What This Calculator Does
The Post Hole Concrete Calculator estimates how much concrete you need to anchor fence posts, mailbox posts, deck footings, or sign posts. It subtracts the space the post itself occupies from the volume of the hole, so you only pay for the concrete that actually fills the gap. Results are given in cubic feet, cubic yards, and the number of pre-mix bags required.
How to Use It
Enter the diameter of your hole, how deep you dig it, the width (or diameter) of the post going in, and how many holes you are setting. All measurements are in inches. The calculator returns the total concrete volume plus an estimate of 60 lb and 80 lb bags, rounded up so you don't come up short.
The Formula Explained
Each hole is a cylinder of volume \(\pi (d/2)^2 h\). The post fills a smaller cylinder \(\pi (p/2)^2 h\), so the concrete needed per hole is the difference. Multiply by the number of holes for the total. Cubic inches are converted to cubic feet (\(\div\, 1728\)) and cubic yards (\(\div\, 46656\)). A 60 lb bag yields about 0.45 cu ft and an 80 lb bag about 0.60 cu ft of mixed concrete.
$$\text{Concrete (ft}^3) = \frac{\pi \left[\left(\frac{\text{Hole Dia}}{2}\right)^2 - \left(\frac{\text{Post}}{2}\right)^2\right] \cdot \text{Depth} \cdot \text{Holes}}{1728}$$
$$\begin{gathered} \text{Bags}_{60} = \left\lceil \frac{V}{0.45} \right\rceil \qquad \text{Bags}_{80} = \left\lceil \frac{V}{0.60} \right\rceil \\[1.5em] \text{where}\quad V = \text{total concrete volume (ft}^3) \end{gathered}$$
Worked Example
For a 12 in hole, 24 in deep, with a 4 in post: hole volume = \(\pi \times 6^2 \times 24 = 2714.34\) cu in; post volume = \(\pi \times 2^2 \times 24 = 301.59\) cu in. Per hole = \(2412.74\) cu in = \(1.396\) cu ft. That's roughly 4 bags of 60 lb mix per hole.
FAQ
Should the hole be 3x the post width? A common rule is a hole diameter about 3 times the post width and depth of 1/3 of the above-ground post height.
Why round bags up? Partial bags can't be bought, and a little extra accounts for spillage and uneven holes.
Does this include gravel at the bottom? No — if you add a gravel base, reduce the hole depth you enter by the gravel thickness.
