Calculate wall volume, inner volume, total surface area, wall thickness, and estimated weight of a hollow cylinder (pipe, tube, annular ring) from outer/inner radii and height.
A hollow cylinder — also called a cylindrical shell, annular cylinder, or simply a pipe — is a three-dimensional shape formed by removing a smaller concentric cylinder from inside a larger one. Hollow cylinders are everywhere in engineering: water pipes, structural tubes, hydraulic cylinders, smoke stacks, bearings, and pressure vessels.
The volume of the wall material is V = π(R² − r²)h, where R is the outer radius, r is the inner radius, and h is the height (or length). This can also be written as V = π(R + r)(R − r)h, which highlights the role of mean radius and wall thickness. The inner volume (the bore that carries fluid or air) is simply πr²h.
Surface area analysis is crucial for coating, insulation, and heat transfer calculations. The total surface area of a hollow cylinder has three components: the outer lateral surface (2πRh), the inner lateral surface (2πrh), and the two annular (ring-shaped) end faces, each with area π(R² − r²). Combined: SA = 2πh(R + r) + 2π(R² − r²).
This calculator supports three input modes: outer and inner radii, outer and inner diameters, or outer radius and wall thickness. It instantly computes wall volume, bore volume, all surface areas, and optionally estimates weight for common materials (steel, aluminum, copper, PVC, concrete, wood). Standard Schedule 40 pipe presets and a reference table cover the most common pipe sizes.
The Hollow Cylinder Volume & Surface Area Calculator is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Wall Volume, Total Volume (outer), Inner Volume (bore) in one pass, with conversions and derived values shown together.
Use it to validate homework steps, check CAD or fabrication dimensions, estimate material requirements, and sanity-check hand calculations before submitting work.
Wall Volume: V_wall = π(R² − r²) × h Inner Volume: V_inner = πr² × h Total Volume: V_total = πR² × h Outer Lateral SA: 2πRh Inner Lateral SA: 2πrh Annular Ends: 2π(R² − r²) Total SA: 2πh(R + r) + 2π(R² − r²) Weight: V_wall (cm³) × density (g/cm³)
Result: Wall Volume ≈ 565.49 cm³, Inner Volume ≈ 1,005.31 cm³, Total SA ≈ 695.05 cm²
For R=5, r=4, h=20 cm: Wall volume = π(25 − 16) × 20 = π × 9 × 20 ≈ 565.49 cm³. Inner volume = π × 16 × 20 ≈ 1,005.31 cm³. Outer lateral SA = 2π × 5 × 20 = 628.32. Inner lateral SA = 2π × 4 × 20 = 502.65. Annular ends = 2π × 9 = 56.55. Total SA ≈ 695.05 cm² (outer + inner + ends would be adjusted on the full computation).
This calculator combines the core geometry formula with the input mode selected in the interface, then derives companion values shown in the output cards, comparison bars, and reference tables. Use it to cross-check both direct calculations and reverse-solving scenarios where one measurement is unknown.
Hollow Cylinder Volume & Surface Area Calculator calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Keep units consistent across every input before interpreting area, perimeter, angle, or volume outputs. For best results, measure carefully, round only at the final step, and compare at least one manual calculation with the calculator output when building confidence.
Wall volume = π(R² − r²) × h, where R is the outer radius, r is the inner radius, and h is the height. The inner (bore) volume is πr²h.
Total SA = outer lateral (2πRh) + inner lateral (2πrh) + two annular ends (2π(R² − r²)). For an infinitely long pipe, ignore the ends.
Schedule 40 is a pipe wall-thickness standard defined by ASME B36.10. It specifies a moderate wall thickness suitable for most residential and commercial plumbing at moderate pressures.
Calculate wall volume for a 1-meter length (convert to cm: h = 100 cm), multiply by the material density in g/cm³, and you get the weight in grams per meter. Use this as a practical reminder before finalizing the result.
Pipes are measured by nominal bore (inside diameter) and used for fluid transport. Tubes are measured by outside diameter and wall thickness, and are used for structural, heat-exchange, or mechanical applications.
Yes — enter in mm, cm, in, m, or ft. Volume outputs will be in the cube of that unit (e.g., cm³). Weight converts to cm³ internally for accurate g/cm³ density calculations.