Hole Volume Calculator
Every fence post, deck footing and mailbox stands in a cylinder of dug earth that must be refilled — usually with concrete, always with something whose volume somebody has to buy, mix and carry. This calculator prices that cylinder: enter the hole’s diameter and depth and the number of holes — all three, counted on the ground and not from the drawing alone — and it returns the excavation volume, the concrete required in cubic feet and yards, and the bag count for the standard 80, 60 and 40 lb bags, so the supply run happens once. A hole looks like a small thing until it is multiplied by a fence line; this page does the multiplying before the auger does.
A Cylinder, and the Post Inside It
The geometry is the pipe-volume formula stood upright: V = π × (d/2)² × depth, with the two unit conversions (inches to feet, at the radius and the depth) the only places error can hide. One refinement distinguishes hole work from pipe work: the post itself occupies the middle of the cylinder. A nominal 4×4 (3.5 in square) set 36 inches deep displaces 3.5 × 3.5 × 36 = 441 in³ ≈ 0.26 ft³ of the hole's volume — roughly a tenth of a 12-inch hole's 2.36 ft³, worth subtracting on large runs and beneath notice on a single mailbox. The same logic, inverted, prices the dirt coming out: excavation expands (the swell factor of soil mechanics, typically 1.2–1.3×), so the spoil heap from a computed 2.36 ft³ hole will occupy nearer 3 ft³ of the wheelbarrow's world — order the concrete by the cylinder, plan the hauling by the swell.
Worked Example: The Standard Fence Hole
The defaults are the fence builder's unit: a 12-inch diameter hole, 36 inches deep (frost-line compliant in much of the temperate US), one hole. Volume = π × 0.5² × 3 = 2.36 ft³ (0.087 yd³ — a usefully humbling figure: even serious holes are small volumes). In bags: 2.36 ÷ 0.6 = 3.93, so 4 bags of 80 lb per hole before displacement credit, 6 bags at 60 lb, 8 at 40 lb. Scale it to a 10-post fence run and the calculator's count field earns its keep: 23.6 ft³ total, 0.87 yd³, 40 bags of 80 lb — the exact borderland where bag-versus-bulk stops being a preference and becomes a price comparison, and where the second trip to the store (the one this page exists to prevent) usually originates from forgetting that the holes are ten, not one.
Diameter: The Expensive Dimension
Area grows with the square of the radius, so diameter errors are squared errors: a hole dug 14 inches wide instead of 12 holds (14/12)² ≈ 1.36 times the concrete — over a third more — while a depth overrun of the same 2 inches on a 36-inch hole costs only 5.6%. Augers wonder, bells flare at the bottom (a belled footing is a frustum, larger than its cylinder — price the flare as a cone at the base if the inspector required one), and hand-dug holes taper. The estimator's defences are the usual ones: measure the actual auger, not its label; add the waste margin on the bag count rather than the geometry (the calculator rounds bags up, which quietly banks about a bag per run); and for engineered footings, where diameter is a structural spec, treat any flare as a separate volume and say so in the order notes. Depth is specified by code (below the frost line); diameter is specified by load; both are measured by nobody until this page makes you.
Frost Depth and the Shape of Requirements
Why 36 inches is the default depth on this page: footings must bear below the local frost line, so the water in the soil beneath them cannot freeze, expand, and jack the post upward — frost heave moves fences and decks by inches per winter, always unevenly, always permanently. Local codes publish the line (12 inches in the warm South, 48+ in the northern tier, deeper in the mountains), and the calculator's depth field is where that number enters; the diameter field carries the other requirement — bearing area and lateral stability, commonly three times the post's width as a rule of thumb (a 4×4 in a 12-inch hole). Sonotube forms make the cylinder honest where soil crumbles: the form's labelled diameter is the hole diameter for volume purposes, and the excavation between form and soil takes backfill, not concrete — a distinction worth real money on a deck's worth of footings.
When the Hole Count Outgrows the Bag
Scale changes the purchasing answer, and the calculator's count field draws the line precisely. Twenty standard holes (12 × 36 in) total 47.1 ft³ of concrete — 79 bags of 80 lb mix, or 1.75 yd³ from a truck or a site mixer. Forty holes double both: 158 bags starts to read as a pallet-and-a-half (a standard pallet holds 42 bags — you would be ordering four) against 3.5 yd³ delivered. The crossover is economic, not geometric: bags win on small counts for their storage and timing freedom, bulk wins once the bag count reaches the dozens, and the exact hole count at which your local prices flip is a knowable number the moment both quotes are in hand. What this page guarantees is that the comparison is made with real volumes on both sides — the failure mode it prevents is the fence quoted at "about a bag a post" and built at four.
The Water Arrives With the Bags
A logistics footnote the bag count drags behind it: bagged mix is not self-contained — each 80 lb bag wants roughly a gallon of mix water at most (manufacturers print the range on the bag; too much water is the strength thief nobody audits). The ten-post fence run's 40 bags therefore imply on the order of 40 gallons of water staged at the mixer, plus wash-down — a hose's presence at the hole line is a computed requirement, not a comfort. Sites that plan concrete to the last bag and water not at all discover the omission with the first batch mixed stiff and wrong; the calculator's bag column is, read properly, also a water order.
Related Tools
More from the Construction Calculators hub: the Pipe Volume Calculator — the same cylinder, horizontal — the Square Feet to Cubic Yards Calculator for flatwork, and the Concrete Column Calculator for the footing's above-ground cousin.
Frequently Asked Questions
How many bags of concrete for a fence post?
For the standard hole on this page (12 in diameter, 36 in deep): about 4 bags of 80 lb per post, before subtracting the post's displacement — the figure most fence guides quote, because it is this cylinder's arithmetic. Shallower or narrower holes fall fast (a 10 × 30 in hole is 1.36 ft³, about 2.3 bags), and gate posts, corner posts and their bigger, deeper holes climb correspondingly — run each size through the count field rather than averaging them in your head.
Should I fill the whole hole with concrete?
Often not: a common detail sets the post on a gravel pad, concretes the lower two-thirds, and backfills the top with soil (or crowns the concrete above grade to shed water) — the concrete volume is then the cylinder up to the fill line, so enter that reduced depth. Full-depth concrete is for engineered footings and high lateral loads; the calculator prices whatever depth of concrete you actually intend, which is the question to settle before the bags are bought.
What about a belled or flared footing?
Price it in two pieces: the cylinder (this page, at the shaft diameter and the shaft's depth) plus the bell, which is a truncated cone — its volume is (π × h/3) × (R² + Rr + r²) over the flare's height, with R the bell radius and r the shaft radius. Add the two for the order. Bells exist to spread load on soft soil; their volume is real concrete and belongs in the count.
How deep should the hole be for a 6-foot fence?
The working rule buries a third of the post: 2 feet for a 6-foot fence in forgiving soil — but the frost line overrules the rule wherever winter is serious, and local codes state the minimum explicitly. Depth is the cheap insurance dimension (5.6% more concrete per 2 inches at these sizes, per the diameter section's arithmetic), while diameter is the expensive one; when in doubt, dig deeper, not wider.
Can I use this for a well or a tree planting hole?
Geometrically yes — any roughly cylindrical excavation prices the same way, and the spoil-volume reading (with the 1.2–1.3 swell in mind) serves planting and boring alike. What changes is the fill: tree holes are backfilled with amended soil at a fraction of the excavated volume replaced by the root ball — the same displacement logic as the fence post, with the tree in the post's role.
Why does the calculator round bags up?
Because a fraction of a bag cannot be bought and a hole cannot be 93% filled: rounding up per the whole job (not per hole — 40 bags for the fence, not 4 × 10 with rounding at each step) banks the spillage and the flare the tape never saw. Unused bags return to the store; a second trip costs more than a bag, which is the entire economics of the round-up.