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Formula methodology

Concrete volume and rounding

The volume, displacement, waste, product-yield, and whole-bag rounding rules used for cylindrical post holes.

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Transparent variables, rounding decisions, and scope limits for every result.

Formula version: post concrete 1.2.0

This page documents cylindrical hole volume, optional post displacement, gravel-depth subtraction, waste, and final bag rounding from the selected product yield. It does not select hole dimensions or embedment; unlike the fence formulas, it starts with a supplied hole count rather than laying out posts.

This formula estimates material volume for cylindrical holes. It does not determine footing dimensions, embedment, soil capacity, frost depth, structural adequacy, or required concrete product.

Variables and units

  • H: whole number of holes.
  • D: circular hole diameter in millimetres.
  • T: total hole depth and G: gravel depth, both in millimetres.
  • Concrete depth C = T - G.
  • Round-post displacement uses post diameter d; rectangular displacement uses post width w and depth p.
  • Y: user-entered yield in litres per bag; W: waste percentage.

US customary and metric measurements normalize to millimetres using the exact NIST SP 811 conversion factors. One litre equals 1,000,000 cubic millimetres.

Volume and displacement

Gross hole volume is H × π × (D / 2)² × C. Round-post displacement is H × π × (d / 2)² × C; rectangular-post displacement is H × w × p × C. If displacement is disabled, it is zero.

Net concrete before waste is gross volume minus displacement. Waste allowance is net × W / 100, and final concrete volume is net + waste. Gravel volume is calculated separately as H × π × (D / 2)² × G and is not included in concrete depth.

Rounding and product yield

Geometry retains full floating-point precision through the calculation. Displayed litre values round to one decimal place. Bag quantity uses the unrounded final volume and always rounds up: ceil(final litres / Y). This means a displayed volume that appears close to a whole yield can still require the next bag.

Yield must be entered from the specific product being purchased. The QUIKRETE Fast-Setting Concrete Mix data sheet is an example of manufacturer product data, not a universal default.

Waste and edge cases

  • Waste may range from 0% through 100% and is shown separately from net concrete.
  • Gravel must be less than total hole depth.
  • A selected round post requires a diameter smaller than the hole diameter.
  • A selected rectangular post requires both dimensions, and its corner-to-corner diagonal must fit inside the circular hole diameter. Equal and near-equal floating-point boundary values are accepted within a tiny numerical tolerance; a genuinely larger diagonal is rejected.
  • Hole count and bags are whole quantities; required dimensions and yield must be positive.
  • Displacement is modeled through the concrete depth. Tapered holes, irregular excavation, post caps, voids, and site spillage beyond the entered waste are not modeled.
  • Hand-dug or irregular holes often need a larger user-selected waste allowance than smooth cylindrical geometry. The estimator does not impose a universal percentage because soil, excavation, and product conditions vary.

References

Manufacturer information: QUIKRETE Fast-Setting Concrete Mix data sheet; check the current sheet for bag yield and installation instructions. Comparable calculators: QUIKRETE and Inch Calculator, which use their own assumptions and are provided for general context only. Measurement conversion: NIST SP 811.