Cylinder Calculator
Enter radius and height to get a cylinder’s volume, total and lateral surface area, and base area — with every step shown.
A cylinder with radius r = 3 and height h = 10 has volume V = πr²h = π × 9 × 10 ≈ 282.7 cubic units and total surface area 2πr(r + h) = 2π × 3 × 13 ≈ 245.0 square units. Its lateral (side) area is 2πrh ≈ 188.5 and each circular base has area πr² ≈ 28.3.
What a cylinder calculator works out
A right circular cylinder is defined by just two numbers: the radius r of its circular base and its height h. From those, every other measurement follows. The volume tells you how much the cylinder holds; the surface area tells you how much material wraps around it. This tool reports all four at once — volume, total surface area, the lateral (curved side) area, and the area of one circular base.
volume = base area × height; total surface area = two bases (2πr²) + the side (2πrh)
Worked example
Take a cylinder with radius r = 3 and height h = 10:
- 1 Square the radius. r² = 3² = 9. This is the shape of the circular base.
- 2 Find the volume with V = πr²h. π × 9 × 10 = 90π ≈ 282.743 cubic units.
- 3 Find the lateral (side) area with 2πrh. 2 × π × 3 × 10 = 60π ≈ 188.496 square units — the label that wraps the side.
- 4 Add the two bases for total surface area. 2πr² + 2πrh = 2π × 3 × (3 + 10) = 78π ≈ 245.044 square units.
Volume and surface area for sample cylinders
Values use V = πr²h, lateral = 2πrh, and total = 2πr(r + h), rounded to 3 decimals.
| Radius r | Height h | Volume | Lateral area | Total area |
|---|---|---|---|---|
| 1 | 1 | 3.142 | 6.283 | 12.566 |
| 2 | 5 | 62.832 | 62.832 | 87.965 |
| 3 | 10 | 282.743 | 188.496 | 245.044 |
| 5 | 12 | 942.478 | 376.991 | 534.071 |
Lateral vs total surface area
Lateral surface area (2πrh) is only the curved side — imagine unrolling the label off a can into a flat rectangle whose width is the circumference 2πr and whose height is h. Total surface area adds the two circular ends, each πr², giving 2πr² + 2πrh = 2πr(r + h). Use lateral area for a label or a pipe that is open at both ends; use total area when the top and bottom are also covered, like a sealed tank.