Cylinder surface area calculator

What is a cylinder surface area calculator?

A cylinder surface area calculator finds the total area covering a right circular cylinder. That area is the sum of three pieces: the two flat circular ends (the top and the bottom) and the curved side that wraps around the cylinder between them. Knowing the surface area is useful whenever you need to coat, wrap, or paint a cylindrical object, or estimate the material needed to build one.

You enter the radius of the base and the height of the cylinder, and the calculator returns the total surface area in the units you choose. Inputs accept any common unit of length, and the output is given in the matching square unit.

Key concepts

• Radius (r) — the distance from the center of the circular base to its edge.
• Height (h) — the perpendicular distance between the two parallel circular bases.
• Lateral surface — the curved side of the cylinder. If you unroll it, it becomes a flat rectangle whose width is the circumference of the base ($2\pi r$) and whose height is $h$.
• Total surface area (A) — the sum of the two circular ends and the lateral surface.

How does the calculator work?

The total surface area can be decomposed into two clearly visible pieces:

• Two disks at the ends, each with area $\pi r^2$, give a combined area of $2\pi r^2$.
• One rectangle, obtained by unrolling the curved side, with dimensions $2\pi r \times h$, has area $2\pi r h$.

Adding them together gives the formula used by the calculator.

Formula

Where:

• $A$ is the total surface area.
• $r$ is the radius of the base.
• $h$ is the height of the cylinder.

Worked examples

Example 1: r = 5 cm, h = 10 cm

Example 2: r = 3 cm, h = 7 cm

Example 3: r = 1 cm, h = 1 cm

Example 4: r = 10 cm, h = 0 cm (two disks only)

When the height drops to zero, the lateral piece disappears and only the two circular faces remain:

Practical uses

• Manufacturing and packaging — estimating the material needed for cans, tubes, drums, or cylindrical containers.
• Painting and coating — figuring out how much paint, primer, or insulation is required to cover a tank or pipe.
• Heat transfer — surface area is a direct input to many heat-loss and cooling calculations for cylindrical components.
• Sheet-metal work — laying out a flat blank that, when rolled, becomes the lateral side of a cylinder.
• Storage and labeling — sizing a wraparound label that fits exactly around a bottle or jar.

Notes

• The formula above is for a closed cylinder. For an open cylinder (no top, or no bottom), subtract one $\pi r^2$; for a tube open at both ends, subtract $2\pi r^2$ and only the lateral area remains.
• Radius and height must both be non-negative. A zero height collapses the lateral side and leaves the two disks; a zero radius collapses the whole shape to a line.
• The units of the inputs determine the unit of the result: a radius and height in metres give an area in square metres. The unit selectors handle the conversion automatically.
• For the volume of the same cylinder, see the cylinder volume calculator.