Cylinder Volume Calculator
Type the radius and height of a right circular cylinder — the calculator returns volume, base area, lateral (curved) surface and total surface, all using exact π.
Volume (V = π·r²·h)
282.743339 cubic units
- Diameter (d = 2r)
- 6
- Base area (π·r²)
- 28.27
- Lateral surface (2π·r·h)
- 188.5
- Total surface (2π·r² + 2π·r·h)
- 245.04
A right circular cylinder has volume V = π·r²·h — the area of the circular base times the height. Total surface area combines the two circular ends (2·π·r²) with the curved side (2·π·r·h).
How to use this calculator
Type the radius of the circular base (r) and the height of the cylinder (h) in any linear unit you like — centimetres, metres, inches or feet — and stay consistent between the two. The calculator returns the volume in cubic units of that unit, alongside the diameter, base area, lateral (curved) surface and total surface area. Linear outputs use the same unit, areas use squared units, and the volume uses cubed units.
How the calculation works
A right circular cylinder is defined by two numbers: the radius r of its circular base and the height h between the two flat ends. The base is a circle, so its area is π·r². Stacking that base through a height h gives the volume V = π·r²·h — the same formula as "base area × height" for any prism. The curved side, if you unrolled it flat, is a rectangle of width 2π·r (the base circumference) and height h, so its area is 2π·r·h. Adding the two circular ends (2·π·r²) gives the total surface area 2π·r² + 2π·r·h. π is taken at full machine precision (~16 significant figures), so rounding happens only at display.
Worked example
Take a cylinder with r = 3 and h = 10. Base area = π·3² = 9π ≈ 28.274334. Volume = 9π·10 = 90π ≈ 282.743339 cubic units. Lateral surface = 2π·3·10 = 60π ≈ 188.495559 square units. Total surface = 2·9π + 60π = 78π ≈ 245.044227 square units. If your r and h are in centimetres, the volume is in cm³ (millilitres); in metres, m³; in inches, in³ (1 in³ ≈ 16.387 mL).
Frequently asked questions
What is the formula for the volume of a cylinder?
V = π·r²·h, where r is the radius of the circular base and h is the height (the perpendicular distance between the two flat ends). This is just "base area times height" — the same rule that gives the volume of any prism — applied to a circular base of area π·r².
What is the difference between lateral and total surface area?
The lateral surface area is the curved side of the cylinder only — the rectangle you would get if you unrolled the side flat. Its area is 2π·r·h. The total surface area also includes the two circular ends, each of area π·r², so total = 2π·r·h + 2π·r². Use lateral when you are wrapping a label around a can; use total when you are painting or coating the whole thing.
Does this work for an oblique cylinder?
The volume formula V = π·r²·h still holds for an oblique cylinder as long as h is the perpendicular height between the two parallel circular ends, not the slant length. The surface-area formulas in this calculator assume a right cylinder, where the side is at 90° to the base — for an oblique cylinder the lateral surface is no longer a simple 2π·r·h rectangle.
How do I convert the volume to litres or gallons?
If your radius and height are in centimetres, the volume comes out in cubic centimetres, and 1 cm³ = 1 millilitre, so divide by 1000 to get litres. In metres, the volume is in m³ and 1 m³ = 1000 litres. For US gallons, 1 US gallon ≈ 3.78541 litres; for UK gallons, ≈ 4.54609 litres. Use the Volume Converter for any other unit pair.
Can I use the diameter instead of the radius?
Many real-world cylinders (pipes, cans, tanks) come labelled with the diameter rather than the radius. The radius is just half the diameter — r = d/2 — so divide your diameter by 2 before typing it in. For a pipe with internal diameter 50 mm, use r = 25 mm.
Why is π used at full precision?
π is irrational, so any short form (3.14, 3.1416, 22/7) introduces small errors that grow when you chain calculations. JavaScript's Math.PI gives about 16 significant figures — far more than any physical measurement of a real cylinder will ever need. Using full precision means the volume of a 1 m radius, 1 m tall cylinder is reported as 3.141593 m³ rather than the slightly-off 3.14 m³ you would get from a school-textbook approximation.