Cylinder volume and surface area
A cylinder is a circle given height — a can, a pipe, a tank. From the radius and height this calculator returns the volume, the curved lateral surface, the total surface including both ends, and the base area and circumference.
The formulas
Volume = pi times radius squared times height — the base area carried up the height. The lateral surface is 2 pi r h, which is the base circumference times the height, as if you unrolled the side into a rectangle. Total surface adds the two circular ends: 2 pi r squared plus 2 pi r h.
Unrolling the side
The curved wall, cut and flattened, is a rectangle as tall as the cylinder and as wide as the base circumference. That is why the lateral area is simply circumference times height — a useful check when sizing labels or wraps.
Related geometry tools
For the circular base on its own, use the circle calculator; for a tapering version, the cone calculator.
Worked example
A radius of 3 and height of 10 give a volume of pi times 9 times 10, about 282.7, with a lateral surface of about 188.5 and a total surface of about 245.
FAQ
What if I only need the liquid capacity?
That is the volume — pi r squared h. Convert cubic units to liters or gallons afterward as needed.
Does wall thickness matter?
These formulas treat the cylinder as a solid or thin-walled shape. For a thick pipe, subtract the inner cylinder from the outer.