▯ • Reviewed 2026-11-05

Cylinder Without Top and Bottom

Separate lateral surface area, enclosed capacity and optional wall-material volume for an open cylindrical shell.

Quick answer

The short version

Removing the ends changes surface area but not the geometric space inside the side wall. Lateral area is 2πrh; wall material with thickness t is π[R² − (R−t)²]h.

Alateral = 2πrh; Vwall = π(R² − r²)h

Interactive tool

Calculate open cylinder walls

Values convert through SI units; displayed digits are rounded only at the end.

Vwall = π(R² − (R−t)²)h

r h inner r
Result
—cm³

Complete the fields to calculate.

How the result changes

Calculated from the current dimensions
How the result changesComplete the calculator to display a graph.
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Checked example

Worked calculation

Result: An open tube with radius 5 cm and height 20 cm has lateral area 200π ≈ 628.319 cm².

01 • Guide

Area is not capacity

Lateral surface area measures sheet material or label coverage. Capacity measures enclosed three-dimensional space. With both ends absent, the mathematical interior volume can be described, but the object cannot retain liquid by itself.

Keep the full precision of intermediate values and round only the final display. This avoids compounding error when a derived radius or converted unit is used in another step.

02 • Guide

Optional wall thickness

A physical tube wall has volume only when inner and outer radii differ. Enter outer radius and thickness; the calculator derives the inner radius and rejects a thickness larger than the radius.

The calculator validates physical limits before displaying a result. Blank or impossible inputs never produce a stale value, NaN or Infinity.

03 • Guide

Manufacturing allowances

Real sheet-metal work may need seam, bend and trim allowances. The geometric lateral area is a baseline, not a fabrication cut plan.

Interpretation

How to use the result responsibly

The answer models an ideal geometric cylinder. Manufacturing tolerances, wall thickness, rounded ends, deformation, tank tilt and measurement uncertainty can all shift a real value. Use inside dimensions for capacity and outside dimensions for occupied space. For safety, compliance, dosing, structural or purchasing decisions, compare the estimate with drawings, calibration data or a qualified professional.

Dimensional checks help catch mistakes: a volume result must carry cubic units, an area result square units and a derived radius or height linear units. If changing one unit alters the represented physical size, a conversion step was missed.

Clear answers

Open cylinder walls: common questions

Does removing the ends change πr²h?

It does not change the space geometrically bounded by extending the side, but an open tube cannot hold that volume of liquid.

What area is needed for the curved side?

The lateral area is circumference times height: 2πrh.

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