Hole Volume Calculator: Cylindrical and Rectangular Holes
Enter your hole dimensions to get the excavated volume for a round or rectangular hole in cubic feet, cubic yards, or cubic metres. The calculator also works out how much concrete you need to fill it, how many pre-mixed bags to buy (40, 60, or 80 lb), accounts for waste, and handles multiple holes at once. Switch between metric and imperial with one click.
How to calculate hole volume
The volume formula depends on the hole shape. For a cylindrical hole (the standard round post hole), the formula is:
Volume = pi x radius2 x depth
where the radius is half the diameter. For example, a 12-inch-diameter hole that is 36 inches deep has a radius of 6 inches (0.5 ft). Volume = 3.14159 x 0.52 x 3 ft = 0.236 ft3 per hole.
For a rectangular hole (a square footing or trench section), the formula is simply:
Volume = length x width x depth
A 12-inch x 12-inch hole that is 36 inches deep gives 1 x 1 x 3 = 3 ft3 - roughly 13 times the volume of the round hole with the same diameter, which shows why round post holes use far less concrete than square excavations.
From hole volume to concrete bags
Once you know the volume in cubic feet, convert to bags in three steps:
- Add waste. Mix losses, spillage, and uneven hole walls mean you need more than the raw volume. The industry standard is a 10% waste allowance, though 5-15% is common depending on conditions.
- Pick a bag size. An 80-lb bag of dry pre-mixed concrete (such as Quikrete or Sakrete) yields about 0.60 ft3 when mixed. A 60-lb bag yields 0.45 ft3, and a 40-lb bag yields 0.30 ft3.
- Divide and round up. Divide the concrete volume (with waste) by the yield per bag, then round up to the nearest whole bag. You always round up: a fraction of a bag still costs a full bag.
For large pours above 1 cubic yard (27 ft3), ready-mix delivered by truck is usually cheaper per cubic foot than buying bags. Use the cubic yard output to get a quote.
Sizing round post holes correctly
The standard rule for fence or deck posts is that the hole diameter should be at least 3 times the post width. A 4-inch post needs a 12-inch hole; a 6-inch post needs an 18-inch hole. The depth should reach below the local frost line (the depth at which soil freezes in winter) plus at least 6 inches. In most of the US, frost lines range from a few inches in Florida to over 60 inches in Minnesota; your local building authority publishes the code depth for your zone.
For structural posts (decks, pergolas, fences taller than 6 ft), consult local building codes. Many jurisdictions require a permit and inspection for footings deeper than a certain threshold.
Metric and imperial unit conversions
This calculator works in either system, but concrete volumes are always shown in cubic feet and cubic yards because US bag yields and ready-mix pricing are quoted in those units. Key conversions:
- 1 cubic yard = 27 cubic feet
- 1 cubic foot = 0.028317 cubic metres
- 1 inch = 2.54 cm
- 1 foot = 30.48 cm
If you are working in metric, enter dimensions in centimetres and the calculator converts them to feet internally before computing concrete volumes.
Pre-mixed concrete bag yields
| Bag weight | Yield per bag | Bags per cubic yard | Common use |
|---|---|---|---|
| 40 lb | 0.30 ft3 | 90 bags | Small repairs, limited lifting capacity |
| 60 lb | 0.45 ft3 | 60 bags | General purpose, most popular size |
| 80 lb | 0.60 ft3 | 45 bags | Fastest to fill, fewer bags to handle |
Approximate mixed concrete volume per bag at standard water ratios. Order at least 10% extra to account for waste.
Frequently asked questions
How do I calculate the volume of a round post hole?
Use the cylinder formula: Volume = pi x (diameter/2)2 x depth. Convert all measurements to the same unit first. For a 12-inch diameter, 36-inch deep hole: radius = 6 in = 0.5 ft; Volume = 3.14159 x 0.52 x 3 = 0.236 ft3.
How many 80-lb bags of concrete do I need for a post hole?
Divide the hole volume in cubic feet by 0.60 (the yield of an 80-lb bag), then round up. Add 10% for waste first. A 12-inch x 36-inch hole holds about 0.236 ft3; with 10% waste that is 0.26 ft3, so you need 1 bag (0.26 / 0.60 = 0.43, rounded up to 1). For 10 such holes: 2.6 ft3 total, rounds up to 5 bags.
What is the difference between a cylindrical and rectangular hole?
A cylindrical hole is circular in cross-section, like a hole drilled with an auger for a fence post. A rectangular hole is square or oblong, typical for poured concrete footings or foundations. For the same diameter, a round hole holds about 78.5% of the volume of a square hole with the same side length (pi/4 = 0.785), so round holes use significantly less concrete.
Why should I add a waste allowance?
Hole walls are never perfectly smooth, the auger undercuts slightly, and some concrete is lost during mixing and pouring. A 10% waste factor is the industry standard. In loose or sandy soil you may want 15%; in very clean, straight auger holes in firm clay, 5% can be enough. It is always cheaper to buy one extra bag upfront than to make a second trip.
How deep should a fence post hole be?
The general rule is that the below-ground depth should be at least one third of the total post length, plus it must reach below the local frost line. For a 6-foot above-ground fence post you typically need at least 2 feet in the ground, but your local frost line may require deeper. Check your local building code or contact your municipality for the required depth in your area.
When should I use ready-mix concrete instead of bags?
Ready-mix concrete delivered by truck is economical once you exceed about 1 cubic yard (27 cubic feet). Below that threshold, pre-mixed bags are more practical. For a typical 10-post fence project at 0.24 ft3 per hole, total volume is about 2.4 ft3 (roughly 4 bags of 80-lb), well within the bag range. A large deck with 20 footings at 1.5 ft3 each hits 30 ft3, where ready-mix pricing is worth getting.
What is the volume of a cubic yard in cubic feet?
1 cubic yard equals exactly 27 cubic feet (3 ft x 3 ft x 3 ft). Concrete is often ordered by the cubic yard, so divide your total cubic-foot requirement by 27 to get cubic yards. The calculator does this automatically in the output.