Cylinder Volume and Surface Area Calculator
Compute the volume, total surface area, lateral area, or base area of a cylinder using its radius and height. Essential for engineering, manufacturing, and fluid capacity problems.
About this calculator
A cylinder consists of two circular bases connected by a curved lateral surface. Given base radius (r) and height (h), four properties can be calculated. Base Area: A_base = πr² (area of one circular end). Lateral (Side) Area: A_lateral = 2πrh (the curved surface, equivalent to unrolling it into a rectangle of width 2πr and height h). Total Surface Area (closed cylinder): A_total = 2πrh + 2πr² = 2πr(h + r). Volume: V = πr²h (base area times height). For an open cylinder (e.g., a tube), the total surface area omits the two base circles and equals only the lateral area. These formulas are used in calculating pipe capacities, paint coverage for cylindrical tanks, and material needed for cans or columns.
How to use
Consider a cylindrical can with a base radius of 4 cm and a height of 10 cm. Volume: V = π × 4² × 10 = π × 16 × 10 = 160π ≈ 502.65 cm³. Lateral Area: A_lateral = 2π × 4 × 10 = 80π ≈ 251.33 cm². Base Area: A_base = π × 4² = 16π ≈ 50.27 cm². Total Surface Area (closed): A_total = 251.33 + 2 × 50.27 ≈ 351.86 cm². Enter 4 for the radius, 10 for the height, select 'Closed Cylinder', and choose your desired calculation type to see the result.
Frequently asked questions
How do I calculate the volume of a cylinder from its radius and height?
Use the formula V = πr²h, where r is the base radius and h is the height. First compute the base area (πr²), then multiply by the height. For a cylinder with r = 3 m and h = 7 m, V = π × 9 × 7 ≈ 197.92 m³. This calculation is commonly used to determine the capacity of cylindrical tanks, silos, pipes, and storage vessels.
What is the difference between lateral surface area and total surface area of a cylinder?
The lateral surface area covers only the curved side of the cylinder, calculated as 2πrh. The total surface area adds the two circular bases: A_total = 2πrh + 2πr². The distinction matters practically — if you're painting only the outside of an open pipe, you need the lateral area; if you're wrapping a closed can entirely in material, you need the total surface area. This calculator lets you choose between open and closed cylinder types to get the correct value.
How does changing the radius versus the height affect a cylinder's volume?
Volume scales with the square of the radius (V = πr²h) but only linearly with height. This means doubling the radius quadruples the volume, while doubling the height only doubles it. For example, a cylinder with r = 2, h = 10 has V ≈ 125.66 units³, but increasing the radius to r = 4 (same height) gives V ≈ 502.65 units³ — four times more. This is why wide, short cylindrical tanks store significantly more than narrow, tall ones of the same height.