What is the formula for cylinder volume?

The volume of a cylinder is V = pi times r squared times h, where r is the radius of the circular base and h is the height (or length, if the cylinder is lying on its side). If you only know the diameter, divide it by two to get the radius before applying the formula. The result is in cubic units matching whatever unit you measured radius and height in, for example cubic metres if you measured in metres.

How do you convert cylinder volume to litres or gallons?

One litre equals 1,000 cubic centimetres, or 0.001 cubic metres. So a volume in cubic metres multiplied by 1,000 gives litres. To convert litres to US gallons, divide by 3.785411784. To convert litres to imperial (UK) gallons, divide by 4.54609. These are the standard conversion factors used worldwide, including in New Zealand, which uses litres as its everyday liquid volume unit.

Does it matter if the cylinder is standing up or lying on its side?

No, total volume is the same either way because volume only depends on the radius of the circular cross-section and the overall length along the cylinder's axis. Orientation only matters if you need the volume of liquid at a partial fill level, which requires a different, more complex partial-volume formula for a horizontal cylinder.

Cylinder Volume Calculator

This calculator works out the volume of a cylinder, such as a water tank, drum, pipe, or silo, from its radius or diameter and its height or length. Choose whether you're measuring by radius or diameter, enter that dimension and the height, and pick your unit from metres, centimetres, millimetres, inches, or feet. It applies the standard formula, volume equals pi times radius squared times height, and returns results in litres, cubic metres, US gallons, and imperial (UK) gallons, with litres highlighted as the main figure. A calculation breakdown shows the radius and height used, the radius squared, and the volume built up step by step, while a full unit results table lists cubic centimetres, cubic metres, litres, US gallons, and imperial gallons side by side, handy for checking an imported tank or pump rated in gallons against its litre capacity. Results update instantly as you adjust any figure, and it works the same whether the cylinder stands upright or lies on its side, since volume only depends on the cross-sectional radius and the overall length. Keep in mind this is a geometric estimate based on the internal dimensions you enter: it doesn't account for wall thickness, tapered ends, fittings, or the volume of liquid at a partial fill level in a horizontal cylinder, so for purchasing or engineering decisions, confirm the manufacturer's stated capacity.

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Method note Standard geometric formula V = πr²h with fixed international unit conversion factors.

1. Dimensions

Measure by

Radius

Diameter

Height / length

Unit of measurement

2. About This Calculator

This calculator uses the standard cylinder volume formula: volume equals pi multiplied by the radius squared, multiplied by the height. All results update live as you change the dimensions above.

Results are shown in litres, cubic metres, cubic centimetres, US gallons, and imperial (UK) gallons, so you can use whichever unit suits your tank, drum, or pipe.

Cylinder Volume

Litres
785.4
L

Cubic Metres

0.7854

m³

US Gallons

207.5

gal (US, liquid)

Imperial Gallons

172.8

gal (UK)

Calculation Breakdown

Radius used0.5000 m

Height / length used1.0000 m

Radius squared0.250000 m2

Volume (radius² × height)0.250000 m3

Volume × π0.785398 m3

All Unit Results

Cubic centimetres (cm³)785,398.2 cm3

Cubic metres (m³)0.7854 m3

Litres (L)785.398 L

US gallons207.48 gal (US)

Imperial (UK) gallons172.76 gal (UK)

How Cylinder Volume Is Calculated

A cylinder is a solid with two parallel circular ends connected by a curved side. Its volume is the area of one circular end multiplied by the height (or length) between the two ends. The formula is:

V = π × r² × h

Where r is the radius of the circular cross-section and h is the height or length of the cylinder. If you have the diameter instead of the radius, divide the diameter by two before squaring it. Pi (π) is approximately 3.14159265.

Converting Volume to Litres and Gallons

Conversion	Factor
1 cubic metre (m³) to litres	1,000 L
1 litre to cubic centimetres	1,000 cm³
1 litre to US gallons	÷ 3.785411784
1 litre to imperial (UK) gallons	÷ 4.54609
1 US gallon	3.785411784 L
1 imperial gallon	4.54609 L

New Zealand uses litres and cubic metres as standard measurements for tanks, drums, and containers, but US and imperial gallons are shown here too since many imported tanks, pumps, and pipe specifications are still labelled in gallons.

Common Uses for This Calculator

Sizing a water tank or rainwater collection cylinder
Working out how much liquid a drum or barrel holds
Estimating the internal volume of a section of pipe
Checking the capacity of a cylindrical planter, silo, or storage container
Converting an imported tank's gallon rating into litres for New Zealand use

Worked Example

A cylinder with a radius of 0.5 m and a height of 1 m has a volume of π × 0.5² × 1 = π × 0.25 = 0.7854 m³. Converting to litres: 0.7854 × 1,000 = 785.4 L. In US gallons that is 785.4 ÷ 3.785411784 = 207.5 gallons, and in imperial gallons it is 785.4 ÷ 4.54609 = 172.8 gallons.

Related Calculators

Sources: Standard geometric formula for cylinder volume (V = πr²h). NIST Handbook 44, Appendix C: General Tables of Units of Measurement (US gallon and imperial gallon conversion factors).

This calculator provides a geometric estimate of internal volume based on the dimensions you enter. It does not account for wall thickness, tapered ends, internal fittings, or partial-fill levels in a horizontal cylinder. For tank purchasing or engineering decisions, confirm the manufacturer's stated capacity.