Quick answer: a tube's material volume is V = π(R² − r²)h — the outer cylinder minus the hollow inside. Only know the wall thickness? The inner radius is R − t. Looking for how much liquid fits inside instead? That's the inner cylinder alone: use the pipe volume calculator.
The hollow cylinder formula, step by step
where R = outer radius · r = inner radius · h = length · wall thickness t = R − r
Worked example — a tube with a 4 cm outer radius, 3 cm inner radius, 10 cm long:
- Outer cylinder: π × 4² × 10 = 502.65 cm³
- Hollow core: π × 3² × 10 = 282.74 cm³
- Material: 502.65 − 282.74 = 219.91 cm³
The subtraction inside the parentheses matters more than it looks. Because both radii are squared, a small increase in wall thickness adds material fast on a large tube: going from a 3 mm to a 4 mm wall on a 50 mm pipe adds about 30% more steel, not 33% more diameter.
Steel tube material volume & weight per foot
Round mechanical tubing at common sizes, using steel's 7.85 g/cm³ (0.2836 lb/in³) density:
| Outer diameter | Wall | Material per ft | Weight per ft |
|---|---|---|---|
| 1 in | 0.065 in | 2.29 in³ | 0.65 lb |
| 1 in | 0.120 in | 3.98 in³ | 1.13 lb |
| 1.5 in | 0.120 in | 6.25 in³ | 1.77 lb |
| 2 in | 0.120 in | 8.51 in³ | 2.41 lb |
| 2 in | 0.250 in | 16.5 in³ | 4.68 lb |
| 3 in | 0.250 in | 25.9 in³ | 7.35 lb |
| 4 in | 0.250 in | 35.3 in³ | 10.0 lb |
For other metals, multiply the material volume by the density: aluminum 2.70 g/cm³, copper 8.96, brass 8.50, PVC 1.40. The volume to weight calculator carries the full density table.
Where tube volume shows up in real life
Ordering metal by weight
Steel and aluminum are priced per pound or kilogram, but specified by dimension. A fabricator quoting 40 ft of 2-inch, 0.120-wall square-shouldered tube needs 40 × 2.41 ≈ 96 lb — the material volume from this calculator times density, which is precisely how supplier weight charts are built.
Concrete pipe and culvert walls
A precast culvert 36 in inside diameter with a 4-inch wall, 8 ft long: R = 22 in, r = 18 in, h = 96 in. Material = π × (484 − 324) × 96 ≈ 48,255 in³ ≈ 27.9 ft³ ≈ 1.03 cubic yards of concrete — and at roughly 150 lb/ft³ that section weighs over two tons, which decides what crane you need.
Insulation sleeves and lagging
Pipe insulation is a tube around a tube. For 1-inch pipe (1.315 in OD) with a 1-inch-thick sleeve: R = 1.658 in, r = 0.658 in, so each foot uses π × (2.749 − 0.433) × 12 ≈ 87.3 in³ of foam. Suppliers sell by linear foot, but manufacturers cost it by exactly this volume.
Common mistakes & pro tips
- Wall thickness subtracted from the diameter. A 50 mm OD tube with a 3 mm wall has a 44 mm bore, not 47 — the wall appears on both sides. Subtract once from the radius, twice from the diameter.
- Mixing a diameter with a radius. If the outer is entered as a diameter and the inner as a radius, the calculator may even reject the input as impossible. Keep both fields on the same mode.
- Material volume vs. capacity. This page gives the solid wall. For flow capacity, use the inner cylinder only.
- Pro tip — nominal pipe sizes lie. "2-inch" pipe is neither 2 in outside nor inside; NPS is a legacy label. Measure the actual part, or look up the schedule dimensions.
- Pro tip — quick sanity check. For thin walls, material volume ≈ π × (average diameter) × wall thickness × length. If that estimate is far from the exact answer, a measurement is wrong.
How to use this calculator
- Measure the outer dimension. Measure the outside radius or diameter of the tube. Calipers across the widest point give the outer diameter.
- Measure the inner dimension. Measure the bore — the hollow inside. If you only know the wall thickness t, the inner radius is R − t.
- Measure the length. Measure end to end along the tube's axis.
- Let it apply V = π(R² − r²)h. The calculator subtracts the hollow core from the solid cylinder, giving the volume of the material itself.
Frequently asked questions
What is the formula for the volume of a tube?
V = π(R² − r²)h, where R is the outer radius, r the inner radius and h the length. It is simply the full cylinder minus the hollow core. A tube with a 4 cm outer radius, 3 cm inner radius and 10 cm length contains π × (16 − 9) × 10 ≈ 219.9 cm³ of material.
Does this give the material volume or the capacity?
The material volume — the metal, plastic or concrete making up the wall. If you want how much liquid the tube can hold, that's just the inner cylinder: V = πr²h. The pipe volume calculator handles that case with per-foot tables for standard pipe sizes.
How do I calculate tube volume from wall thickness?
Subtract the wall thickness from the outer radius to get the inner radius: r = R − t. A tube 50 mm in outer diameter (R = 25 mm) with a 3 mm wall has r = 22 mm. Note that the wall is subtracted once from the radius but twice from the diameter.
How do I find the weight of a metal tube?
Multiply the material volume by the metal's density: steel ≈ 7.85 g/cm³, aluminum ≈ 2.70, copper ≈ 8.96. A steel tube containing 219.9 cm³ of material weighs about 1.73 kg. This is exactly how mill weight tables are generated.
Why can't the inner radius be larger than the outer?
Because the hollow core would be bigger than the tube itself, which is physically impossible — the formula would return a negative volume. If the calculator flags this, the two measurements have most likely been swapped, or one is a diameter and the other a radius.