The short version
A round tube is a cylinder: volume = π × radius² × depth. A 12-inch tube 4 feet deep holds π × (0.5 ft)² × 4 ft ≈ 3.14 cubic feet. An 80-lb bag of concrete yields about 0.60 cubic feet, so 3.14 ÷ 0.60 = 5.24 → buy 6 bags. Add ~10% for spillage on bigger jobs. The concrete tube calculator does this for any size, but the hand method below takes thirty seconds.
The formula, and the one trap in it
V = πr²h — pi times the radius squared times the height (depth). The trap is the radius: the tube is sold by diameter, and the formula wants the radius, which is half. A 12-inch tube has a 6-inch radius. The second trap is units: keep radius and depth in the same unit. Inches are the natural choice for the radius, feet for the depth, so convert once — 6 inches = 0.5 feet — and the volume comes out in cubic feet.
In one line, working entirely in inches and converting at the end:
V (ft³) = π × (diameter ÷ 2)² × depth(in) ÷ 1,728. The 1,728 is 12³ — cubic inches per cubic foot.
Worked example: 12-inch tube, 4 feet deep
This is the single most common residential footing — a deck post pier. Step by step:
1. Radius: 12 ÷ 2 = 6 inches = 0.5 ft.
2. Radius squared: 0.5 × 0.5 = 0.25.
3. Times pi: 3.1416 × 0.25 = 0.7854 ft² (the cross-section).
4. Times depth: 0.7854 × 4 = 3.1416 ft³.
5. Bag count: 3.1416 ÷ 0.60 = 5.24 → 6 bags of 80-lb (round up, always).
6. Waste: 3.1416 × 1.10 = 3.46 ft³ ÷ 0.60 = 5.76 → still 6 bags.
In cubic yards — the unit ready-mix plants sell — that is 3.46 ÷ 27 = 0.13 yd³, far below any truck’s minimum. Bagged mix is the right call for tube work.
Bag math: 80-lb vs 60-lb vs 40-lb
Bag yields are printed on every bag, but the standard figures are: 80-lb → 0.60 ft³, 60-lb → 0.45 ft³, 40-lb → 0.30 ft³. They scale almost perfectly — two 40-lb bags equal one 80-lb bag — so buy whichever size you can carry. For the 12-inch example: 3.46 ÷ 0.45 = 7.68 → 8 bags of 60-lb; 3.46 ÷ 0.30 = 11.5 → 12 bags of 40-lb.
Bag counts by tube size (4 ft deep, 80-lb bags)
| Tube | Volume | Bags (no waste) | Bags (+10%) |
|---|---|---|---|
| 8″ | 1.40 ft³ | 3 | 3 |
| 10″ | 2.18 ft³ | 4 | 4 |
| 12″ | 3.14 ft³ | 6 | 6 |
| 16″ | 5.59 ft³ | 10 | 11 |
| 18″ | 7.07 ft³ | 12 | 13 |
| 24″ | 12.57 ft³ | 21 | 24 |
Depths other than 4 feet scale linearly: a 3-foot tube needs three-quarters of the table value (round up after scaling).
The 10% rule and multi-tube jobs
Buy one spare bag for every 2–3 piers — roughly 10% extra. It covers spillage, the base pad many footings sit on, and topping off as the concrete settles in the tube. Running dry mid-pour is far more expensive than returning one unopened bag. For multiple tubes, multiply one tube’s volume by the count before rounding the bags: six 12-inch × 4-ft tubes = 6 × 3.14 = 18.8 ft³, plus 10% = 20.7 ft³ → 35 bags of 80-lb. Rounding each tube first would have cost you a phantom bag.
Picking the tube size and depth
Diameter: the rule of thumb is a tube at least 3× the post width. A 4×4 post (really 3.5″) takes an 8-inch tube minimum; 10–12 inches is the standard deck-post choice. Heavier beams and multi-story decks step up to 14–16 inches — and your local code’s footing tables outrank any rule of thumb.
Depth: footings must extend below the frost line, or frost heave will lift the pier. That is 42–60 inches across the northern US and 24–30 inches in the South; your county building department publishes the exact figure. Add 6 inches of gravel at the bottom of the hole for drainage.
Three mistakes that waste concrete
1. Diameter in place of radius. Squaring the full diameter quadruples the volume — you will buy four times the concrete. Halve it first.
2. Mixing inches and feet. A 12-inch radius (not 0.5 ft) in the formula gives a volume 144× too big. Convert to one unit before you multiply.
3. Forgetting the extras. The tube is not the whole pour: the base pad under it, the bell of a hand-dug hole, and settling all drink concrete. That is what the 10% is for.
After the pour
Below ground, leave the tube in place — the cardboard decomposes over years without affecting the pier. Above ground, peel it off 24–48 hours after pouring for a clean exposed column (score it with a utility knife first). Fast-setting mix works fine in tubes and reaches working strength in a few hours, but for structural piers use a standard 3,000–4,000 PSI mix and give it the full cure time. Piers carrying real loads want rebar — at least one vertical bar, better a small cage — and an inspector’s sign-off beats a calculator’s.