How to use this calculator
- Enter or choose i know the.
- Enter or choose radius or diameter.
- Enter or choose height.
- Enter or choose length unit.
- The total surface area (closed) updates as you type. Use Copy result or Share to keep it.
Method
Lateral = 2πrh; End = πr²; Total = 2πrh + 2πr² = 2πr(r + h); Open top = 2πrh + πr²
- r
- radius (half the diameter)
- h
- height
Worked example
- Lateral = 2π × 3 × 10 = 60π ≈ 188.495559 cm².
- Each end = π × 3² = 9π ≈ 28.274334 cm².
- Total = 60π + 18π = 78π ≈ 245.044227 cm².
A closed cylinder 3 cm in radius and 10 cm tall has a surface area of about 245.04 cm².
What the result means
Use the lateral area for a label or pipe insulation, the open-top figure for a cup or tank without a lid, and the total for a sealed can.
Assumptions and limits
- A right circular cylinder: the sides are perpendicular to circular ends.
- Sheet thickness, seams and overlaps are ignored.
- For material orders, add an allowance for seams and waste.
Questions
Why is the curved area 2πrh?
Unroll the side and it is a rectangle whose width is the circumference 2πr and whose height is h.
How does a pipe with no ends work?
Use the lateral area only; for the inside and outside of a thick pipe, use each radius separately.