Cylinder Volume Calculator
Find the volume and surface area of a cylinder in metric or imperial units. Choose between a solid or hollow cylinder, enter radius or diameter, and get the capacity in cubic units, litres, and US gallons. A reverse-solve mode lets you find the missing radius or height from a known volume.
Formula
Worked example
Solid cylinder, radius 5 cm, height 12 cm: base area = pi * 25 = 78.54 cm2, volume = 78.54 * 12 = 942.48 cm3 = 0.942 litres. Surface area = 2 * 78.54 + 2 * pi * 5 * 12 = 157.08 + 376.99 = 534.07 cm2. Hollow tube, outer radius 5 cm, inner radius 3 cm, height 12 cm: volume = pi * (25 - 9) * 12 = pi * 192 = 603.19 cm3.
The cylinder volume formula
A right circular cylinder is a solid with two parallel circular ends joined by a straight curved side. Its volume equals the area of one circular base multiplied by the height: V = pi * r^2 * h, where r is the radius of the base and h is the perpendicular distance between the two ends. The radius is half the diameter, so if you measured across the full width of the circle, divide by two before entering it. Because the base area uses r squared, the radius has a much stronger effect on volume than the height: doubling the radius quadruples the capacity, while doubling the height only doubles it.
Hollow cylinder (tube or pipe)
A hollow cylinder, also called a cylindrical shell, has an outer radius and an inner radius with the material occupying the ring between them. The volume of the shell is V = pi * (r_outer^2 - r_inner^2) * h, which is simply the outer cylinder volume minus the inner bore volume. You can also specify the wall thickness instead of the inner radius: inner radius = outer radius minus wall thickness. The total surface area of a hollow cylinder includes the two annular (ring-shaped) ends, the outer curved side, and the inner curved side.
Oblique cylinder
An oblique cylinder is one whose axis is not perpendicular to its circular bases, meaning the sides are slanted. By Cavalieri's principle, the volume of an oblique cylinder is the same as a right cylinder with the same base radius and the same axial (perpendicular) height: V = pi * r^2 * h. The slant height is longer than the axial height by a factor of 1/cos(angle), where angle is the lean from vertical. Enter the tilt angle and the calculator reports the slant height as a reference, which is useful when measuring a physical tank or container.
Reverse-solve: find radius or height from a known volume
If you know the volume of a cylinder and one of its dimensions, you can back-calculate the other. To find the radius: r = sqrt(V / (pi * h)). To find the height: h = V / (pi * r^2). Switch the "Solve for" selector to Radius or Height, enter the volume and the known dimension, and the calculator returns the missing value along with the full surface-area breakdown.
Surface area: lateral surface plus two caps
The total surface area of a closed solid cylinder has two parts. The lateral surface is the curved side, which unrolls into a rectangle with width equal to the circumference (2 * pi * r) and height h, giving an area of 2 * pi * r * h. Added to that are the two circular ends, each with area pi * r^2, for a combined 2 * pi * r^2. The total is A = 2 * pi * r^2 + 2 * pi * r * h. If you only need the curved side (for example, a label around a can), use the lateral area alone.
Liquid capacity: litres and gallons
The calculator converts the computed volume into litres and US gallons for practical use. If you enter dimensions in centimetres, 1 cm^3 equals 1 millilitre, so dividing by 1000 gives litres. If you enter in other units the tool first converts to cubic centimetres using the appropriate factor (1 inch = 2.54 cm, 1 foot = 30.48 cm, 1 metre = 100 cm, 1 millimetre = 0.1 cm) before dividing. One US gallon equals 3785.41 cm^3. Litres and gallons appear for all three modes: forward-solve, find-radius, and find-height.
Keeping units consistent
Always enter both radius (or diameter) and height in the same unit. Use the "Units" selector to switch between centimetres, inches, millimetres, metres, and feet: the unit labels next to each input update automatically. Volume comes out in cubic units of the chosen length unit, and the litres and gallons outputs account for the conversion. To convert between unit systems after the fact, remember that 1 in^3 is approximately 16.387 cm^3 and 1 ft^3 is approximately 28,316.8 cm^3.
Cylinder volume and liquid capacity for common dimensions
| Radius (cm) | Height (cm) | Volume (cm^3) | Litres | US Gal |
|---|---|---|---|---|
| 1 | 5 | 15.71 | 0.016 | 0.004 |
| 2 | 10 | 125.66 | 0.126 | 0.033 |
| 3 | 15 | 423.90 | 0.424 | 0.112 |
| 5 | 12 | 942.48 | 0.942 | 0.249 |
| 7 | 20 | 3078.76 | 3.079 | 0.813 |
| 10 | 30 | 9424.78 | 9.425 | 2.490 |
| 15 | 50 | 35342.92 | 35.343 | 9.337 |
| 25 | 100 | 196349.54 | 196.350 | 51.876 |
V = pi * r^2 * h. Liquid capacity is in litres (1 litre = 1000 cm^3), computed assuming centimetre inputs.
Frequently asked questions
What if I only know the diameter, not the radius?
Select "Diameter" under "Specify outer size as" and enter the full width across the circular base. The calculator divides by two internally. For example a 10 cm diameter pipe has a 5 cm radius and a volume of pi * 25 * h.
How do I calculate the volume of a hollow pipe or tube?
Choose "Hollow (tube / shell)" from the Cylinder type selector. Enter the outer radius (or diameter) and then either the inner radius or the wall thickness. The calculator subtracts the inner bore from the outer cylinder: V = pi * (r_outer^2 - r_inner^2) * h.
How do I find the radius if I know the volume and height?
Switch "Solve for" to "Radius (given volume + height)". Enter the known volume and the height. The calculator applies r = sqrt(V / (pi * h)) and returns the radius, diameter, and surface area.
How do I find the height if I know the volume and radius?
Switch "Solve for" to "Height (given volume + radius)". Enter the known volume and the radius. The calculator applies h = V / (pi * r^2) and returns the height together with the surface-area breakdown.
How do I convert the volume to litres or US gallons?
The litres and US gallons outputs appear automatically. If you entered dimensions in centimetres, volume in cm^3 divided by 1000 gives litres. For other unit systems the tool converts to cm^3 first (1 in = 2.54 cm, 1 ft = 30.48 cm, etc.) before dividing. One US gallon is 3785.41 cm^3.
Does the volume formula change for an oblique (slanted) cylinder?
No. By Cavalieri's principle an oblique cylinder has the same volume as a right cylinder with the same base area and the same axial (perpendicular) height: V = pi * r^2 * h. Enter the perpendicular height, select "Oblique" and enter the lean angle; the calculator reports the slant height as an extra output.
Why does a small change in radius have such a big effect on volume?
Volume depends on the square of the radius. Increasing the radius from 5 cm to 6 cm (a 20% increase) raises the base area from 78.54 cm^2 to 113.10 cm^2, a 44% jump, so the volume grows by 44% for every fixed height. The height, by contrast, scales volume linearly.