Quick answer: the volume of a cylinder is V = π r² h, which is 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, with 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.
Solve a cylinder from any two measurements
Choose the pair you have, including the circumference from a tape wrapped around a tank or the volume printed on a can, and the solver returns the rest.
Cylinder solver: any two measurements
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Pick the pair you know. The solver returns the radius, diameter, circumference, height, volume and surface areas.
Find the height from the volume
Use h = V ÷ (πr²). A 2-litre (2,000 cm³) jug with a 6 cm radius needs a height of 2,000 ÷ (π × 36) = 17.7 cm. For the radius instead, use r = √(V ÷ (πh)).
Hollow cylinder (pipe or tube wall)
Subtract the inner cylinder from the outer one: V = π(R² − r²)h, where R is the outer radius and r the inner radius. A pipe 10 cm across the outside and 8 cm across the inside, 1 m long, has π × (25 − 16) × 100 = 2,827 cm³ of material. The space inside that pipe holds π × 16 × 100 = 5,027 cm³, or 5.03 litres; the pipe volume calculator covers that side of the problem.
Oblique (slanted) cylinder
A cylinder leaning to one side holds the same volume as an upright one with the same base and perpendicular height, so V = πr²h still applies. Measure h straight up from the base, not along the slanted side. This follows from Cavalieri's principle: every horizontal slice keeps the same circular area.
Cylinder surface area
The curved side unrolls into a rectangle of 2πr × h, and the two ends add 2πr². The total is 2πr(r + h). A can 7.5 cm across and 11 cm tall uses 259.2 cm² of side plus 88.4 cm² for the ends, 347.5 cm² in all.
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.
How do you find the volume of a hollow cylinder?
Subtract the inner cylinder from the outer one: V = π(R² − r²)h. A tube with a 5 cm outer radius, a 4 cm inner radius and a 100 cm length contains π × 9 × 100 = 2,827 cm³ of material.
How do I find the height of a cylinder from its volume?
Divide the volume by the base area: h = V ÷ (πr²). A 2,000 cm³ container with a 6 cm radius is 2,000 ÷ 113.1 = 17.7 cm tall. Keep the volume and radius in matching units, such as cm³ and cm.