Concrete Estimator — Tube

Background.

A hollow cylinder holds much less concrete than its outline suggests. Take a ring 1.2 m across with a 0.8 m bore: the inner diameter is two-thirds of the outer, yet the hole removes 44% of the solid volume, because a circle's area grows with the square of its diameter. Judging a pipe section, a precast well ring, a manhole riser or a hollow column by eye tends to go wrong, and on pour day that means either running short or paying for concrete that goes back to the plant.

The arithmetic here is pure geometry. Take the area of the outer circle, subtract the area of the inner one, and multiply the ring-shaped cross-section that remains by the length of the tube. All three measurements go in as metres and the answer comes out in cubic metres, the unit ready-mix suppliers quote.

Two measuring habits cause most of the mistakes. One is confusing radius with diameter: the equation expects full diameters, taken straight across through the centre, and entering half-widths shrinks the answer to a quarter. The other is reading the inner diameter off the wrong surface. For formwork, the inner diameter is the outside of the core or void former, and the outer diameter is the inside face of the outer shutter.

The result is the net volume of the wall and nothing more. It adds no margin for spillage, bulging forms or ragged ends, does not subtract the space taken by reinforcing steel, and does not round up to what a truck will deliver. Those adjustments belong to the job and the supplier, so make them yourself before you order.

What is concrete estimator — tube?

The quantity is the volume of an annular cylinder: the solid material between two circular surfaces running the full length of a tube. Its cross-section is a ring, or annulus, with area π/4 × (D² − d²), where D is the outer diameter and d the inner. Multiplying that area by the length gives the volume in cubic metres. The bore does not have to be centred, since the ring's area is the same wherever the hole sits as long as it lies wholly inside, but both diameters must stay constant along the length.

How to use this calculator.

1. 01Enter the outer diameter in metres, measured straight across through the centre. For a cast-in-place form this is the inside face of the outer sleeve or shutter, where the concrete's outer surface will be.
2. 02Enter the inner diameter: the outside of the core, void former or inner shutter. It must be smaller than the outer diameter; an equal or larger value is refused because there would be no wall to fill.
3. 03Enter the length of the tube in metres. Drawings in millimetres convert by dividing by 1,000, so a 1,200 mm pipe with a 150 mm wall has diameters of 1.2 m and 0.9 m.
4. 04For a run of identical rings, enter the combined length, or work out one ring and multiply by the count.
5. 05Read the volume in cubic metres, then add your own waste allowance and round up to your supplier's delivery increment before placing the order.

The formula.

V = πL(D² − d²) / 4. The term πD²/4 is the area of a circle of diameter D: the familiar πr² written with diameters, since r = D/2 and so r² = D²/4. Subtracting πd²/4 leaves the area of the ring, and multiplying by the length L turns that area into a volume. With all three lengths in metres, V is in cubic metres. An equivalent form is easier to check by hand: V = π × mean diameter × wall thickness × L, where the mean diameter is (D + d)/2 and the thickness is (D − d)/2; multiplied out, the two forms are identical. Because the diameters are squared, the outer diameter dominates. In the 1.2 m by 0.8 m example, a 1% error in D shifts the volume by about 3.6%, a 1% error in d by about 1.6% the other way, and a 1% error in length by exactly 1%.

A worked example.

Frequently asked questions.

References& sources.

1. [1]ACI 318-25, Building Code for Structural Concrete (BIBLIOGRAPHIC/PAYWALL), notation and circular-member geometry context.
2. [2]NIST Special Publication 811, SI derived volume units.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.