Pier footing concrete

From tube geometry to wet volume — and from volume to whole bags

The geometry is a circle taken downward. The engine halves the entered diameter and converts it into the feet the depth is measured in, sweeps the circle’s area down the full depth of the tube, and repeats the cylinder once per pier. Diameter is the input with the sharpest teeth, because the volume grows with its square: a modestly wider tube is a much heavier pour.

Waste is an allowance, not a fact of nature. The percentage entered inflates the wet volume to cover spillage, over-dig and uneven hole bottoms; the default is the pack’s shipped figure, and a pourer with clean holes and steady hands may enter less, or none at all.

The volume is read out twice — in cubic yards, the language ready-mix is ordered in, and in cubic metres for metric suppliers. Both are the same wet volume with the same waste on top, passed through different conversions, so either line can check the other.

The bag count is where volume meets the merchant. The engine divides the wasted volume by the fixed yield the pack carries for a sixty-pound bag and rounds up, because bags are sold whole. When that count grows long, the same page’s volume lines are the argument for a delivery of mixed concrete instead.

What this page never does is size the footing. Diameter, depth and count arrive here as decisions already made — by the plan, the frost line and the load above — and the arithmetic prices the concrete those decisions imply, nothing more.

When this calculation is used

• Ordering bagged concrete for deck, pergola or fence footings once the layout fixes the pier count.
• Deciding between bags and a ready-mix delivery by reading the bag count against the volume lines.
• Seeing what a wider tube or a deeper embedment does to the pour before any hole is dug.
• Pricing the concrete line of an outdoor structure estimate alongside its lumber take-off.

Worked example

The pack’s golden vector runs the calculator’s own defaults: piers a foot across and three feet deep, four of them, with a tenth added for waste — beside a companion vector that pours a slimmer, shallower but more numerous set with the waste allowance switched off entirely.

The anchor’s whole order stays under half a cubic yard yet still rounds to two dozen bags — the scale at which bagged concrete makes sense. The no-waste companion asks for roughly the same volume from its slimmer, more numerous tubes, and its bag count lands a single bag higher: at this size the order turns on whole-bag rounding, not on the allowance.

The figures here are not stored on the page: the certified engine computes them at load and they are checked against the test vectors the signed pack declares. Enter a diameter of zero and the engine refuses the pour — that refusal is itself one of the declared vectors.

What each input represents

Assumptions and limits

• The cylinders are true and full: belled bottoms, over-dig beyond the entered allowance and part-filled tubes are outside the geometry.
• The waste allowance is the pourer’s input — a judgement about the site, defaulted by the pack, never a claim about what pouring requires.
• The bag count uses the fixed per-bag yield the pack carries for a sixty-pound bag; other bag sizes and mixes change the count and belong to their own arithmetic.
• Diameter, depth and count are design decisions this page never makes: it is an educational quantity reference, not engineering advice — frost depth, bearing, reinforcement and connections must be verified against your local code and the professionals responsible for the work.

What the guards protect against

• The diameter must be strictly greater than zero, and the pack ships that refusal as a declared test vector: a circle of no width has no volume to pour, and the engine refuses rather than dressing an empty order up as a real one.
• The depth must be strictly positive and is capped far beyond any residential footing, and the count starts at a single pier and stops at a bounded run — so a mistyped figure surfaces as a refusal, not a fleet of imaginary holes.
• The waste allowance runs from nothing — the pack declares a no-waste vector of its own — up to a ceiling that would double the pour, so the allowance can express any honest site but cannot silently dominate the order.

Provenance

Standard cylinder-volume concrete estimating (whole-bag convention)

Radius from the diameter with its unit conversion; wet volume as the circle’s area times depth times count; a percentage waste factor on top; readouts in cubic yards and cubic metres, and a sixty-pound bag count rounded up at the pack’s fixed per-bag yield.

An educational quantity reference, not engineering advice: footing size, depth and reinforcement are matters for your local code and a qualified professional, and nothing on this page determines them. The signed pack carries its own citation, and the page reports the verification state of the release it mounted.