How to use the cylinder volume calculator
- Choose the Unit of length. Inches are selected to start.
- Under Measure the circle by pick Radius or Diameter. Tank and pipe sizes are usually diameters. Switching keeps the same cylinder by doubling or halving your number.
- Enter the Radius (r) or Diameter (d) and the Height (h). For a tank lying on its side, the height is its length.
- Read the Volume, the same volume in liters, US gallons, cubic feet and cubic meters, and the base area, circumference and surface areas.
The formulas
V = π × r² × h
The base is a circle of area πr², stacked h high. The curved side unrolls into a rectangle, so the lateral area is 2πrh, and the total surface area adds the two ends: 2πr² + 2πrh (MathWorld). Gallons use the exact US definition, 1 US gallon = 231 cubic inches = 3.785411784 liters (NIST SP 811, Appendix B.8).
Worked example
The calculator opens with r = 3 inches and h = 10 inches. V = π × 3² × 10 = 282.7433 in³. That is 4.6333 liters or 1.224 US gallons (282.7433 ÷ 231). The base area is 28.2743 in², the lateral area is 188.4956 in² and the total surface area is 245.0442 in².
Limits and edge cases
- The result is for a full cylinder. An upright tank filled to a depth holds depth ÷ height of the total, but a tank on its side does not fill in proportion to depth, so this page cannot give that.
- Capacity uses inside measurements. Tank and pipe sizes are often quoted on the outside, so subtract the wall thickness twice from a diameter.
- Gallons are US gallons. An imperial gallon is about 20% bigger.
- Every number must be greater than 0 and at most 1,000,000,000,000. Thousands commas are fine; use a period for decimals.
- A ball is on the sphere volume calculator and a box on the cube and box volume calculator. Other unit swaps are quick in the volume converter, and the concrete calculator starts from the same volume for a round column.
Cylinder volume FAQ
How do I find the volume of a cylinder from its diameter?
Halve the diameter to get the radius, then use V = π × r² × h. A tank 48 inches across and 60 inches tall has r = 24, so V = π × 24² × 60 = 108,573.4421 cubic inches. In one step, V = π × d² × h ÷ 4.
How many gallons does a cylindrical tank hold?
Find the volume in cubic inches and divide by 231, because one US gallon is 231 cubic inches. The 48 by 60 inch tank above holds 108,573.4421 ÷ 231 = 470.0149 US gallons.
How do I convert a cylinder's volume to liters?
Convert the volume to cubic centimeters and divide by 1,000, or to cubic meters and multiply by 1,000. Pick your unit in the calculator and read the Liters row. The starting 282.7433 cubic inches is 4.6333 liters.
What is the surface area of a cylinder?
The total surface area is 2πr² + 2πrh: two circular ends plus the curved side. The lateral area, 2πrh, leaves out the ends. For r = 3 and h = 10 the lateral area is 188.4956 and the total is 245.0442 square units.
How do I find the volume of a pipe wall or any hollow cylinder?
Subtract the inside from the outside: V = π × (R² − r²) × h, with R the outer radius and r the inner radius. With R = 3, r = 2 and h = 10 the material volume is 157.0796. To find how much a pipe holds, enter its inside diameter and its length.
Sources: Wolfram MathWorld, Cylinder; NIST Special Publication 811, Appendix B.8.