Round Hole Volume Calculator finds the volume of a round hole from its diameter and depth. It also shows cubic yards, concrete bags, weight, and material cost.
Round Hole Volume Calculator finds the volume of a round hole from its diameter and depth. It shows cubic feet, cubic yards, concrete bags, weight, and cost for one hole or many.
Round Hole Volume Calculator: Cylinder Formula
A round hole is a cylinder. Its volume is the area of the circle times the depth.
$$V=\pi\left(\frac{d}{2}\right)^{2}h$$
V is the volume of one hole. The diameter is d and the depth is h. Both must be in the same unit. With feet, the answer is in cubic feet.
The calculator converts every entry to feet first. You can mix units, such as a diameter in inches and a depth in feet.
The total adds the hole count and the waste factor.
$$V_{total}=V\times n\times\left(1+\frac{w}{100}\right)$$
Here n is the number of holes and w is the waste percent. The large result at the top is this total in cubic yards. One cubic yard is 27 cubic feet.
With the default inputs, a 24 in by 36 in hole holds 9.42 cu ft. Adding 5% waste gives 9.90 cu ft, or 0.37 cu yd.
Weight is volume times density.
$$W=V_{total}\times\rho$$
The density ρ is in pounds per cubic foot. The concrete preset is 145 lb/ft³. The default hole weighs about 1,435 lb when filled with concrete.
Hole Volume Chart
The chart shows cubic feet for one hole with no waste added. The last column is 80 lb concrete bags for a 36 in deep hole.
| Diameter | 24 in deep | 36 in deep | 48 in deep | 80 lb bags at 36 in |
|---|---|---|---|---|
| 6 in | 0.39 | 0.59 | 0.79 | 1 |
| 8 in | 0.70 | 1.05 | 1.40 | 2 |
| 10 in | 1.09 | 1.64 | 2.18 | 3 |
| 12 in | 1.57 | 2.36 | 3.14 | 4 |
| 14 in | 2.14 | 3.21 | 4.28 | 6 |
| 16 in | 2.79 | 4.19 | 5.59 | 7 |
| 18 in | 3.53 | 5.30 | 7.07 | 9 |
| 24 in | 6.28 | 9.42 | 12.57 | 16 |
| 30 in | 9.82 | 14.73 | 19.63 | 25 |
| 36 in | 14.14 | 21.21 | 28.27 | 36 |
Volume grows with the square of the diameter. A 24 in hole holds four times as much as a 12 in hole of the same depth.
Concrete Bags per Hole
Bag counts come from yield, not bag weight. The QUIKRETE Concrete Mix data sheet lists these yields.
| Bag size | Yield | Bags per cubic yard |
|---|---|---|
| 40 lb | 0.30 cu ft | 90 |
| 50 lb | 0.375 cu ft | 72 |
| 60 lb | 0.45 cu ft | 60 |
| 80 lb | 0.60 cu ft | 45 |
The main figure on the bag card uses 0.60 cu ft per bag. That matches an 80 lb bag. The count is always rounded up to a whole bag.
For another bag size, divide the Total Output Volume by the yield. A total of 9.90 cu ft needs 9.90 ÷ 0.45 = 22 bags of 60 lb mix.
Fence Post Hole Example
A fence needs ten holes. Each is 10 in across and 30 in deep. The soil is loose, so the waste factor is 10%.
Enter 10 in, 30 in, 10 holes, and 10%. One hole is 1.36 cu ft. Ten holes are 13.64 cu ft. With waste the total is 15.00 cu ft, or 0.56 cu yd. That is 25 bags of 80 lb mix.
That figure is for an empty hole. A post takes up part of the space. A 4×4 post is 3.5 in square. Over 30 in of depth it displaces 0.21 cu ft.
Subtract that from each hole. The net volume is 1.15 cu ft per hole. Ten holes with 10% waste need 12.66 cu ft. That is 22 bags instead of 25.
For a round post, find its volume with the same cylinder formula and subtract it.
Deck Footing Example
Eight deck footings are drilled 16 in wide and 42 in deep. The auger leaves rough walls, so the waste factor is 8%. Concrete costs $155 per cubic yard.
One hole is 4.89 cu ft. Eight holes are 39.1 cu ft. With waste the total is 42.2 cu ft, or 1.56 cu yd.
The weight is about 6,120 lb. The material cost is about $242. About $18 of that is the waste allowance.
At 45 bags per yard, this job would take 71 bags of 80 lb mix. That is a lot of hand mixing. It is worth pricing a short-load delivery.
Bags or Ready-Mix
The Bulk Delivery Check card compares your total with 5 yd and 10 yd truck loads. Under 3 cu yd it shows Small quantity. From 3 cu yd it shows Bulk order range. From 10 cu yd it shows Full-load range.
Small orders from a ready-mix plant often carry a short-load fee. Ask your supplier for the minimum before you choose. Bags usually win for a few post holes. A truck usually wins once the job passes a yard or two.
Choosing a Waste Factor
The formula assumes a perfect cylinder. Real holes are not perfect. Augers leave grooves. Soft soil caves in near the top. A hole dug by hand is often wider at the bottom.
The default is 5%. Use 10% or more in loose or sandy soil. Drilled piers in unstable ground can need 15% to 25% extra. Zero is allowed when you want the exact geometric volume.
The cost card shows the waste allowance as its own line. You can see what the extra margin costs before you order.
Holes Deeper Than 5 Feet
The calculator shows a notice when the depth passes 5 ft. OSHA rule 29 CFR 1926.652 requires a protective system for excavations 5 ft or deeper that workers enter, unless the dig is entirely in stable rock. A narrow drilled hole that nobody enters is a different case. Check the rule that applies to your job.
Frequently Asked Questions
How do you calculate the volume of a hole?
Measure the diameter and the depth. Halve the diameter to get the radius. Multiply π × radius × radius × depth. Keep every measurement in feet to get cubic feet. Example: a hole 12 in wide and 3 ft deep has a radius of 0.5 ft. The volume is 3.1416 × 0.5 × 0.5 × 3 = 2.36 cu ft. Divide by 27 for cubic yards, which gives 0.087 cu yd.
How much concrete does a post hole need?
Find the hole volume, subtract the post, and add waste. A 10 in by 30 in hole is 1.36 cu ft. A 4×4 post removes 0.21 cu ft. That leaves 1.15 cu ft, or two 80 lb bags per hole. A 12 in by 36 in hole with the same post needs about 2.1 cu ft, or four 80 lb bags.
How do I subtract the post from the hole?
Work out the buried post volume and take it off the hole volume. For a square post, multiply width × width × buried depth. A 6×6 post is 5.5 in square. Buried 36 in, it displaces 5.5 × 5.5 × 36 ÷ 1,728 = 0.63 cu ft. For a round post, use the cylinder formula with the post diameter. A 4 in round post buried 36 in displaces 0.26 cu ft.
Does doubling the diameter double the concrete?
No. It takes four times as much. Volume depends on the radius squared. A 12 in hole 3 ft deep holds 2.36 cu ft. A 24 in hole at the same depth holds 9.42 cu ft. Doubling the depth does double the volume. Going up one auger size adds more concrete than most people expect.
Is the price per cubic yard or per cubic foot?
The price field is per cubic yard. US suppliers quote concrete and bulk fill that way. The calculator divides cubic feet by 27 and then applies the price. If your supplier quotes per cubic meter, multiply that price by 0.7646 to get the price per cubic yard. A price of 200 per cubic meter is about 153 per cubic yard.
What about a square or rectangular hole?
Use length × width × depth instead. A hole 2 ft by 2 ft by 3 ft deep is 12 cu ft. A round hole 2 ft across and 3 ft deep is only 9.42 cu ft. A round hole holds about 79% of the square hole that fits around it. For square footings, a cubic yard calculator is the better tool.
References
- QUIKRETE Concrete Mix No. 1101 data sheet, bag yields.
- OSHA 29 CFR 1926.652, requirements for protective systems in excavations.