How this instrument works
A post hole dug with an auger or clamshell digger is, geometrically, a short cylinder: a circular cross-section swept straight down through a fixed depth. That means its volume follows the same formula as any cylinder — the area of the circular top, pi times the radius squared, multiplied by how deep the cylinder runs. Fence posts, deck footings, mailbox posts and sign posts are all set into holes of essentially this shape, which is why a single formula covers all of them.
This instrument takes the two measurements you actually have on site — the hole's diameter and its depth, both in inches, since that is how post-hole diggers and augers are sized and how most people eyeball a hole with a tape measure. It halves the diameter to get a radius, squares that, multiplies by pi and by the depth to get a volume in cubic inches, then divides by 1,728 — the exact number of cubic inches in a cubic foot, since a foot is 12 inches and 12 cubed is 1,728 — to hand back an answer in the cubic feet that bagged concrete and backfill are actually sold and estimated in.
Knowing the hole's volume ahead of time matters because concrete, gravel and backfill soil all have a cost and a delivery lead time attached, and guessing low means a second trip to the supply yard mid-project. It also matters in the other direction: a hole dug wider or deeper than needed, common when ground caves in around an auger, quietly eats far more concrete than the post itself required, since volume grows with the square of the radius, not with it directly.
Real dug holes are rarely perfect cylinders — the sides can bell outward where loose soil sloughs off, or narrow near the bottom where an auger bites less cleanly — so treat this figure as a close working estimate rather than a guaranteed exact pour volume, and round up rather than down when you are close to a delivery minimum.
- Enter Hole diameter (in) — measure across the actual opening, not just the auger's stated bit size, since caved-in soil often widens a hole beyond it.
- Enter Hole depth (in) — how deep the hole is dug or planned to be dug, in inches.
- Read Volume (cubic feet) beneath both fields; it recalculates the instant either measurement changes.
- Compare this figure against the yield printed on your bag of premixed concrete to work out how many bags to buy.
- If a post will occupy part of the hole, remember this reading is the hole's total volume — the concrete you actually pour is that total minus the post's own volume.
Worked example — a 12 in wide, 24 in deep post hole
Enter 12 into Hole diameter (in) and 24 into Hole depth (in) — a typical fence-post hole dug with a two-person auger. Radius is 12 ÷ 2 = 6 in, so volume works out to π × 6² × 24 = π × 864 ≈ 2,714.336 cubic inches.
Volume (cubic feet) reads 1.5708 — that same 2,714.336 cubic inches divided by 1,728, the exact number of cubic inches packed into one cubic foot. Matching this figure against the yield printed on a bag of premixed concrete tells you how many bags a single hole like this one will use.
Questions
Does this assume a perfectly round, straight-sided hole?
Yes — the formula treats the hole as a true cylinder with a constant diameter from top to bottom. Real auger and hand-dug holes rarely match that exactly: loose soil can slough off and bell the sides outward, adding volume, while a stiff auger sometimes narrows slightly near the bottom, removing a little. Treat the reading as a close working estimate and round up rather than down, especially if you are close to a delivery minimum.
How do I turn this volume into a number of concrete bags?
Check the yield printed on your specific bag — premixed concrete bags state how many cubic feet one bag makes once mixed, and that figure varies by brand and bag weight. Divide this instrument's Volume (cubic feet) reading by your bag's stated yield and round up, since a partial bag still has to be opened.
Does setting a post reduce how much concrete I actually need?
Yes. This instrument reports the hole's total volume as an empty cylinder. If a post fills part of that space once it's dropped in and centered, the concrete you pour is the hole's volume minus the post's own volume — for a round post, roughly its own small cylinder; for a square post, its cross-sectional area times the buried length.
Why divide by 1,728 instead of 12?
Because volume is a cubic measurement, not a linear one. Converting a length from inches to feet only needs dividing by 12, but converting a volume from cubic inches to cubic feet needs dividing by 12³ = 1,728, since each of the three dimensions — length, width and height — contributes its own factor of 12.
Can I use this for a square or rectangular post hole?
No — this formula is specifically for round holes, the shape an auger or clamshell digger produces. A square or rectangular hole holds length × width × depth instead, without pi or a radius anywhere in the calculation, so it needs a different formula entirely.
Is this the same math as the site's tank or pipe volume instruments?
The underlying geometry is identical — every one of them is pi times radius squared times height or length, the volume of a cylinder. What differs is scale, orientation and unit: this instrument answers a short, squat hole dug in dirt in cubic feet, while the pipe and tank instruments size long or standing liquid-holding cylinders and answer in US gallons, the unit water and fuel are actually metered in.