Calculation method
How Post Hole and Post Volumes Are Calculated
The concrete space is the hole’s cross-section minus the post’s cross-section, extended through the filled depth.
Define both cylinders
The hole is represented by a radius and a filled depth. A round post occupying that same depth has its own radius. Multiplying each circular area by depth gives two volumes; subtracting them leaves the annular space.
The model needs the shapes and occupied depths to match its assumptions. A square post cannot be represented accurately just by entering its side as a round diameter. A post occupying only part of the filled depth also requires a corresponding section-based calculation.
Keep radius and diameter distinct
A diameter spans the whole circle; a radius runs from its centre to its edge. Radius is half the diameter. Because the radius is squared in the area formula, confusing these fields has a large effect on the result.
The form accepts diameters and performs this conversion internally. Entering a 0.30 m hole diameter gives a radius of 0.15 m; entering a 0.10 m round-post diameter gives a radius of 0.05 m. Do not enter the smaller radius values in those diameter fields.
Work through the subtraction
Using a 0.15 m hole radius, 0.05 m post radius and 0.6 m depth, the difference of squared radii is 0.02 m². Multiplying by π and by 0.6 m gives approximately 0.0376991118 m³.
The displayed decimal is a readable approximation. Use the underlying calculation, rather than that shortened display, when multiplying by a hole count or converting to bags.
Extend the model to several holes
Six identical holes have a net volume of approximately 0.2261946711 m³. A chosen 10% allowance gives approximately 0.2488141382 m³. Different hole dimensions belong in separate groups, whose unrounded material requirements can later be combined when the purchasing specification agrees.
Do not round every individual hole to bags before calculating one shared order. That changes the purchasing model by reserving a partly used final package for every hole.
Reject impossible geometry
The tool requires the post diameter to be strictly smaller than the hole diameter. Equal diameters leave no annular space and are rejected, as are larger posts. Hole diameter and filled depth must be positive; a zero post diameter can represent no post displacement. The calculation does not choose hole size, depth, spacing or structural capacity.
Frequently asked questions
Does the formula include the empty centre occupied by the post?
No. The post’s cylindrical volume is subtracted over the entered filled depth.
Sources and method
- PackLedge quantity methods
Original derivations using geometry, ratios, sums and whole-package rounding. Each calculator explains its assumptions and worked examples.
- NIST — SI Units ↗
Reference for length, mass, area, volume and the distinction between base and derived units.