Cylinder Volume Calculator

V = π × r² × h

Circle area times height. The most-used 3D volume formula in plumbing, brewing, and storage. Two inputs and a constant.

Worked example, backyard rain barrel: A 55-gallon rain barrel is typically about 22 in diameter and 33 in tall. r = 11 in. V = π × 121 × 33 ≈ 12,544 in³ = 54.3 gallons. Manufacturers round up to 55 to account for the slight bulge above the cylindrical part.

Worked example, concrete sonotube: You’re pouring a 10-inch-diameter concrete footing, 4 ft deep. r = 5 in = 0.417 ft. V = π × 0.174 × 4 ≈ 2.18 ft³ = 0.081 cubic yards. Do not phone that number in to a ready-mix plant. They sell in quarter-yard steps with a one-yard minimum and a short-load fee on top, so a footing this size is a bag job. An 80 lb bag of pre-mix yields about 0.6 ft³, and 2.18 divided by 0.6 is 3.6, so buy 4 bags and pick up a fifth.

Where cylinder volumes show up:

• Water heaters. A 50-gallon residential tank measures roughly 20" across and 60" tall on the outside, but that includes two inches of foam jacket and the top fittings. The steel tank inside is nearer 18" by 50", which is where the 50 gallons actually comes from.
• Propane tanks. A 100 lb tank holds 23.6 gallons of propane, filled to 80% because the rest has to stay vapor space.
• Hot tubs. Here the formula lies to you, usefully. A 7 ft round tub 36" deep is 115.5 ft³ of cylinder, which is 864 gallons. Real 6-person tubs of that size are rated near 380. The seats, the footwell step and the fact that nobody fills to the rim take away more than half the geometric volume. Trust the plate on the cabinet, not the cylinder.
• Pipe and tube contents. Sprinkler line, HVAC duct, beer line, fuel line.
• Silo and grain bin capacity. Steel grain bins are typically 15-50 ft diameter, 18-72 ft tall.
• Paint and chemical cans. A US gallon paint can is 6.5 in diameter × 7.5 in tall, which works out to 249 in³ against the 231 in³ in a gallon. The extra 8% is headspace for stirring.

Conversion shortcuts:

Common gotcha, diameter vs. radius:

People casually say “the pipe is 3 inches” without specifying whether that’s diameter or radius. For commercial pipe and tube, “nominal size” refers to a rough inside diameter, never the radius. Always halve it before squaring. A “4-inch pipe” has r = 2", not r = 4". Getting this wrong over-estimates volume by 4×, and it is the single most common mistake on this page.

Cylinder vs. sphere of the same diameter: A cylinder of diameter d and height d has volume (π/4) × d² × d = πd³/4 ≈ 0.785 × d³. A sphere of diameter d has volume (π/6) × d³ ≈ 0.524 × d³. So a sphere fills about two-thirds of the cylinder it just fits inside. Archimedes was proud enough of that result to ask for the figure on his tombstone.

Sanity check:

• h = 0: V = 0 (zero-height “cylinder” is a flat disc). ✓
• r = 0: V = 0 (zero-radius is a line). ✓
• r = h (cylinder as tall as it is wide): V = π × r³.