Volume of a Cylinder Calculator

This volume of a cylinder calculator takes the diameter or radius and the height, with a separate unit for each one, and gives the volume in gallons, litres, cubic feet and every other common unit. Measure a 6 inch pipe 20 feet long and enter exactly that. It also handles pipes with a wall, tanks that are only partly full, weight, and working back from the volume you need.

About the volume of a cylinder calculator

The formula takes one line. The mistakes happen around it: mixing inches and feet, using the diameter where the radius belongs, or assuming a tank on its side is a quarter full at a quarter of its height. This volume of a cylinder calculator handles each of those.

• Mixed units. Each length has its own unit box, so nothing needs converting first.
• Diameter or radius. Enter whichever you measured.
• Every unit at once. Cubic inches, feet, yards, centimetres and metres, litres, millilitres, US and imperial gallons, quarts and fluid ounces.
• Work backwards. Find the height or radius needed to hold a volume.
• Pipes and tubes. Add a wall thickness to split what it holds from the material in the wall.
• Partly full tanks. Upright or lying on its side, from the depth of the liquid.
• Rough weight. Water, oil, concrete, steel, aluminum or your own density.
• The working. The sum with your numbers in it, for checking or homework.

It runs in your browser. Nothing you enter is sent anywhere or saved.

How to use it

1. Choose what to find: the volume, the height or the radius.
2. Enter the size, each length with its own unit.
3. Add any options: wall thickness, liquid depth, material, or how many cylinders.
4. Read the result. It updates as you type. Open “Show the working” to see the sum.

How to calculate the volume of a cylinder

Volume = π × r² × h

Here r is the radius, h is the height, and π is about 3.1416. If you have the diameter d, the same formula becomes π × d² × h ÷ 4. The reason it works: a cylinder is a stack of identical circles, each with an area of π × r². Multiply that area by the height and you have the volume.

A worked example

A pipe 6 inches across and 20 feet long. These are the calculator’s defaults.

1. Radius: 6 in ÷ 2 = 3 in.
2. Same unit: 3 in is 0.25 ft.
3. Square it: 0.25 × 0.25 = 0.0625.
4. Multiply by π: 0.0625 × 3.1416 = 0.19635 sq ft. That’s the area of the end.
5. Multiply by the height: 0.19635 × 20 = 3.927 cubic feet.
6. In gallons: 3.927 × 7.48 = about 29.38 US gallons, or 111.2 litres.

A metric example

A bucket-sized cylinder 30 cm across and 50 cm tall. The radius is 15 cm, so 3.1416 × 15 × 15 × 50 = 35,342.92 cubic centimetres. Divide by 1,000 and that’s 35.34 litres.

Calculate volume of a cylinder from the diameter

You don’t have to find the radius first. Use π × d² × h ÷ 4. With a 6 inch diameter and a 240 inch height: 3.1416 × 36 × 240 ÷ 4 = 6,785.84 cubic inches, the same answer as the pipe above.

Calculate volume of a cylinder from the circumference

If you can only measure around it, divide the circumference C by π to get the diameter, or use V = C² × h ÷ (4 × π) directly. A cylinder 18.85 inches around is 6 inches across.

Converting the answer

Measuring a real cylinder

• Diameter: measure across the widest part of the end, through the centre.
• Can’t get across it? Wrap a tape around it and divide by π. A distance of 18.85 inches around is 6 inches across.
• Height: for something lying down, the length is the height. The formula doesn’t care which way up it is.
• For what it holds, measure the inside. A pipe’s nominal size often isn’t either of its true diameters, so check its actual figures.

Pipes and hollow cylinders

A hollow cylinder has two useful volumes: what it holds, and the material in its wall.

• Holds: π × r² × h, using the inside radius.
• Wall: π × (R² − r²) × h, where R is the outside radius.

Take a pipe 4 inches across on the outside, with a 1/4 inch wall, 10 feet long. The inside radius is 1.75 inches. It holds about 5 US gallons, and the wall is 353.43 cubic inches of material. In steel that’s about 100 pounds. Tick “It is hollow” and enter the wall thickness.

Tanks that are only partly full

Standing upright, a tank is simple: the liquid is a shorter cylinder, so a tank at a quarter of its height is a quarter full.

On its side, it isn’t. The tank is narrow near the bottom and wide in the middle, so the first few inches hold much less than the middle ones. The liquid’s end is a shape called a circular segment:

Area = r² × acos((r − d) ÷ r) − (r − d) × √(2rd − d²)

Here d is the depth of the liquid. Multiply the area by the tank’s length to get the volume. A tank 48 inches across and 10 feet long holds about 940 US gallons when full:

So a 12 inch reading on that tank means about 184 gallons, not the 235 you’d guess from a quarter of the height. Real tanks with rounded ends hold a little more than a plain cylinder does.

Working backwards from a volume

Sizing a tank or a mold? Turn the formula around.

• Height: h = V ÷ (π × r²). To hold 500 US gallons in a tank 4 feet across, it needs to be about 5.32 feet tall.
• Radius: r = √(V ÷ (π × h)). To hold 500 gallons in a tank 4 feet tall, it needs a radius of about 2.31 feet, or 4.61 feet across.

Everyday uses

• Concrete for footings and tube forms. Eight footings 12 inches across and 4 feet deep take 0.93 cubic yards, about 3,766 pounds of concrete. The cubic yard calculator handles slabs and other shapes.
• Tanks and water butts. Gallons held, and how much weight the floor or stand has to carry. Water is about 8.34 pounds a US gallon.
• Round pools. The gallons in a round pool come from the same formula. The pool salt calculator turns those gallons into a salt dose.
• Pipes. The water sitting in a run of pipe, or how much the pipe weighs.
• Homework. The working is laid out in the order a teacher expects.

Surface area of a cylinder

The calculator gives this too, useful for paint, insulation or wrapping.

• Curved side: 2 × π × r × h.
• One end: π × r².
• Whole outside: 2 × π × r × h + 2 × π × r².

With a 3 inch radius and a 5 inch height, the curved side is 94.25 square inches and the whole outside is 150.80.

Cylinders, cones and spheres

The volume of a cylinder is a handy yardstick for other round shapes with the same radius and height:

A cylinder that leans over, called an oblique cylinder, has the same volume as a straight one with the same base and the same vertical height. Measure the height straight up, not along the slant.

Common mistakes

• Using the diameter as the radius. The answer comes out four times too big.
• Mixing units. Inches for the radius and feet for the height gives nonsense unless you convert first.
• Squaring the wrong thing. Only the radius is squared, not π or the height.
• Assuming a lying tank is proportional. A quarter of the height is 19.55% of the volume.
• Measuring the outside for capacity. A thick wall takes a noticeable share of what you think it holds.

What it can’t tell you

• Tanks with domed ends. It treats the ends as flat.
• Exact weights. Densities vary with the mix and grade: 2,400 kg per cubic metre for concrete and 7,850 for steel are typical figures.
• Whether a tank is level. A tilted tank changes every depth reading.

Comparing a cylinder with a flat area? Our guide on how to calculate square footage covers circles and odd shapes. More tools are on the full tools list.