typical upright cylinder, this is its vertical length. If the object lies on its side, its height is still the distance between the circular faces, not necessarily its vertical height above a surface.

For example, a cylinder with a diameter of 8 cm and a height of 12 cm has radius 4 cm. Its volume is π × 4² × 12 = 192π, or approximately 603.19 cm³.

Units and Conversions

Radius and height must use the same length unit. The output unit is that unit cubed: centimetres produce cm³, metres produce m³, inches produce in³, and feet produce ft³. The base-area result uses square units instead. If one measurement is in centimetres and another in metres, convert one before using the formula.

Useful conversions include 1 in = 2.54 cm and 1 ft = 12 in. Convert lengths first, then calculate, or convert the final volume using a cubic conversion factor. For example, 1 ft³ = 1,728 in³ because each of the three dimensions contributes a factor of 12. Similarly, 1 m³ = 1,000,000 cm³. A cubic centimetre is also equal in volume to 1 millilitre, which can help when interpreting small container capacities.

Volume and capacity are related but are not always reported in the same units. A geometrical calculation gives cubic units; a container’s stated capacity may use litres, millilitres, or US customary units such as gallons. Check which gallon definition is intended when converting: the US liquid gallon and the Imperial gallon are different sizes.

When the Formula Applies—and Its Limits

The formula gives the volume of a right circular cylinder: a solid with circular, parallel ends and straight sides perpendicular to those ends. It is suitable for an ideal cylinder, such as a geometrical model of a can or pipe. Real objects may have rounded edges, tapered sides, thick walls, or irregular interiors, so their actual usable capacity can differ from the result.

The equation calculates the volume enclosed by the cylinder’s outer dimensions. For a hollow cylinder such as a pipe, that is not the volume of material in its wall or the space inside it. If the inner and outer radii are known, the material volume is πh(R² − r²), where R is the outer radius, r is the inner radius, and h is the length. The interior capacity is πr²h using the inner radius.

For a cylinder filled only to a particular level, use the filled height rather than the full height if the liquid’s surface is level and the container has straight sides. A slanted or tilted cylinder, a partly filled horizontal cylinder, or an object with changing cross-sections needs a different calculation or a more detailed geometric model.

Common Calculation Mistakes

• Using diameter instead of radius: halve the diameter first. Since the radius is squared, this error has a large effect.
• Mixing units: convert radius and height to the same unit before multiplying.
• Forgetting the square and cube: the radius is squared in the base area, and multiplying by height makes the final unit cubic.
• Rounding too early: retain the calculator’s full precision during intermediate steps and round the final volume to a sensible precision.
• Confusing capacity with exterior volume: wall thickness and rounded or tapered parts can reduce a real container’s usable interior volume.

Measurement precision also matters. If dimensions are approximate, the calculated volume is approximate too. A small error in the radius can affect the result more strongly than an equally sized error in height because the radius is squared.

Frequently Asked Questions

What is the formula for the volume of a cylinder?
Use V = πr²h: multiply pi by the radius squared and then by the perpendicular height.

How do I find cylinder volume from its diameter?
Divide the diameter by 2 to get the radius, then use V = π(d/2)²h. Do not square the diameter as if it were the radius.

Does cylinder volume use square or cubic units?
It uses cubic units, such as cm³ or ft³. The circular base area uses square units, but multiplying that area by a length gives cubic units.

How do I calculate the volume of a hollow cylinder?
For the material in a straight hollow cylinder, subtract the inner-cylinder volume from the outer-cylinder volume: V = πh(R² − r²). For its internal capacity, use the inner radius alone.

Can I use this formula for a cone?
No. A cone’s volume is one-third of the volume of a cylinder with the same base radius and height: V = ⅓πr²h.

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in r | Radius | cm | 3 | 0
in h | Height | cm | 10 | 0
out v | Volume | cm³ | pi * r ^ 2 * h | 2
out a | Base area | cm² | pi * r ^ 2 | 2