Quick answer: the volume of a cylinder is V = π r² h — pi times the radius squared times the height. If you have the diameter instead, halve it first (or use V = π d² h / 4). Measurements in feet give cubic feet; multiply by 7.4805 for US gallons.
The cylinder volume formula, step by step
A cylinder is a circle extended straight upward, so its volume is the area of that circle multiplied by the height:
where π ≈ 3.14159 · r = radius of the circular end · h = height (or length)
Worked example — a cylinder with radius 3 and height 5:
- Square the radius: 3² = 9
- Multiply by π: 9 × 3.14159 = 28.274 (that's the base circle's area)
- Multiply by the height: 28.274 × 5 = 141.37 cubic units
The units follow your measurements: centimeters in, cm³ out; feet in, ft³ out. Because the radius is squared, it dominates the result — a cylinder twice as wide holds four times as much, while one twice as tall holds only twice as much. That's why a short, wide tank so often out-holds a tall, narrow one that looks bigger.
How to use this calculator
- Choose Radius or Diameter in the first field's menu. Pipes, tanks and drums are usually labeled by diameter; the calculator halves it for you.
- Enter the height — or the length, if the cylinder is lying on its side. Its unit can differ from the radius unit.
- Pick your output unit. Cubic feet for construction, liters for lab work, gallons for tanks — switching converts the same result, no re-entry.
- Verify with the formula bar, which shows your numbers substituted into V = πr²h, ready to copy into homework or a work order.
Cylinder capacity by diameter — quick reference
Contractors and tank owners often just need "how much per foot of height." This table gives the volume of one vertical foot of cylinder at common diameters:
| Diameter | ft³ per ft of height | US gal per ft | Liters per ft |
|---|---|---|---|
| 1 ft (12 in) | 0.785 | 5.88 | 22.24 |
| 2 ft (24 in) | 3.142 | 23.50 | 88.96 |
| 3 ft (36 in) | 7.069 | 52.88 | 200.2 |
| 4 ft (48 in) | 12.566 | 94.00 | 355.8 |
| 5 ft (60 in) | 19.635 | 146.9 | 556.0 |
| 6 ft (72 in) | 28.274 | 211.5 | 800.6 |
| 8 ft (96 in) | 50.265 | 376.0 | 1,423 |
| 10 ft (120 in) | 78.540 | 587.5 | 2,224 |
Multiply the per-foot figure by your cylinder's height. A 4-ft-diameter tank standing 6 ft tall holds 94.00 × 6 ≈ 564 gallons.
Where cylinder volume shows up in real life
Sizing a rain barrel or drum
A standard 55-gallon drum measures about 22.5 in across and 33.5 in tall. Check it: r = 11.25 in, so V = π × 11.25² × 33.5 ≈ 13,320 in³, and at 231 in³ per gallon that's 57.7 gallons — the "55" is the nominal fill, with headspace left on top.
Water in a length of pipe
Pipe is just a long, thin cylinder. A 100-ft run of 2-inch (inside diameter) pipe: r = 1 in = 0.0833 ft, V = π × 0.00694 × 100 ≈ 2.18 ft³ ≈ 16.3 gallons. The pipe volume calculator has per-foot tables for every standard pipe size, and the tube calculator handles the wall material itself.
Concrete in a round footing
A sonotube 12 in across and 4 ft deep: r = 0.5 ft, V = π × 0.25 × 4 = 3.14 ft³ — about 0.116 cubic yards, or roughly five 80-lb bags of concrete per tube. The concrete volume calculator converts straight to bags and yards.
Common mistakes & pro tips
- Diameter entered as radius. The classic. It inflates the result 4×. If the number came off a label or a tape measure across the top, it's almost certainly a diameter — use Diameter mode.
- Mixed units without converting. A radius in inches and a height in feet can't go into the formula together. This calculator converts per field automatically; on paper, convert everything to one unit first.
- Measuring the outside of a container. For capacity (what fits inside), measure inside dimensions. On a thick-walled vessel the difference is real — subtract twice the wall thickness from the outer diameter.
- Pro tip — no ruler across a tank? Wrap a tape around it: radius = circumference ÷ 2π. A tank measuring 12.57 ft around has a radius of exactly 2 ft.
- Pro tip — partial fills aren't proportional on their side. A horizontal tank at a quarter of its diameter holds ~20% of capacity, not 25%. Use the tank calculator's fill-level mode.
Frequently asked questions
How do you find the volume of a cylinder with the diameter?
Divide the diameter by 2 to get the radius, then apply V = πr²h. Equivalently, V = π d² h / 4. For example, a cylinder 10 cm across and 20 cm tall has V = π × 5² × 20 = 1,570.8 cm³. This calculator has a Diameter mode that does the halving for you.
How do I calculate cylinder volume in gallons?
Compute the volume in cubic feet with V = πr²h (dimensions in feet), then multiply by 7.4805 gallons per cubic foot. A tank 2 ft in radius and 5 ft tall holds π × 4 × 5 = 62.83 ft³ ≈ 470 US gallons. Or simply select US gal as the output unit here.
How many liters are in a cylinder?
Work in centimeters: V = πr²h gives cubic centimeters, and 1,000 cm³ = 1 liter. A cylinder with a 10 cm radius and 30 cm height holds π × 100 × 30 = 9,424.8 cm³ ≈ 9.42 liters.
What if I only know the circumference?
Divide the circumference by 2π (6.2832) to get the radius, then use V = πr²h. A tree trunk measuring 62.8 inches around has a radius of 62.8 ÷ 6.2832 ≈ 10 inches. Wrapping a tape measure around is often the most practical way to measure pipes, tanks and logs.
Does it matter if the cylinder is lying on its side?
Not for total volume — orientation doesn't change how much a cylinder holds, so use the length as h. It matters enormously for partial fills though: a horizontal tank filled to half its diameter is exactly half full, but at a quarter of its diameter it holds only about 20% of capacity. Use the tank volume calculator with fill-level mode for that.
What is the volume of a cylinder with radius 3 and height 5?
V = π × 3² × 5 = π × 45 = 141.37 cubic units. If the measurements were in centimeters the answer is 141.37 cm³; in feet it is 141.37 ft³, which is about 1,057.6 US gallons.