Cylinder Volume Calculator
Compute cylinder volume from radius and height.
For water tanks, pipe contents, paint cans, and silos.
With unit conversion to liters and gallons.
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 ≈ 12,539 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. Order 0.1 cubic yards from the plant (concrete is sold in 0.25 yd³ increments) or buy 4 bags of pre-mix at 0.6 ft³ each.
Where cylinder volumes show up:
- Water heaters. A typical residential tank is 40-50 US gallons, roughly 18-20" diameter × 50-60" tall.
- Propane tanks. A 100 lb tank holds 23.6 gallons of propane at 80% fill — the rest is vapor space.
- Hot tubs. A round 6-person tub at 7 ft diameter × 36" deep holds about 380 gallons.
- 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.
Conversion shortcuts:
| Convert | Formula |
|---|---|
| in³ → US gallons | ÷ 231 |
| in³ → liters | × 0.01639 |
| ft³ → US gallons | × 7.481 |
| ft³ → liters | × 28.32 |
| cm³ → mL | × 1 (same number) |
| m³ → liters | × 1,000 |
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” usually refers to a rough inside diameter — not 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×.
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 fits about two-thirds of the bounding cylinder — Archimedes’ famous discovery.
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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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