A hollow cylinder is a tube: an outer cylinder with an inner one removed from it. This calculator gives you the material that is left. It works out the annular cross-section of the wall, the volume of that wall over the length, what it weighs at the density you supply, and the surface area you would have to coat, insulate or paint.
The distinction matters, so it is worth stating plainly at the top. Our pipe volume calculator computes the internal volume of a pipe run and the weight of the fluid it holds — the contents. This page computes the material: the wall itself and what the pipe weighs empty. Our cylinder volume calculator handles a solid cylinder with no bore at all. Three different questions, three pages, and picking the wrong one is how a pipe rack ends up designed for the weight of the water instead of the weight of the steel. Arb Digital publishes all three.
What This Hollow Cylinder Calculator Does
It solves the annulus. Take the area of the outer circle, subtract the area of the inner circle, and what remains is the cross-section of the wall. Multiply by length and you have the volume of material. Multiply by density and you have the mass.
It accepts the section in whichever form you have it: outside and inside diameter, outside diameter and wall thickness, or inside diameter and wall thickness. It also reports the weight per unit length, which is the figure that actually gets used in practice, and the total surface area including the bore and both end faces.
Density is an input and stays one. The density of a material depends on the alloy, the grade, the polymer and sometimes the process, and the right number is on the data sheet for the product you are actually buying. Dimensional standards for pipe are equally specific: outside diameters and wall thicknesses for welded and seamless steel pipe are set in documents such as ASME B36.10M, catalogued through the ASME codes and standards library. Neither the dimensions nor the densities are tabulated on this page.
How to Use It
- Choose your units. Diameters are read in inches or millimetres, length in feet or metres, because that is how tube is normally described.
- Pick the input mode that matches your data. Tube is usually sold by outside diameter and wall; pipe by nominal size and schedule, which you convert to a real outside diameter and wall.
- Enter the length of one piece. The weight per unit length figure will be the one you use most.
- Enter the density of the actual material. Not a generic figure for the metal family — the one for the grade you are buying.
- Set the quantity to scale the whole result to a bundle or a delivery.
The Formula and How It Is Calculated
Wall cross-sectional area = π ÷ 4 × (D² − d²), where D is the outside diameter and d the inside diameter. This is the annulus, and it is exactly equivalent to the more memorable π × mean diameter × wall thickness, since the difference of two squares factorises into the sum times the difference.
Material volume = wall area × length. Mass = volume × density. Weight per unit length = wall area × density, which needs no length at all — it is a property of the section.
Surface area = the outer lateral surface πDL, plus the bore surface πdL, plus the two annular end faces, which together equal twice the wall cross-sectional area. Where the wall is thin, the two end faces are negligible and the surface is essentially the two curved faces. One caution runs through all of it: diameters are quoted in inches or millimetres while lengths are quoted in feet or metres, so every one of these products crosses a unit boundary, and the tool converts internally rather than trusting you to. The NIST guide to the use of the International System of Units is the reference for doing that consistently.
Worked example against the loaded values. A cylinder with a 4.5 inch outside diameter and a 4.026 inch bore has a wall area of π ÷ 4 × (20.25 − 16.209) = 3.174 square inches, which is 0.02204 square feet. Over 20 feet that is 0.4408 cubic feet of material, and at 490 pounds per cubic foot it weighs 216 pounds, or 10.8 pounds per foot. The outer surface is π × 0.375 × 20 = 23.56 square feet and the bore adds another 21.08, giving 44.68 square feet of surface in total once the end faces are included. For comparison, the bore itself would hold 1.77 cubic feet, which is about 13.2 US gallons of water weighing roughly 110 pounds — half what the pipe weighs, and a number the pipe volume calculator handles properly.
The Trap in the Squares
A hollow cylinder is where intuition about area goes wrong, and it goes wrong in a specific way.
Take a tube and increase the wall thickness by twenty per cent, holding the outside diameter fixed. The wall area does not go up by twenty per cent. It goes up by rather more, because the bore shrinks and area follows the square of the diameter. Conversely, take a thin-walled tube and shave a small amount off the wall and you lose more material than you expect. This is why a small change in schedule can move the weight of a piping run by a surprising margin, and why estimating a rack loading from nominal sizes rather than actual sections is unreliable.
The same squaring is behind a fact that catches people out in a completely different context: for a given weight of material, a tube is far stiffer in bending than a solid rod, because moving material away from the neutral axis increases the second moment of area enormously. That is why bicycles, scaffolding and aircraft use tube. Our cross-sectional area calculator handles areas for other shapes, and the section modulus calculator gives the bending property of a section once you have its geometry.
Where the Wall Weight Actually Gets Used
The weight of the pipe, as opposed to the weight of its contents, is the number behind several practical problems.
Support and hanger loading. A pipe support carries the pipe, the fluid and the insulation. Empty weight matters on its own during erection and hydrotest planning, and it is the number that governs when a line is drained.
Lifting and handling. A bundle of tube going onto a lorry or under a crane hook is priced and planned by mass, and the quantity multiplier here exists for exactly that.
Buying by weight. Steel and many other metals are sold by mass while they are specified by dimension. The bridge between the two is the wall area times the density, which is what this page computes.
Buoyancy. A capped empty pipe in a wet trench floats, and it floats surprisingly early, because the displacement is set by the outside diameter while the weight is set by the much smaller wall area. Comparing the material weight here with the displaced water volume is the first check on that, and our density calculator and mass to volume converter handle the conversions around it.
Surface Area Is Two Numbers, Not One
The surface area figure covers the outer face, the bore and the two end annuli. Which parts of that you care about depends entirely on what you are doing.
For external painting or wrapping, only the outer lateral surface counts, and that is πDL. For internal lining or for working out the wetted perimeter of a flow, it is the bore surface, πdL. For heat transfer, both matter and so does the wall thickness between them. Coating estimators very often quote total surface without saying which faces are included, and the difference between outer-only and total is roughly a factor of two on a thin-walled tube.
The end faces are usually trivial, but not always. On a very short, thick-walled ring — a bush, a spacer, a bearing shell — the two annular faces can be a large fraction of the total, and the geometry stops looking like a pipe and starts looking like a washer. The formula is identical; only the proportions change. Our surface area calculator covers other solids.
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Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Weighing the contents when you meant the pipe — internal volume and fluid weight are the pipe volume calculator's job, and the two answers are entirely different numbers.
- Using nominal size as the outside diameter — steel pipe is named by a nominal size that stopped matching its outside diameter a very long time ago.
- Confusing wall thickness with the difference of the diameters — the wall is measured radially, so it is half that difference.
- Assuming a generic density — alloys, grades and polymers differ, and the data sheet for the product you are buying is the only reliable source.
- Quoting total surface area for an external coating — on a thin wall the bore roughly doubles the figure, and a coating estimate based on it is roughly double too.
Related Free Tools From Arb Digital
Pair this with the pipe volume calculator for what a pipe holds, the cylinder volume calculator for solid cylinders, the cross-sectional area calculator for other sections, the density calculator for the material property itself, the surface area calculator for other solids and the tank volume calculator for vessels. The full free online tools hub lists every calculator we publish.
Frequently Asked Questions
That page computes the internal volume of a pipe run and the weight of the fluid it holds, which is the contents. This page computes the material: the annular cross-section of the wall, the volume of the wall over its length, and what the pipe itself weighs empty.
That one solves a solid cylinder with no bore, giving base area, lateral and total surface area and volume at a fill level. A hollow cylinder is that shape with an inner cylinder removed, which changes the area formula and the weight completely.
Because area follows the square of the diameter, not the diameter itself. The annulus is pi over four times the difference of the squares, which is the same as pi times the mean diameter times the wall thickness.
Yes. Wall is measured radially, so the outside diameter exceeds the inside diameter by two wall thicknesses. Entering the full difference as a wall thickness doubles the material and is one of the commonest errors on this calculation.
Because density varies with the alloy, the grade and the polymer, and a generic figure produces a plausible answer that is quietly wrong. The manufacturer's data sheet or the material standard for the exact product is the right source.
Yes, and both end faces. For an external coating you want only the outer lateral surface, which on a thin wall is roughly half the total. Always state which faces a coating quantity refers to.
Yes. The geometry is the same for tube, sleeves, bushes, spacers, bearing shells, cored castings and drilled bar. On a short thick ring the two end faces become a large share of the surface area, but the formulas do not change.
No. Pressure capacity depends on the material, the grade, the temperature, the manufacturing route, corrosion allowance and the design code, and it is a piping engineering calculation. This page is geometry and mass only.
This tool computes geometry and mass from dimensions and a density you supply. It publishes no dimensional or density tables, and it says nothing about pressure rating, structural capacity or fitness for service. Piping and pressure equipment must be specified to the applicable design code by a qualified engineer.
