For a typical 8″ diameter × 36″ deep fence post hole, the volume is 0.04 cubic yards exact— that's 1.05 ft³ of concrete per hole. Bag count: 2× 80 lb bags or 3× 60 lb (Quikrete data-sheet yield). For a 12″ diameter × 42″ deep deck footing on a Chicago frost line, the volume is 0.10 yd³ exact and the bag count is 5× 80 lb per footing. Both fall well below the residential ready-mix minimum, so post holes and individual footings are almost always a bagged job.
Run the same math on the concrete yardage calculator (cylinder mode) for any diameter and depth; it surfaces the bag count and flags the below-ready-mix-minimum case that applies to nearly every post-hole job.
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Quick answers about SiteworkMath's calculators and material take-offs — concrete yardage, topsoil + mulch volume, tile box-count, deck-surface materials. Free, no signup. Not structural-engineering or code advice — for joist / beam / footing / permit decisions, talk to a structural engineer, licensed contractor, or your local building department.
Hi, I'm the SiteworkMath assistant. I answer questions about the calculators and guides on this site — concrete yardage, topsoil, mulch, tile, and decking material math. I'm not a structural engineer or a licensed contractor; I'm a calculator built around the math that James Wu — Chicago-area flipper — uses on his own jobs. For structural decisions (joist sizing, beam spans, footing depth in your soil + climate, anything that needs a permit) talk to a licensed structural engineer or your local building department.
How pros actually do this
The math is the easy part — the part the volume formula doesn't tell you is that an augered post hole never comes back round. Bell-out at the bottom from the auger flutes biting wider than the shaft. Sidewall sloughing in Chicago clay subsoil after a rain. Stragglers in the dry mix that don't hydrate when you soak fast-set with a hose. Augered holes never come back round. Bell-out at the bottom, sidewall sloughing in clay, and stragglers in the mix pull a quarter-bag's worth of yield off every hole — one extra bag per hole pays for the trip you don't have to make back to Home Depot.
This came up most painfully on a fence post replacement at a Chicago-suburb flip in summer 2022 — twelve cedar posts going back in along a property line, 8″ holes, 36″ deep, fast-setting Quikrete. The engine math said two bags per hole, so I bought 24 bags. Halfway through the row, three holes had visible bell-out at the bottom and two had sloughed walls from a thunderstorm the night before. Twenty- four bags weren't going to do it. The trip back for an extra eight bags cost ninety minutes of working daylight on a hot day, and the second leg of the row got finished in the dark. Now the rule is simple: bag count from the calculator, plus one bag per hole. That's about $6/hole insurance against a wasted trip.
The other thing that catches new contractors is depth. Chicago and Cook County frost depth is 42 inches — that's the published number in the Chicago Building Code and the floor IRC 2021 R403.1.4 sets for footings carrying load. Fence posts don't carry structural load the way a deck footing does, so the convention is one-third the post height buried (a 6 ft post → 24″ down). But that rule of thumb assumes a non-freezing climate. In Chicago, anything shallower than the frost line will heave over winters — sometimes the first one, sometimes not until year three. A 6 ft fence post buried 24″ is a fence post that's leaning by year five. Bury 36″ minimum for fence posts, 42″ for anything carrying load.
For deck footings, the math swaps. AWC DCA-6 is the prescriptive standard most jurisdictions reference for residential deck construction; it sizes the footing diameter to the tributary load on the post. A 12″ diameter footing 42″ deep is the typical Chicago residential entry — 0.10 yd³ per footing, 5× 80 lb bags. Eight footings on a 12×16 deck is 0.8 yd³ total and 40 bags — still a bagged job, still well below the ready-mix minimum, but you're mixing for a couple of hours in a wheelbarrow or a small electric mixer. That's the cutover where renting an electric mixer for $40/day starts to look like the cheaper call than ordering a small ready-mix delivery and eating a $100+ short-load fee per NRMCA CIP 31.
The four steps
1. Measure diameter and depth (in inches).
Diameter is what the auger or post-hole digger cuts — typically 6″, 8″, 10″, or 12″ for residential work. Depth is from grade down to the bottom of the hole. Both go in as inches because that's how augers and post-hole diggers are sized; the formula converts to feet internally.
2. Compute volume in cubic feet.
A cylinder's volume is π × radius² × height. Convert diameter to radius in feet (D″ ÷ 24), and depth to feet (H″ ÷ 12), then multiply by π. For an 8″ × 36″ hole the math is π × (4/12)² × 3 = π × 0.111 × 3 ≈ 1.047 ft³. If you have an irregular hole — bell- out, side cavity, anything that isn't a clean cylinder — treat the irregularity as extra volume on top, or use a footing- specific calculator for belled designs.
3. Convert to cubic yards.
Divide by 27. For 1.047 ft³ that's 1.047 ÷ 27 ≈ 0.04 yd³. For one or two post holes the cubic-yard answer is mostly informational — at this volume you'll always be buying bags, not calling a dispatcher. Cubic yards become useful when you're computing totals across a row of footings or the entire fence run.
4. Convert to bag count.
80 lb Quikrete or Sakrete bags yield 0.60 ft³ each per the manufacturer data sheets. Divide cubic feet by 0.60 (or multiply cubic yards by 45) and round up. For a 1.047 ft³ post hole: ceil(1.047 / 0.60) = 2 bags. Add one bag per hole on top as the augered-hole cushion. Don't double-cushion at the cubic-yard AND bag-count layer — buy bags for the EXACT geometry, then add the +1/hole hand cushion.
Two worked examples, end to end
The two most common cylinder pours on a residential job are very different in scale, so both are worth walking through.
Example 1: Fence post hole — 8″ diameter × 36″ deep
- Volume in cubic feet:
π × (8/24)² × (36/12) = π × 0.111 × 3 ≈ 1.047 ft³ - Cubic yards exact:
1.047 / 27 ≈ 0.04 yd³ - Practical order, quarter-yard rounding:
ceil(0.04 × 1.05 × 4) / 4 = 0.25 yd³(mostly informational at this scale — bag count is the actionable number) - Bag count, 80 lb at 0.60 ft³ each:
ceil(0.04 × 45) = 2 bags - Bag count, 60 lb at 0.45 ft³ each:
ceil(0.04 × 60) = 3 bags - Practical: 3× 80 lb bags per hole (engine count + 1 bag augered-hole cushion). For 12 holes: 36 bags total.
Example 2: Deck footing — 12″ diameter × 42″ deep (Chicago frost line)
- Volume in cubic feet:
π × (12/24)² × (42/12) = π × 0.25 × 3.5 ≈ 2.749 ft³ - Cubic yards exact:
2.749 / 27 ≈ 0.10 yd³ - Practical order, quarter-yard rounding:
ceil(0.10 × 1.05 × 4) / 4 = 0.25 yd³(still bagged territory below ready-mix minimum) - Bag count, 80 lb at 0.60 ft³ each:
ceil(0.10 × 45) = 5 bags - Bag count, 60 lb at 0.45 ft³ each:
ceil(0.10 × 60) = 6 bags - Practical: 6× 80 lb bags per footing (5 + 1 cushion). Eight footings on a typical 12×16 deck: 48 bags total, $300 in concrete, half a Saturday with an electric mixer.
Both fall below the residential ready-mix minimum (~3 yd³), so neither is a delivery call. The deck-footing job is right at the cutover where renting a $40/day electric mixer pays for itself versus mixing in a wheelbarrow.
Run the math yourself
Type your hole diameter and depth. The calculator below is the same one used on the cluster anchor page; it covers slab, footing, post hole, and stairs.
Where this number breaks down
A few traps that put cylinder math on the wrong side of the order:
- Augered hole bell-out.Auger flutes cut wider at the bottom than the nominal shaft diameter — an 8″ auger bit can leave a hole that's 9-10″ at the very bottom. The cylinder formula assumes uniform diameter; it undercounts by the bell volume. Across a row of 12 fence posts, that's a quarter-bag of yield per hole adding up to 3 missing bags. The +1 bag/hole cushion is built for exactly this.
- Belled footings (intentional). Drilled-pier foundations sometimes spec an intentional bell at the bottom — a wider base for load distribution. Cylinder mode UNDERCOUNTS these by 30-50% depending on bell geometry. For belled designs, compute the cylinder portion and the bell (truncated cone) separately, sum, then convert. This is rare in residential but common in light commercial.
- Sidewall sloughing in clay subsoil.Chicago and most of the Midwest sit on heavy clay. Auger a hole in clay, leave it open through a thunderstorm, and the walls collapse inward — the volume you actually pour is bigger than what you measured. If you're digging more than a day ahead of the pour, expect 10-15% sidewall loss. The fix is to dig and pour same day, or accept the cushion.
- Freeze-thaw post heave.The math doesn't change, but the depth does. Posts buried shallower than the local frost line lift over winters as ice forms in the surrounding soil. In Chicago that's 42 inches. Upper Michigan goes to 60+. A fence post that math-checked at the right volume but went in 24″ deep will heave a half-inch per year and be visibly leaning by year five.
- Concrete cap vs full hole fill. Some installers cap fence posts with 6-8″ of concrete over a gravel base, instead of filling the whole hole. The volume math becomes π × (D/2)² × (cap depth), which is dramatically less than the full hole — a quarter or less of the bag count. This is a regional convention, not a structural recommendation; check what your inspector expects in your area.
- Dry-set vs wet-set bag math.Fast-setting Quikrete (the red bag) is dry-set — pour dry mix in the hole, soak with water, walk away. The yield is the same per bag but the workflow is different from wet-mixing. For wet-set you're mixing in a wheelbarrow or mixer, so wheelbarrow loss applies and the +1 cushion still earns its keep. Don't use fast-setting for footings where finish quality matters.
Frequently asked
How much concrete do I need for a fence post?
For a typical 8″ diameter × 36″ deep post hole, the geometric volume is π × (4/12)² × 3 ≈ 1.05 cubic feet, which is 0.04 cubic yards exact. With a 5% cushion that rounds to 0.25 yd³ on the calculator, but you would never order ready-mix at that volume. The practical answer is bagged: ceil(0.04 × 45) = 2× 80 lb bags per hole, or 3× 60 lb. Buy one extra bag per hole on top of that — augered holes never come back round, and the bell-out at the bottom plus sidewall sloughing in clay pulls a quarter-bag's worth of yield off every hole.
How deep should a post hole be in Chicago?
42 inches minimum for any post or footing carrying load through the winter. That's the published Chicago / Cook County frost depth and the floor IRC 2021 R403.1.4 sets for footings — they have to extend below the local frost line so the freeze-thaw cycle can't lift them. Fence posts that don't carry structural load can be shallower, but the convention of burying one-third of the post height stops working in freeze-thaw zones. In Chicago I bury at least 36″ for a 6 ft fence post and 42″ if the soil is clay-heavy or poorly drained. Upper Michigan goes deeper still — 60+ inches in some counties.
Can I use Quikrete fast-setting concrete for fence posts?
Yes — fast-setting Quikrete (the red bag, not the yellow) is the dry-set product made specifically for fence posts. You pour the dry mix into the hole, soak it with water from a hose, and walk away. It reaches handling strength in about 40 minutes per the Quikrete fast-setting data sheet. The yield is the same as standard Concrete Mix #1101 — 0.60 ft³ per 80 lb bag — but the bag count math is identical to wet-mix. The catch is finish quality: fast-setting bags don't level cleanly, so for a deck footing or any visible cap, mix-and-pour standard Concrete Mix is the better call. Fence posts where the concrete is buried out of sight are the right use case for fast-setting.
How many 80 lb bags for a 4×4 fence post?
For a standard 8″ diameter × 36″ deep hole around a 4×4 post, the engine answer is 2× 80 lb bags. Bag count is ceil(0.04 yd³ × 45 bags/yd³) = ceil(1.8) = 2. In practice I pick up 3 per hole — one for the math, one for the bell-out and sidewall sloughing in clay, and one because the trip back to Home Depot for a missing bag costs more than the spare bag does. For a 6×6 post in a 10″ × 42″ hole, it's 3 bags engine count and 4 bags practical.
What's the difference between a fence post and a deck footing?
Diameter and depth — a fence post is typically an 8-10″ hole, 36-42″ deep, holding a wood post in dry-set concrete. A deck footing is a 10-12″ hole minimum, 42″+ deep in Chicago to clear frost, and it carries actual structural load through a post base or saddle bracket per AWC DCA-6. The math is the same cylinder formula, but the deck footing carries dead and live load (the deck itself plus people, furniture, snow), so the geometry is sized to the load path, not the post you're attaching. AWC DCA-6 has the load-table guidance; the IRC 2021 references it for prescriptive deck construction. If the deck attaches to the house with a ledger, that's a separate engineering question from the footing itself.
Why does the calculator round up to a quarter-yard for one post hole?
Because the practical-order rounding is a ready-mix dispatch convention, not a useful number for a single post hole. The calculator's quarter-yard rounding works for the slab and footing modes where ready-mix is the realistic supply chain. For one post hole at 0.04 yd³, ignore the quarter-yard line and read the bag-count line instead — that's the actionable number. The below-ready-mix-minimum warning surfaces for exactly this reason: at any hole count under maybe 30 posts, bagged is the only sensible answer.
Related guides
- Concrete yardage for a slab →
- Concrete yardage for footings →
- Concrete yardage for steps and stairs →
- How many bags of concrete make a yard? →
Once the post-hole and footing math is dialed, the next decision is usually the bag-count vs ready-mix break-even — at what hole count or footing count does ordering ready-mix start to make sense? How many bags of concrete make a yard covers the cutover.
By James Wu. Volume math is site arithmetic, formulas shown above. Bag yields trace to Quikrete Concrete Mix #1101 data sheet and Sakrete High-Strength Concrete Mix. Frost-line depth and footing-below-frost requirement from IRC 2021 Chapter 4 (Foundations, R403.1.4). Residential code framing from ACI 332-20 Residential Code. Deck-footing prescriptive guidance from AWC DCA-6 (Prescriptive Residential Wood Deck Construction). Engine logic in lib/sitework/concrete.ts. Not structural-engineering advice — for code questions, footing design, or load-path review on a deck, work with a licensed structural engineer or your local building inspector. Full methodology.