Cylinder Volume Calculator

Volume is V = π × r² × h, where r is the radius of the circular base and h is the height. A cylinder is essentially a stack of identical circles, so its volume is the base area (π × r²) multiplied by the height. A cylinder with radius 3 in and height 10 in has volume π × 9 × 10 ≈ 282.74 in³.

Lateral surface area — the curved side only — is 2 × π × r × h. Imagine unrolling the side: it becomes a rectangle of width 2πr (the circumference) and height h. Total surface area adds the two circular ends: SA = 2πr² + 2πrh = 2πr(r + h). Use lateral when you only need the side (labels, paint on the body), and total when you need everything (heat loss, full powder coating).

A standard 50-gallon water heater has an inside diameter of about 18 in and an inside height of about 50 in. Radius = 9 in. Volume = π × 9² × 50 ≈ 12,723 in³ ≈ 55.1 gallons. The marketing 'capacity' is rounded down to the nearest 5-gallon increment because the top few inches are reserved for thermal expansion and the dip tube.

A 12 oz aluminum soda can has an outside diameter of 2.6 in and a height of 4.83 in (the famous '211 × 413' can spec). Internal radius is about 1.275 in once you subtract wall thickness. Volume = π × 1.275² × 4.7 ≈ 24.0 in³ ≈ 12.46 fl oz — the extra 0.46 oz is headspace for carbonation pressure. Lateral surface area is 2π × 1.3 × 4.83 ≈ 39.4 in², which is the printed-label area you see on the can.

1 US gallon = 231 in³. A 282.74 in³ cylinder holds about 1.22 US gallons.

1 liter = 1,000 cm³ = 61.024 in³. The same cylinder holds about 4.63 liters.

Water weight. 1 gallon of water weighs about 8.345 lb. A full 55-gallon drum of water weighs 459 lb plus the empty drum (about 40 lb for steel, 20 lb for poly). Forgetting this is the most common mistake in DIY rainwater harvesting plans — the elevated tank platform has to support far more than people guess.

Pipe volume. The volume of a pipe is identical to a cylinder's: π × r² × length. A 100 ft run of 1-inch copper pipe (inner radius about 0.4 in) holds π × 0.16 × 1,200 ≈ 603 in³ ≈ 2.61 gallons — what you have to drain before sweating a fitting.