Cylinder Calculator

How it works

A cylinder is a circle swept straight up through a height. Its volume is therefore the area of that circle, πr², times the height. If you know the diameter instead of the radius, the calculator halves it first. The curved side, unrolled, is a rectangle whose width is the circumference 2πr and whose height is h, so the lateral area is 2πrh; adding the two circular ends gives the total surface area 2πr(r + h).

A hollow cylinder, such as a pipe or a tube, is one solid cylinder with a smaller one removed from its middle. Its volume is the difference of the two, πh(R² − r²), which is the amount of material in the wall. Its total surface area counts the outside, the inside and the two rings at the ends. The lateral area shown is the outer curved surface only, which is what you would paint or wrap.

The unit you pick labels the lengths, areas and volumes; the numbers themselves are the same whatever the unit. It does matter for the capacity line, where the volume in cubic inches, feet, yards, centimetres or metres is converted to US gallons and litres from the legal definitions of those units, so a cylinder measured in feet reports how many gallons it holds.

Formula

solid:   V = πr²h       lateral = 2πrh       total = 2πr(r + h)       r = d ÷ 2
hollow:  V = πh(R² − r²)   end = π(R² − r²)   lateral = 2πRh   total = 2πRh + 2πrh + 2π(R² − r²)
capacity: 1 US gal = 231 in³ = 3.785411784 L;  1 ft³ = 7.48052 gal;  1 m³ = 1,000 L

Example

A tank 1 ft in radius and 3 ft tall has an end area of π ≈ 3.1416 ft², a volume of π × 1² × 3 = 3π ≈ 9.4248 ft³, a lateral area of 2π × 1 × 3 ≈ 18.8496 ft² and a total surface area of 2π × 1 × (1 + 3) ≈ 25.1327 ft². Its capacity is 9.4248 × 7.48052 ≈ 70.50 US gallons, or 266.88 litres.

A standard steel drum is about 22.5 in across and 33.5 in tall. Entering those in inches with the diameter option gives π × 11.25² × 33.5 ≈ 13,319.86 in³, which is 57.66 gallons or 218.27 litres; it is sold as a 55-gallon drum because the fill line sits below the lid.

A pipe with an outer radius of 2 ft, an inner radius of 1 ft and a length of 10 ft contains π × 10 × (4 − 1) = 30π ≈ 94.2478 ft³ of material, and its total surface area, outside, inside and both end rings, is 40π + 20π + 6π = 66π ≈ 207.3451 ft².

Assumptions and limitations

• The cylinder is a right circular cylinder: the ends are circles and the axis is square to them. A tilted (oblique) cylinder has the same volume but a larger lateral area.
• For a hollow cylinder the volume is the material in the wall, and the capacity figures convert that same wall volume. To find what a pipe carries, use the solid option with the inside diameter.
• The capacity assumes the whole volume is usable; a real tank holds less once wall thickness, headspace and fittings are taken out.
• The gallon is the US liquid gallon of 231 cubic inches, not the imperial gallon.
• Results are rounded for display only.

Frequently asked questions