Cylinder Calculator

The volume of a cylinder is the area of its circular base times its height, V = πr²h. A tank 36 inches across (radius 18 in) and 48 inches tall holds π × 18² × 48 = 48,858.05 in³, which is 211.51 US gallons or 800.64 liters. Its total surface area is 2πr(r + h) = 7,464.42 in².

Enter any two known values and the calculator works out the rest, including the backward cases: the height of a 100-gallon tank, or the radius from a volume and an area. For the outside of other solids use the Surface Area Calculator, for boxes, spheres and cones the Volume Calculator, and for a single circle the Circle Calculator.

The cylinder volume formula and its relatives

A cylinder is a circle pushed straight up, so every formula starts from the radius r and the height h:

Why the formula works: slice the cylinder into thin disks, like a stack of coins. Each disk has the area of the end, πr², and the stack is h tall, so the volume is the end area times the height. By the same reasoning, known as Cavalieri's principle, a leaning stack of the same coins holds the same volume, so an oblique cylinder also holds πr²h when h is its vertical height.

Because volume grows with the square of the radius, a tank twice as wide holds four times as much, while doubling the height only doubles it. The lateral area also links neatly to the volume, L = 2V ÷ r, which makes a quick check on any answer.

Worked example 1: a 36 × 48 inch tank in gallons

An upright tank measures 36 inches across the inside and 48 inches tall. Halve the diameter to get r = 18 in, then:

In other units the tank holds 28.27 ft³, 1.05 yd³ or 800.64 liters. Each inch of depth holds 4.41 gallons, the number to use with a dipstick. The side measures 37.70 ft² and the whole outside 51.84 ft². This is the calculator's default, so these figures appear as soon as the page loads.

Worked example 2: how tall is a 100-gallon tank 30 inches wide?

Working backwards needs the volume in cubic inches first. Choose Radius (or diameter) and volume, switch to Diameter and US gallons, and enter 30 and 100:

The tank needs 32.68 inches (2.72 ft) of straight wall on the inside. Its side has an area of exactly 3,080 in², which the shortcut L = 2V ÷ r = 2 × 23,100 ÷ 15 confirms, and the total area with both ends is 4,493.72 in². Add headroom above that height if the liquid must not reach the lid.

Worked example 3: two cans with the same volume and area

Volume and total area do not always pin down a single cylinder. Substituting h = V ÷ (πr²) into T = 2πr² + 2πrh gives the cubic 2πr³ − Tr + 2V = 0, which has two positive roots whenever T is above the minimum. For a 1-liter can (1,000 cm³) made from 600 cm² of sheet:

The table shows how the proportions of a 1-liter cylinder drive the material it needs. Lengths are in centimeters and areas in square centimeters.

The minimum, 553.58 cm², comes when the height equals the diameter. Below that area no 1-liter cylinder exists, and the calculator says so instead of returning a meaningless number.

Solving from any two values

Each pair of known values has its own rearrangement of the formulas. The calculator applies the right one for the pair you pick:

Gallons per foot of pipe and well casing

A pipe is a long, thin cylinder, so its capacity per foot depends only on the inside diameter d in inches: gallons per foot = π × (d ÷ 2)² × 12 ÷ 231 ≈ 0.0408 × d². Every value below is computed from the exact 231 cubic inches per gallon.

The last column shows how many feet of pipe hold one gallon: 98.04 ft for a 1/2-inch bore. A hot-water line that long holds a full gallon of standing water, which runs out of the faucet before hot water arrives. Use the actual inside diameter: pipe sold by nominal size often measures differently inside, depending on the material and wall thickness.

Vertical tank capacity by diameter and height

For upright round tanks, cisterns and stock tanks measured in feet, gallons = π × (D ÷ 2)² × H × 7.4805 ≈ 5.875 × D² × H. The first two columns give the capacity per inch and per foot of depth, for gauging a tank that is partly full.

The capacities are geometric, to the brim, and rounded to whole gallons in the height columns. Usable volume is lower once you leave headroom and allow for fittings.

How to use this calculator

Choose the two values you know from the menu, then the length unit. Say whether you measured a radius or a diameter, and whether a known volume is in cubic units, US gallons or liters. Results appear as you type: the volume with its gallon and liter equivalents, a table of every dimension and area with the given values marked, the volume in seven units, the capacity per unit of height and the algebra behind each step. The Try buttons load the three worked examples and a length of pipe.

Measuring a real tank or pipe

• Inside or outside: measure inside dimensions for capacity and outside dimensions for paint, wrap or insulation.
• Measuring around: if you cannot measure straight across, wrap a tape around the tank and divide the circumference by π. A circumference of 113.10 in means a diameter of 36 in.
• Straight wall only: measure the height of the vertical wall. Domed tops and cone bottoms hold volume the cylinder formula does not count.
• One unit: a 36-inch diameter with a 4 ft height must become 36 in and 48 in, or 3 ft and 4 ft, before you multiply.
• Concrete forms: work in feet and read the cubic yards. A round form 12 inches across and 4 ft deep takes 3.14 ft³, or 0.12 yd³, so eight piers need about 0.93 yd³ before waste. The Concrete Calculator adds bag counts.

Who this calculator is for

Homeowners size water tanks, rain barrels and stock tanks in gallons. Plumbers and well drillers estimate the water held in a pipe run or a casing. Contractors convert column and pier forms to cubic yards. Students check homework that asks for a missing radius or height, and engineers and packaging designers compare cylinders that hold the same volume with different amounts of material.

Key terms

• Radius (r): the distance from the center of a circular end to its edge, half the diameter.
• Height (h): the length of the straight side, at a right angle to the ends.
• Lateral area: the area of the curved side only, 2πrh.
• Total surface area: the lateral area plus both circular ends.
• Capacity: how much a container holds, usually stated in gallons or liters.
• US gallon: exactly 231 cubic inches.

Limitations

The formulas describe a right circular cylinder: straight walls at a right angle to two flat, circular ends. Tanks with domed or conical ends, tapered buckets and oval tanks need other formulas or a split into pieces, and a leaning (oblique) cylinder keeps the volume πr²h but not the side-area formula. A horizontal tank that is partly full does not fill in proportion to depth, so the per-inch capacity applies only to upright tanks. Results ignore wall thickness, fittings and the expansion of liquids with temperature.

Related calculators

• For the surface area of cones, spheres, prisms and pyramids, use the Surface Area Calculator.
• For the volume of boxes, spheres, cones and pyramids, use the Volume Calculator.
• For the area and circumference of the circular end, use the Circle Calculator.
• For the flat area of the pad under a tank, use the Area Calculator.
• To paint the walls of a room rather than a tank, use the Paint Calculator.
• For concrete piers and slabs in bags or yards, use the Concrete Calculator.

Sources

The geometry is exact. The unit definitions behind the gallon and liter figures come from primary sources:

• National Institute of Standards and Technology, NIST Handbook 44 (2026), Appendix C, General Tables of Units of Measurement: the US gallon is exactly 231 cubic inches (3.785411784 liters), the inch is exactly 2.54 centimeters, and the British imperial gallon is 277.42 cubic inches.
• National Institute of Standards and Technology, NIST Special Publication 811, Appendix B.8: the exact length factors (1 ft = 0.3048 m, 1 yd = 0.9144 m) used for the unit conversions.
• Tables and worked examples: computed with the formulas on this page, using the same code the calculator runs.