Cylinder Volume Calculator
Volume of a cylinder from its radius and height.
Input sheet
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Tanks, cans, pipes, and silos are cylinders, and their capacity depends on the radius of the circular end and the height. This computes the volume and the total surface area.
How it works
Volume is pi × radius² × height (base area times height).
A cylinder is a stack of identical circles, so its volume is simply the area of the circular base times the height. Surface area adds the two circular ends to the rectangular wall that wraps around them.
Volume scales with the square of the radius but only linearly with height, so a slightly wider tank holds far more than a slightly taller one of the same added dimension.
Volume = π × radius² × height; surface area = 2 × π × radius × (radius + height)
Worked examples
A cylinder with a radius of 3 and a height of 10. → ≈ 282.74 cubic units
π × 3² × 10 = π × 90 ≈ 282.74.
A water drum, radius 1 ft and height 3 ft. → ≈ 9.42 cubic feet
π × 1² × 3 = π × 3 ≈ 9.42 cubic feet, about 70 gallons.
Tips & gotchas
- Measure to the inside wall, not the outside, when you want the holding capacity rather than the displaced volume.
- To convert cubic feet to US gallons, multiply by about 7.48.
- Keep radius and height in the same unit; the volume comes out in that unit cubed.
FAQ
How do I find volume if I only know the diameter?
Halve the diameter to get the radius, then apply π × radius² × height. The radius is always half the diameter.
Why does width matter more than height for capacity?
Volume grows with the radius squared but only directly with height. Adding to the radius compounds, while adding to the height does not.
How do I convert the volume into liquid units?
Convert the cubic units first: one cubic foot ≈ 7.48 US gallons, and one liter equals 1,000 cubic centimeters.
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