Capacity and Mass of a Pipe

From the outside diameter and the wall thickness, finds how much a pipe holds and how much the pipe itself weighs. Enter the diameter and thickness in millimetres, the length in metres, and the density in grams per cubic centimetre.

A pipe is a cylinder with a hole through it. Asking how much it holds and asking how much it weighs mean looking at two different parts of that shape.

Start with the inside diameter. The wall has the same thickness all the way round, and in cross-section it eats into the bore from both sides, so twice the thickness comes off the outside diameter.

d = D - 2t

The capacity is the area of the bore multiplied by the length. The volume of the pipe itself is the area of the ring between the two circles multiplied by the length.

V = \pi\left(\left(\dfrac{D}{2}\right)^2 - \left(\dfrac{d}{2}\right)^2\right) L

$D$ is the outside diameter, $d$ the inside diameter, $t$ the wall thickness
$L$ is the length and $V$ the volume of the pipe wall

Mass follows by multiplying that volume by the density.

Example

The default input is a steel pipe of outside diameter 60.5 mm and wall thickness 3.8 mm, 4 m long, with steel's density of 7.85 g/cm³.

The inside diameter is $60.5 - 7.6$ , or 52.9 mm. The capacity is about 8.7915 L, the pipe wall itself about 2707.55 cm³, and the mass about 21.2543 kg.

Per metre that is 5.3136 kg. This size is a standard Japanese structural steel pipe, and the published table lists its unit mass as 5.31 kg/m, confirming the calculation against an independent source.

Typical densities

Enter grams per cubic centimetre. Steel is 7.85, stainless steel 7.93, copper 8.96, aluminium 2.70, and PVC around 1.4.

To weigh the contents instead, multiply the capacity by the density of the liquid. Water is about 1 kg per litre, so this pipe holds roughly 8.8 kg of water.

Points to watch

A frequent error is subtracting the wall thickness only once. Sketching the cross-section makes it plain that the bore is squeezed from both sides; the thickness must be doubled.

The units are deliberately mixed to match how pipe is catalogued: millimetres for diameter and thickness, metres for length, grams per cubic centimetre for density.

The result is a theoretical mass. Real pipe carries manufacturing tolerances, and published tables are themselves computed from nominal sizes, so a weighed length will differ slightly.