SpecBase

Pipe weight formula

A pipe is a hollow cylinder, so its mass is the area of an annulus multiplied by length and density. That single idea produces both the full formula and the two shortcuts printed on chart tables — and, once the constants are derived rather than quoted, it also shows exactly what those shortcuts assume.

From the annulus

Mass per unit length

m = π/4 · (D² − d²) · 10⁻⁶ · ρ, d = D − 2t

D outside diameter (mm), t wall thickness (mm), d resulting bore (mm), ρ density (kg/m³), m mass per metre (kg/m). The factor 10⁻⁶ converts mm² to m².

Worked through with the default dimensions:

D = 168.3 mm, t = 7.11 mm (NPS 6, Schedule 40)d = D − 2t = 168.3 − 14.22 = 154.08 mmA = π/4 × (168.3² − 154.08²)A = 0.785398 × (28,324.9 − 23,740.6) = 3,600.0 mm²m = 3,600.0 × 10⁻⁶ × 7,850 = 28.260 kg/m (18.99 lb/ft)
D
Outside diameter, from ASME B36.10M — fixed per nominal size
t
Wall thickness — the schedule designates this, and only this
d
Bore, D − 2t. Flow, volume and water capacity all follow this
ρ
Density. 7,850 kg/m³ for carbon steel; use the real value for anything else

The shortcut — and why it is exact

Chart tables do not print the annulus formula. They print a one-line rule with a magic constant in it. Here is that constant, derived rather than quoted:

D² − d² = D² − (D − 2t)² = 4tD − 4t² = 4t(D − t)

The π/4 in front then cancels the 4, leaving π·t·(D − t) — the whole annulus area in one term. Multiply by 10⁻⁶ and by density, and the metric shortcut appears:

m (kg/m) = π × ρ × 10⁻⁶ × t × (D − t) = 0.0246615 × t × (D − t) [t, D in mm]

The imperial version collects the inches-to-feet conversion instead, and its constant is where the trouble starts:

W (lb/ft) = π × 12 × ρlb/in³ × t × (D − t) = 10.69144 × t × (D − t) [t, D in inches]

The 10.68 you were taught assumes a rounded density

The constant printed in most chart tables is 10.6802, which implies a steel density of 0.28330 lb/in³ — about 7,842 kg/m³. That is a rounded nominal figure from an era of slide rules, and it makes every weight in those tables about 0.11 % lighter than the same geometry at 7,850 kg/m³. On a single length it is noise. On a fabricated order measured in hundreds of tonnes it is a real discrepancy, and it is the most common reason a mill’s chart and a calculated weight do not agree. We compute from the material’s specification density, so the figure here is the physically correct one and the chart is the approximation.

Worked examples — both routes, same answer

Schedule 40 carbon steel: full annulus formula against the 0.02466 shortcut
Size Schedule Outside dia. mm Wall mm Metal area mm² m = π/4(D²−d²)ρ kg/m m = 0.0246615t(D−t) kg/m Full formula lb/ft W = 10.69144t(D−t) lb/ft
NPS 2 / DN 50 Sch 40 60.3 3.91 693.2 5.442 5.442 3.657 3.657
NPS 6 / DN 150 Sch 40 168.3 7.11 3,600.9 28.267 28.267 18.994 18.994
NPS 12 / DN 300 Sch 40 323.8 10.31 10,157.8 79.739 79.739 53.582 53.582
NPS 24 / DN 600 Sch 40 609.6 17.45 32,461.8 254.825 254.825 171.234 171.234

The two mass columns agree to every displayed digit, because the shortcut is an exact rearrangement of the annulus formula — not an approximation. Only the density assumption changes the answer.

The imperial column is worth checking against any printed chart you have: our lb/ft figures run about 0.11 % high against a chart built on 10.6802, which is the whole of the discrepancy in a single sentence.

Two more quantities from the same geometry

Once the bore is known, two figures that a printed chart does not carry fall out immediately — and they are the two a piping estimator needs most often after the mass.

Internal volume
V = π/4 · d² · 10⁻³ L/m with d in mm. This sizes a hydrostatic test charge and a flush volume. It is why bore matters more than nominal size: two pipes sold as NPS 6 can differ by 30 % in the water they hold if the schedules differ enough.
External surface
S = π · D · 10⁻³ m²/m with D in mm. This is the coating, wrapping or insulation quantity. It depends only on the outside diameter, so it is identical in every schedule at a given size — which is convenient, because coating is priced before the schedule is always fixed.
Water mass
The internal volume × 1,000 kg/m³ at the conventional density of water. Documented on methodology : real water is 998.2 kg/m³ at 20 °C, so a test mass computed this way is about 0.2 % high at room temperature and 4 % high at 100 °C.

Pipe weight calculator — any OD and wall →

Frequently asked questions

What is the formula for pipe weight per metre?

m = π/4 × (D² − d²) × 10⁻⁶ × ρ, where D is the outside diameter in mm, d is the bore (D minus twice the wall) in mm, ρ is the density in kg/m³, and m is the mass in kg per metre. Because d = D − 2t, the same formula collapses to the shortcut m = 0.0246615 × t × (D − t) with t and D in millimetres for steel at 7,850 kg/m³ — which is the version printed on chart tables. The two are algebraically identical; the shortcut is just easier to use on a calculator.

Where does 10.68 in the imperial formula come from?

W = 10.6802 × t × (D − t), with t and D in inches and the result in lb/ft. The constant is π × 12 × ρ: the π and the 4 cancel against the annulus expansion (D² − d² = 4t(D − t)), the 12 converts inches to feet, and the remaining ρ is the steel density in lb/in³. 10.6802 therefore implies a density of 0.28331 lb/in³, about 7,842 kg/m³ — a rounded nominal figure. At the real specification density of 7,850 kg/m³ the constant is 10.6914, so a chart built on 10.6802 reads about 0.1 % light.

Why does the shortcut give the same answer as the full formula?

Because it is the same formula after expanding the annulus. D² − d² with d = D − 2t gives D² − (D − 2t)² = 4tD − 4t² = 4t(D − t). Multiplying by π/4 leaves π·t·(D − t). Nothing is approximated and nothing is dropped — the shortcut is an exact rearrangement, which is why the two agree to the last displayed digit in the table on this page.

How do I calculate the water capacity of a pipe?

Internal volume per metre is V = π/4 × d² × 10⁻⁶ × 1,000 litres, i.e. π/4 × d² in mm² × 10⁻³ L/m, with d the bore in millimetres. A 100 mm bore holds 7.854 L per metre. The mass of that water is the volume in litres × 1 kg/L at the conventional density of 1,000 kg/m³ — so the same pipe holds 7.854 kg of water per metre, against maybe 28 kg of steel. That ratio is why a hydrostatic test mass is dominated by the contents rather than the pipe.

Does pipe weight include the wall tolerance?

No. Every weight here is the nominal-wall figure: the mass of a pipe whose wall is exactly the tabulated thickness. Real pipe has a manufacturing tolerance, and for seamless and welded pipe the permitted wall variation is a percentage of nominal with a minimum-wall condition — which means an acceptable pipe can be lighter than the nominal figure, and on a large order the difference accumulates. If you need the worst case for a lifting or shipping limit, apply the standard’s minimum-wall allowance to the wall thickness before computing, or ask the mill.

Pipe reference and tools

The formula applied to real dimensions.

Data source and method

The constants 0.0246615 (metric) and 10.69144 (imperial) are computed in this page’s own build from π and the carbon steel density of 7,850 kg/m³ / 0.28360 lb/in³ — none is hard-coded from a chart. The chart constant 10.6802 is quoted only as the thing being compared against.

  • Elementary plane geometry. The circle, polygon and hollow-section area formulas.
  • ASME B36.10M — Welded and Seamless Wrought Steel Pipe (dimensional tables).
  • BIPM / NIST definitional constants: international inch = 25.4 mm, foot = 0.3048 m, pound = 0.45359237 kg.

Dataset version 2026.09.1 · dimensions last verified against source 2026-09-21. Found an error? Report it — corrections are issued with a version bump.