Cylinders show up everywhere from soda cans to septic tanks to steel pipe, and the same three formulas — volume, total surface area, and lateral area — answer almost every practical question about one. This calculator handles all three, plus the reverse problem of sizing a cylinder to a target capacity.
How the formulas work
A right circular cylinder is built from two congruent circles (the bases) connected by a curved surface. Volume follows directly from the area of one circular base (πr²) multiplied by how far that base extends through the height: V = πr²h. Surface area adds the area of both circular bases (2πr²) to the area of the curved side unrolled flat into a rectangle (2πrh, where 2πr is the circle's circumference and h is the rectangle's other side). Lateral area is just that second piece by itself.
Inputs and what they mean
Radius (r) is the distance from the center of a base to its edge — half the diameter. Height (h) is the distance between the two bases. Both must use the same unit (inches, feet, centimeters, or meters); the calculator does not convert between mismatched units automatically. Radius has an outsized effect on volume because it's squared in the formula — a small measurement error in radius distorts the volume far more than the same error in height.
Limits and edge cases
These formulas assume a right circular cylinder — bases perpendicular to the axis, not an oblique or elliptical cylinder. For a tank or pipe with wall thickness, decide whether you need internal capacity (use the inner radius) or external material volume (use the outer radius minus the inner). When solving for radius from a known volume and height, only positive real solutions are returned; a negative or zero volume, or a zero/negative height, has no valid cylinder and the calculator reports no solution.