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.