Calculate round or rectangular hole volume from diameter, length, width, depth and quantity, with concrete bag or bucket estimates.
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Hole Volume Formula
The calculator uses one of two formulas depending on the hole shape.
Round hole (cylinder):
V = π × (D / 2)² × H × N
Rectangular hole (prism):
V = L × W × H × N
- V = total hole volume
- D = hole diameter (round)
- L = length (rectangular)
- W = width (rectangular)
- H = hole depth
- N = number of identical holes
Convert all dimensions to the same unit before multiplying. The calculator converts internally and reports the result in ft³, yd³, m³, or liters depending on the input units. The bag count rounds up and does not include waste, spillage, or over-excavation.
Reference Tables
Use these tables to sanity check the result and pick a bag size.
| Round hole (D × depth) | Volume per hole | 80 lb bags |
|---|---|---|
| 8 in × 2 ft | 0.70 ft³ | 2 |
| 10 in × 3 ft | 1.64 ft³ | 3 |
| 12 in × 3 ft | 2.36 ft³ | 4 |
| 12 in × 4 ft | 3.14 ft³ | 6 |
| 18 in × 4 ft | 7.07 ft³ | 12 |
| Bag size | Approx. yield | Bags per yd³ |
|---|---|---|
| 40 lb | 0.30 ft³ | 90 |
| 60 lb | 0.45 ft³ | 60 |
| 80 lb | 0.60 ft³ | 45 |
Worked Examples
Fence post, round hole. A 10 in diameter hole, 3 ft deep:
V = π × (10/12 / 2)² × 3 = π × 0.347² × 3 ≈ 1.13 ft³ × 1.45 = 1.64 ft³ per hole. For 6 posts, total ≈ 9.8 ft³, or 17 bags of 80 lb mix.
Trench footing, rectangular. 4 ft × 2 ft × 1.5 ft:
V = 4 × 2 × 1.5 = 12 ft³, or about 0.44 yd³.
Why does the bag count seem high? Bag yields are nominal. Add 5 to 10 percent for spillage, uneven hole walls, and bell-shaped bottoms. Order one extra bag per 10 if the holes were augered rough.
Should I use diameter or radius? Enter diameter. The calculator divides by 2 internally to get the radius before squaring it.
