Quick answer: a round hole holds V = π r² × depth. A 12″ × 36″ post hole is 2.36 ft³; set a 4×4 post in it and you need 2.10 ft³ of concrete — five 60 lb bags or four 80 lb bags. An 80 lb bag yields ~0.60 ft³, a 60 lb bag ~0.45 ft³.
The calculation, in three steps
Square hole: V = width × length × depth
Concrete = hole volume − post volume
Bags = concrete ÷ bag yield, rounded up
Worked through on the most common job — a 12-inch auger hole, 36 inches deep, with a nominal 4×4 post:
- Hole: radius 6″ = 0.5 ft, depth 3 ft → π × 0.25 × 3 = 2.356 ft³
- Post: a "4×4" is actually 3.5″ × 3.5″ = 0.2917 ft each way → 0.2917² × 3 = 0.255 ft³
- Concrete: 2.356 − 0.255 = 2.101 ft³
- Bags: 2.101 ÷ 0.60 = 3.5 → 4 × 80 lb bags
The nominal-versus-actual timber trap. A "4×4" measures 3.5″ × 3.5″, a "6×6" measures 5.5″ × 5.5″, and a "2×4" is 1.5″ × 3.5″. North American softwood is sold at its rough-sawn nominal size and delivered planed down. Using 4″ instead of 3.5″ overstates the post volume by 31%, which under-orders your concrete. The calculator uses actual dimensions and shows both.
Bag yields and how many you need
Bag yield is set by the mix, not the bag, and the figures below are the standard published yields for pre-mixed concrete.
| Bag size | Yield (ft³) | Yield (L) | Bags per yd³ |
|---|---|---|---|
| 40 lb | 0.30 | 8.5 | 90 |
| 50 lb | 0.375 | 10.6 | 72 |
| 60 lb | 0.45 | 12.7 | 60 |
| 80 lb | 0.60 | 17.0 | 45 |
Concrete for common post holes, with a 4×4 post set in each:
| Hole size | Hole volume | Concrete after post | 60 lb bags | 80 lb bags |
|---|---|---|---|---|
| 8″ × 24″ | 0.70 ft³ | 0.53 ft³ | 2 | 1 |
| 8″ × 36″ | 1.05 ft³ | 0.79 ft³ | 2 | 2 |
| 10″ × 30″ | 1.36 ft³ | 1.15 ft³ | 3 | 2 |
| 10″ × 36″ | 1.64 ft³ | 1.38 ft³ | 4 | 3 |
| 12″ × 36″ | 2.36 ft³ | 2.10 ft³ | 5 | 4 |
| 12″ × 48″ | 3.14 ft³ | 2.80 ft³ | 7 | 5 |
| 16″ × 36″ | 4.19 ft³ | 3.93 ft³ | 9 | 7 |
| 18″ × 48″ | 7.07 ft³ | 6.73 ft³ | 15 | 12 |
Bag counts are the raw division rounded up, with no waste allowance. The calculator adds an adjustable allowance on top — 10% is a sensible default.
The crossover worth knowing. Once you pass about 1 cubic yard — roughly 45 × 80 lb bags — mixing by hand stops making sense on cost, time and consistency. That is around 12 large post holes. At that point ready-mix or a hired mixer is usually the better call, and the concrete volume calculator handles bulk ordering.
Sizing the hole in the first place
Two rules cover almost every domestic post, and they interact — take whichever gives the deeper hole.
Depth ≥ ⅓ of the post's above-ground height, and below the frost line
| Post | Actual size | Hole width | Typical use | Depth for a 6 ft fence |
|---|---|---|---|---|
| 4×4 | 3.5″ | 10–12″ | Fence, light rail | 24″ minimum |
| 4×6 | 3.5 × 5.5″ | 12–14″ | Gate post, corner | 30″ |
| 6×6 | 5.5″ | 16–18″ | Deck, pergola, heavy gate | 36″+ |
| 8×8 | 7.5″ | 22–24″ | Structural post | Engineered |
Frost line depth is the rule that overrides the others, and it varies enormously — from essentially zero in a frost-free climate to well beyond four feet in the coldest inland regions. Water in the soil expands as it freezes and lifts anything sitting above the freeze depth; a post that ends short of it will heave, and a fence line that has heaved once will keep doing it. Your local building department publishes the required depth for your area, and it is the number to build to rather than any general figure.
The corollary people miss: the bottom of the footing must be below the frost line, not the top. A 36-inch hole does not satisfy a 36-inch frost line by much once you have gravel in the base.
The soil you dig out takes up more room than the hole
Undisturbed soil is compacted. Break it up and it occupies more space than the hole it came from — a property called bulking or swell. This surprises people on the first hole and becomes a real problem across a fence line.
| Soil type | Bulking | Spoil from a 2.36 ft³ hole |
|---|---|---|
| Sand, gravel | +10–15% | 2.6–2.7 ft³ |
| Loam, mixed soil | +20–25% | 2.8–2.9 ft³ |
| Clay | +30–40% | 3.1–3.3 ft³ |
| Rock, broken | +50%+ | 3.5 ft³+ |
Ten post holes in clay produce over 30 cubic feet of loose spoil — more than a cubic yard, which is a substantial pile and often more than the garden can absorb. Decide where it is going before you start, not after hole three. The dirt volume calculator covers removal and disposal volumes in more depth.
Other holes this covers
- Deck footings and piers. Same maths; often a cardboard tube form sets the diameter. The concrete column calculator handles sonotube runs specifically.
- Tree pits. Dig two to three times the width of the root ball but only as deep as the ball itself — planting too deep is a leading cause of establishment failure. Volume tells you how much backfill or compost you need.
- Fence spikes versus concrete. A driven spike needs no hole at all, but carries much less lateral load. Worth the concrete on gate posts and corners regardless of what the runs use.
- Soakaways and drainage pits. The hole volume tells you the aggregate needed; remember voids in clean stone are only about 30–40% of the total, so a pit does not store its full volume of water.
- Umbrella and sign bases. Same round-hole calculation, usually shallower and wider.
Common mistakes & pro tips
- Using nominal timber sizes. A 4×4 is 3.5″. Using 4″ overstates the post volume by 31% and leaves you short of concrete.
- Forgetting to subtract the post at all. Over-orders by roughly half a bag per hole — noticeable across twenty holes.
- Mixing units mid-calculation. Diameter in inches with depth in feet is the classic. Convert first.
- Buying exactly the calculated number of bags. Holes are never perfectly cylindrical, augers wander, and some concrete is always lost. Add 10%.
- Ignoring the frost line. The single most expensive omission here, because the fence has to come out and be redone.
- No gravel in the base. A few inches of compacted gravel lets water drain away from the post end instead of sitting against it.
- Pro tip — crown the top of the pour. Slope the concrete slightly away from the post at ground level so water runs off rather than pooling at the joint, which is where rot starts.
- Pro tip — one spare bag per run. Cheaper than a second trip, and far cheaper than a hole that sets half-filled.
How to use this calculator
- Pick round or square — augered holes are round, dug footings are often square.
- Enter diameter (or width and length) and depth, in inches, feet, centimetres or metres.
- Choose the post size to subtract, or leave it as "no post" for a plain excavation.
- Set the number of holes and a waste allowance to get the total order.
- Read the bag counts for all four bag sizes, plus cubic yards and spoil volume.
Frequently asked questions
How do you calculate the volume of a hole?
For a round hole, volume = π × radius² × depth. A hole 12 inches across and 36 inches deep has a radius of 6 inches, so the volume is π × 36 × 36 = 4,071 cubic inches, which is 2.36 cubic feet. For a square hole, multiply width by length by depth. Keep all three measurements in the same unit before multiplying.
How many bags of concrete do I need for a post hole?
For a typical 12″ × 36″ hole with a 4×4 post set in it, you need about 2.1 cubic feet of concrete, which is five 60 lb bags or four 80 lb bags. An 80 lb bag yields roughly 0.60 ft³ and a 60 lb bag roughly 0.45. Always round up and buy one spare bag per run of holes.
How deep should a post hole be?
Deep enough to reach below the local frost line, and at least one third of the post's above-ground height. A 6 ft fence post therefore wants at least 2 ft in the ground, and more in a cold climate where the frost line may be 4 ft or deeper. Frost line depth varies enormously by region and is usually specified by the local building department, so check locally rather than relying on a general figure.
How wide should a post hole be?
About three times the width of the post. A 4×4 post, which actually measures 3.5 inches, wants a hole of roughly 10 to 12 inches. A 6×6 post wants 16 to 18 inches. The concrete collar carries the load and resists overturning, so a hole barely wider than the post gives it very little to work with.
Do I subtract the post volume from the hole volume?
Yes, if the post is set before the pour, which is the usual method. The post occupies space the concrete would otherwise fill. For a 4×4 post in a 36-inch deep hole that is about 0.26 ft³, roughly eleven percent of a 12-inch hole. Ignoring it means over-ordering by about half a bag per hole, which across a long fence line adds up.
How much soil comes out of a post hole?
More than the hole volume, because excavated soil bulks up as it is broken apart. Loose spoil typically occupies 20 to 30 percent more space than it did in the ground, and clay can bulk by 40 percent. A 2.36 ft³ hole therefore produces roughly 2.8 to 3.1 ft³ of loose spoil, so plan where it will go before you start digging a run of holes.
References & further reading
- Published bag-yield figures for pre-mixed concrete (40, 50, 60 and 80 lb bags).
- International Residential Code provisions on footing depth and frost protection.
- Local building department frost-depth requirements — the governing figure in every jurisdiction.
- Standard excavation bulking (swell) factors by soil classification.
Sizing rules here are general good practice, not a structural specification. Load-bearing posts, retaining structures and anything supporting a building should be sized by an engineer and built to the local code. See our accuracy policy.