A cylinder is a circle extended straight up: two identical round ends joined by a curved side. Water heaters, rain barrels, silos, cans, columns and every length of pipe are cylinders, which makes this one of the most practical shapes to calculate. This cylinder calculator finds the volume, capacity in liters and US gallons, and every area, and it can also run backwards to find the height or radius that gives a required volume or area.
How to use the cylinder calculator
- Choose what you have under I know the: Radius and height, Diameter and height, Volume and radius (find the height), Volume and height (find the radius), Total surface area and radius (find the height) or Side (lateral) area and radius (find the height).
- Fill in the fields that appear: Radius (r), Diameter (d), Height (h), Volume (V) in cubic units, or Area in square units.
- Pick the Units. Everything is measured in that length unit.
- The headline is the volume, or the height or radius you asked for. The list shows radius, diameter, height, volume, capacity in liters and US gallons, lateral (side) area, area of each base, total surface area and base circumference.
Cylinder formulas
| Solving for | Formula |
|---|---|
| Height from volume | h = V ÷ πr2 |
| Radius from volume | r = √(V ÷ πh) |
| Height from total area | h = (S − 2πr2) ÷ 2πr |
| Height from lateral area | h = lateral area ÷ 2πr |
The lateral area is easy to picture: slit the side and unroll it into a rectangle whose width is the circumference, 2πr, and whose height is h. That rectangle is the size of a label for a can.
Worked example: a water tank
A round water tank is 4 ft across and 6 ft tall. How much does it hold, and how deep is 400 gallons?
- Choose Diameter and height, enter d = 4 and h = 6, units feet.
- Volume: π × 2² × 6 ≈ 75.40 ft³, which is about 564 US gallons or 2,135 liters.
- For the depth of 400 gallons, work in inches, because a gallon is exactly 231 in³: 400 × 231 = 92,400 in³.
- Choose Volume and radius (find the height), enter r = 24 in and V = 92,400 in³.
- Height: 92,400 ÷ (π × 24²) ≈ 51.06 in, about 4 ft 3 in of water.
Gallons per foot of pipe
A pipe is a long, thin cylinder, so the water it holds per foot is π(D ÷ 2)² × 12 ÷ 231 gallons for an inside diameter D in inches. That simplifies to about 0.0408 × D². Useful when you are draining, filling or treating a run of pipe:
| Inside diameter | Gallons per foot | Liters per foot |
|---|---|---|
| 1/2 in | 0.0102 | 0.0386 |
| 3/4 in | 0.0229 | 0.0869 |
| 1 in | 0.0408 | 0.1544 |
| 1 1/2 in | 0.0918 | 0.3475 |
| 2 in | 0.1632 | 0.6178 |
| 3 in | 0.3672 | 1.3900 |
| 4 in | 0.6528 | 2.4711 |
| 6 in | 1.4688 | 5.5600 |
Nominal pipe sizes are labels, not measurements: a “1-inch” pipe’s bore can be noticeably larger or smaller than 1 in depending on material and wall schedule. Use the real inside diameter. To check a single length, choose Diameter and height, enter the bore as the diameter and the pipe length as the height. For the metal in the pipe wall, use the tube calculator.
The most economical can
For a fixed volume, the cylinder with the least total surface area has a height equal to its diameter. For 1,000 cm³ that is a radius of about 5.42 cm and a height of 10.84 cm, using 553.6 cm² of material. A slimmer can with a 4 cm radius needs to be 19.89 cm tall and uses 600.5 cm², about 8% more. Real cans often depart from the ideal because their ends are made of thicker metal and the shape has to suit hands and shelves, but the rule is a good starting point for any container you design.
Common mistakes
- Using the diameter as the radius. The volume comes out four times too large.
- Mixing units. A radius in inches and a height in feet gives nonsense; convert one first.
- Entering gallons or liters as the volume. Convert to cubic units: 1 gal = 231 in³, 1 L = 1,000 cm³.
A cone with the same base and height holds exactly one third as much; see the cone calculator.
Frequently asked questions
What is the formula for the volume of a cylinder?
V = πr²h: the area of the circular base times the height. A cylinder 3 in in radius and 8 in tall holds π × 9 × 8 ≈ 226.19 in³, just under one US gallon.
How many gallons are in a cylindrical tank?
Work out the volume in cubic inches and divide by 231, since a US gallon is exactly 231 in³; for cubic feet, multiply by about 7.4805. The calculator shows the capacity in gallons and liters automatically for any unit you choose.
How do I find the height of a cylinder from its volume?
Divide the volume by the base area: h = V ÷ πr². Choose 'Volume and radius (find the height)', enter both, and the calculator solves it. Make sure the volume is in cubic units of the same length unit as the radius.
Does the total surface area include the top and bottom?
Yes. Total surface area is the side plus both circular ends, 2πrh + 2πr². If your cylinder is open at one end, like a cup or an open tank, subtract one base area, which the calculator lists separately.
Why do I get four times the volume when I use the diameter?
The radius is squared in πr²h, so using the diameter (twice the radius) multiplies the volume by four. If you only know the diameter, choose 'Diameter and height' and the calculator halves it for you.