The cylinder volume formula
The volume of a cylinder is the area of its circular face times its length, and the cylinder volume formula people reach for is V = π r² h, with r the radius and h the height. If you have the diameter instead, the same circular volume formula is V = (π ÷ 4) d² h, because the radius is half the diameter. That is the whole formula for calculating the volume of a cylinder — a cylindrical volume calculation is just a circle area carried along a length. Keep the radius and height in the same units and the raw answer is in that unit cubed, which the calculator converts into every capacity unit for you. This one formula handles a vertical tank, a barrel on end, or any straight round container.
Calculating the volume of a cylindrical tank
The volume of a cylindrical tank is π × r² × height — written V = π r² h, the radius squared, times π, times the height. Keep the radius and height in the same length unit and the raw answer comes out in that unit cubed, which this tank volume calculator converts into litres, US and UK gallons, cubic metres and more. That one formula gives the full cylindrical tank capacity of any upright vessel — a water tank, a fuel tank, or a drum stood on end — so a single set of dimensions returns the water tank capacity in every common unit at once. Tanks lying on their side need a different sum: a horizontal tank filled partway holds its liquid in a circular segment rather than a flat fraction of the total, so partial fills are handled in their own section below. Enter the diameter and height to read the capacity instantly.
Tank capacity in gallons and litres
Once you have a volume in one unit, the conversions to capacity are exact — no rounding:
| From | Equals |
|---|---|
| 1 US gallon | 231 cubic inches |
| 1 UK (imperial) gallon | 277.4194 cubic inches |
| 1 cubic foot | 1728 cubic inches |
| 1 cubic yard | 27 cubic feet |
| 1 cubic inch | 16.387064 cubic centimetres |
| 1 litre | 1000 cubic centimetres |
| 1 cubic metre | 1,000,000 cubic centimetres |
The catch most people meet is that a US gallon and a UK gallon are different sizes — the imperial gallon is about 20 % larger — so this circular tank capacity calculator always shows both, alongside litres, cubic metres, cubic feet, cubic inches and cubic yards. Want to know the cubic yards in a cylinder, or how many gallons in a cylinder of a given size? Enter the diameter and height and read every figure at once.
Horizontal tanks and partial fill
A horizontal cylinder is where the simple calculators go wrong. Because the cross-section is a circle, the volume does not grow evenly with depth: at the bottom each inch adds a thin sliver, the area grows fastest through the middle, then tapers near the top. The volume of a horizontal cylinder tank, partly full to a liquid depth h, comes from the area of the circular segment the liquid fills:
r = d ÷ 2
A = r² · arccos((r − h) ÷ r) − (r − h) · √(2rh − h²)
Vshell = A × L
so a half-full (centreline) tank holds exactly half, but a quarter-deep tank holds far less than a quarter. The horizontal tank volume calculator here applies that segment area directly and reports the liquid volume, the total capacity, the percent full and the ullage (the empty space above the liquid).
End caps: flat, hemispherical and elliptical
Curved heads stick out past the straight shell and add real capacity that flat-end calculators miss. For both ends combined at liquid depth h:
hemispherical = (π h² ÷ 3)(3r − h) [full = (4/3)πr³]
2:1 elliptical = (π h² ÷ 3)(3r − h) × 0.5 [full = (2/3)πr³]
flat = 0
Two hemispherical heads together make a full sphere, adding about a third of the shell volume; two 2:1 semi-elliptical heads add about a sixth. Pick the head type and the tool folds the matching filled portion of the ends into both the capacity and the partial-fill reading. This covers the drum volume, the hemispherical-end and elliptical-tank cases people search for.
Hollow cylinders and tubes
The volume of a tube, pipe wall or annulus is the outer cylinder minus the inner bore:
V = (π ÷ 4)(D² − d²) h
with D the outside diameter, d the inside diameter and h the length. That hollow cylinder volume is the material in a tube or the gap in a jacketed vessel. It is the volume-of-a-hollow-pipe formula — the wall, not the bore. If you want the water a pipe carries, that is the bore, and the dedicated pipe volume calculator is the right tool.
Cones and spheres
For a complete set of round shapes, a cone is one-third of its bounding cylinder, V = (1 ÷ 3) π r² h, handy for conical tank bottoms and hoppers, and a sphere is V = (4 ÷ 3) π r³. Between the vertical and horizontal cylinder, the hollow tube, the oval tank, the cone and the sphere, this covers the volume of cylinders, cones and spheres in one calculator.
A worked example
A horizontal tank, 48″ diameter and 120″ shell, with 2:1 elliptical ends, filled to 24″ (the centreline):
- Shell, half full = ½ × (π ÷ 4) × 48² × 120 ≈ 108,573 in³.
- Both elliptical ends, half full = (π × 24² ÷ 3)(3×24 − 24) × 0.5 ≈ 14,476 in³.
- Liquid ≈ 123,050 in³ ≈ 533 US gallons (about 2016 litres), exactly half the full capacity at the centreline.
Find or measure the volume of a cylinder
To find the volume of a cylinder you only need two measurements: the diameter (or radius) and the height or length. Measure the inside diameter if you want the capacity it holds; measure carefully, since the diameter is squared and a small error doubles in the answer. For a horizontal tank, also measure the liquid depth from the inside bottom. For US and UK readers alike, “litre” and “liter”, “metre” and “meter”, and “cubic centimetre” and “cc” are the same thing; the arithmetic is identical and only the spelling of the unit changes.