Enter radius and height to calculate the surface area of a closed circular cylinder.
Cross-check every major cylinder measure and a material allowance.
| Measure | Value | Proof |
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Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
Use the interactive product above first. These notes add interpretation, verification and limits below the results and product controls.
The curved side is 2πrh, while two circular ends add 2πr². A tank label, sheet-metal wrap or open container may need only part of the total surface, so select the area that matches the physical job.
Entering a diameter as if it were a radius can produce a large mistake because circular area depends on r². Convert diameter to radius explicitly and keep the measurement label with the input.
A mathematical rectangle of circumference by height describes the curved side exactly, but fabrication may require overlap, kerf, hems or trim. Add those allowances separately rather than hiding them inside the geometric dimensions.
Surface area can be reported to many decimals even when radius and height were measured coarsely. Round the final material estimate to a precision supported by the measurements and the fabrication process.
For a closed cylinder, add the curved rectangle area 2πrh to the two circle areas 2πr². Recomputing those pieces separately is a useful way to catch a swapped dimension, unit conversion error or missing end cap before ordering material.
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