Cylinder Surface Area Calculator
From a radius and a height, get the total surface area, the lateral (side) area, and the base area — the numbers behind the metal in a can or the paper in a label.
Two inputs, three areas
Enter the base radius and the height and the calculator returns the total surface (2πr² + 2πrh), the lateral side (2πrh), and the base area (πr²) at once.
Keep units consistent
The radius and height are unit-agnostic — every answer comes back in square units of the same length unit, so don't mix centimetres with inches.
What is a cylinder surface area calculator?
Radius and height in, full surface out
A cylinder surface area calculator turns two measurements — the base radius and the height — into the areas that describe a closed right circular cylinder: the whole outside (total surface area), the curved wall on its own (lateral surface area), and one flat circular end (base area). Each is fixed once you know the radius and height, because every cylinder shares the same constant π (pi). That makes those two inputs all you need to estimate the metal in a can, the paper for a wrap-around label, the paint for a tank, or the answer to a geometry problem.
Enter the radius and height in any length unit to get the total, lateral, and base surface area instantly.
The surface area of a closed cylinder is the curved side plus the two circular ends, all built from the radius, the height, and the constant π (about 3.14159).
total = 2 × π × r² + 2 × π × r × hThe lateral (side) area is 2 × π × r × h — the label that wraps around a can. The base area is π × r² for a single circular end. Because a cylinder has two identical ends, the total surface adds twice the base area to the lateral area: total = 2πrh + 2πr².
Suppose you have a cylinder with a radius of 3 and a height of 5.
Lateral surface
2 × π × 3 × 5 = 94.247780 square units — the curved wall, the wrap-around label.
Base area
π × 3² = 28.274334 square units — one circular end (there are two).
Total surface
94.247780 + 2 × 28.274334 = 150.796447 square units — the whole outside.
The three outputs answer three different everyday questions. The lateral surface area (about 94.247780 square units for r = 3, h = 5) is the curved side on its own — exactly the area that wraps around a can, so it is the figure to use when sizing a label or estimating the paper for a tube. The base area (about 28.274334 square units) is one flat circular end; a cylinder has two of them, which is why the total adds twice the base to the side. The total surface area (about 150.796447 square units) is the whole outside — the right number for the metal in a sealed can, the paint for a tank, or material for a closed package. The key insight is how the shape drives the numbers: a taller cylinder adds only side area, because the height appears just in 2πrh, while a wider cylinder grows both the side and the two caps, and the caps scale with r², so widening adds area fastest. π is the thread tying it all together — the same constant links the radius and height to every area of the cylinder, large or small.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Closed right circular cylinders and consistent units
These formulas describe a closed right circular cylinder — a circular cross section with both ends sealed and the wall perpendicular to them. An open tube (no lids), an oblique cylinder (slanted), or a real object with rims, seams, or rounded edges will differ from the computed value; for an open tube use just the lateral surface, or add one base for a cup. The radius and height are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a radius and height in centimetres give every area in square centimetres, never a mix.