What Is a Cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. The most common type is the right circular cylinder, where the sides are perpendicular to the bases. You encounter cylinders every day in cans, pipes, drinking glasses, and batteries. The volume of a cylinder depends on the area of its circular base and its height, while the surface area includes both circular ends and the curved wall connecting them.
Understanding cylinder geometry is essential in engineering, manufacturing, and fluid dynamics. A water tank's capacity, a pipe's flow rate, and a can's material requirements all depend on cylinder calculations. For the base circle properties, see our Circle Calculator.
What This Calculator Does
This cylinder calculator takes a radius and height and computes four key properties: volume, total surface area, lateral surface area, and base area. It also shows the circumference of the base and the formulas used with the substituted values.
- Inputs: Radius (r) and height (h) of a right circular cylinder
- Outputs: Volume, total surface area, lateral surface area, base area, and circumference
How the Calculation Works
Volume: V = πr²h
Total Surface Area: SA = 2πr(r + h)
Lateral Surface Area: LSA = 2πrh
Base Area: A = πr²
The volume is the base area multiplied by the height, which makes intuitive sense: you are stacking circles on top of each other. The total surface area adds the two circular bases (2 × πr²) and the lateral wall (2πrh). The lateral surface area alone, without the bases, is what you would need to label or wrap the side of a can. For general 3D volume calculations, try our Volume Calculator.
Example Calculation
Example: A cylindrical water tank has a radius of 5 feet and a height of 10 feet. The volume is π × 5² × 10 = π × 250 ≈ 785.4 cubic feet, which holds about 5,875 gallons. The total surface area is 2π × 5 × (5 + 10) = 2π × 75 ≈ 471.2 square feet, telling you how much material is needed to build the tank. The lateral surface area is 2π × 5 × 10 ≈ 314.2 square feet.
Real-World Applications
Cylinder calculations are used in plumbing to size pipes, in packaging to design cans and bottles, in construction to estimate concrete for pillars, and in engineering to design pressure vessels. The lateral surface area determines how much paint or label material is needed, while the volume determines capacity. For surface area of other shapes, see our Surface Area Calculator.