Concrete Yard Calculator for Post Holes

This calculator works out the volume of concrete you need to fill one or more post holes. You enter the hole diameter, hole depth, and the number of posts, and it returns the total concrete volume in cubic yards, cubic feet, and cubic meters. It also accounts for the space taken up by the post itself, so you do not over-order.

Formula

The volume of concrete needed for a post hole is the volume of the hole minus the volume of the post that sits inside it. For a cylindrical hole and a cylindrical post, the formula is:

V = n × (π/4) × (D² − d²) × H

• V = total concrete volume (cubic feet, then converted to cubic yards)
• n = number of posts
• D = hole diameter (feet)
• d = post diameter (feet)
• H = hole depth (feet)

If you are using a square post, use the diagonal of the post as the diameter, or better, calculate the post’s cross‑sectional area and subtract it from the hole area. For a square post with side s, the area is s². For a round post, the area is π/4 × d².

Worked Example

Using the default values: hole diameter = 12 inches (1 ft), hole depth = 3 ft, post diameter = 4 inches (0.333 ft), number of posts = 1.

1. Convert hole diameter to feet: 12 in ÷ 12 = 1 ft
2. Convert post diameter to feet: 4 in ÷ 12 = 0.333 ft
3. Hole cross‑sectional area: π/4 × (1)² = 0.7854 ft²
4. Post cross‑sectional area: π/4 × (0.333)² = 0.0873 ft²
5. Net area: 0.7854 − 0.0873 = 0.6981 ft²
6. Volume per hole: 0.6981 × 3 = 2.0943 ft³
7. Total for 1 post: 2.0943 ft³
8. Convert to cubic yards: 2.0943 ÷ 27 = 0.0776 yd³, rounded to 0.08 yd³

The calculator shows 0.08 yd³, 2.1 ft³, and 0.06 m³. That matches the manual calculation.

How to Use the Calculator

Measure the diameter of the hole at the top – most post holes are not perfectly cylindrical, but the top diameter is a good approximation. For the depth, measure from the ground surface to the bottom of the hole. If you plan to put gravel at the bottom, subtract that depth from the hole depth. Enter the post diameter – for a square post, measure the width of the post, not the diagonal, unless you use the area method. The calculator assumes the post is centered and runs the full depth of the hole, which is typical for fence and deck posts.

For multiple posts, just enter the total number. The result is the total concrete volume for all posts combined.

Common Mistakes and How to Avoid Them

• Mixing units: Always check that you are entering inches for diameters and feet for depth. If your hole is 12 inches wide, enter 12, not 1 foot, unless the calculator accepts feet. This calculator uses inches for diameters and feet for depth.
• Forgetting the post volume: Many people order concrete for the full hole volume, which overestimates by 20–30% because the post displaces a significant amount. This calculator subtracts it automatically.
• Ignoring bell‑shaped holes: If your hole is wider at the bottom (common for frost heave resistance), the top diameter underestimates volume. In that case, measure the bottom diameter and use the average of top and bottom.
• Rounding too early: If you round the volume to 0.08 yd³ for one post, you might order 0.08 yd³ for ten posts, which is correct. But if you round each post to 0.1 yd³, you overorder by 25%. Use the total volume, not per‑post rounding.

How to Read the Results

The first result is in cubic yards, which is how ready‑mix concrete is usually ordered in the US. A typical 80‑lb bag of concrete mix yields about 0.022 cubic yards (0.6 ft³). So for the default example (0.08 yd³), you would need about 4 bags of 80‑lb mix. If you are mixing by hand, one 94‑lb bag of Portland cement makes about 1 cubic foot of concrete when mixed with sand and gravel. The cubic feet and cubic meters results help if you are buying pre‑mixed bags or working in metric regions.

Always add a small waste factor – 10% is common – to account for spillage, uneven holes, or slight measurement errors. For the default example, 0.08 yd³ × 1.1 = 0.088 yd³, so you would order 0.1 yd³ or 5 bags.

Limitations of the Formula

This formula assumes perfectly cylindrical holes and posts. Real holes are often irregular, especially if dug by hand. The formula also ignores the concrete that may be mounded around the base of the post above ground level, which is sometimes done for extra support. If you plan to flare the concrete at the top, add that volume separately. The formula does not account for gravel drainage layers – if you put 6 inches of gravel at the bottom, reduce the hole depth by 0.5 ft before calculating.

For frost line depth, the hole must extend below the frost line in your area. The calculator only computes volume; it does not tell you how deep to dig. Check local building codes for required post hole depths.

Alternatives and Related Calculations

If you are setting posts in tubes (cardboard forms), the tube diameter is the hole diameter, and the tube height is the hole depth – the same formula applies, but you do not subtract the post volume because the post is placed inside the tube after concrete is poured? Actually, for a tube, you pour concrete into the tube, then insert the post, so the post still displaces concrete. The same subtraction holds.

For a sonotube that is filled with concrete and then the post is set, you still subtract the post volume. If you are using a metal post anchor that is embedded in concrete, the anchor displaces a small volume – usually negligible, but you can subtract it if you know its dimensions.

For square holes (rare), use the formula for a rectangular prism: length × width × depth, minus the post volume. For tapered holes, use the average diameter.

Frequently Asked Questions

How many 80‑lb bags of concrete do I need for one 12″×3′ hole with a 4″ post?
From the example, you need 2.1 ft³ of concrete. An 80‑lb bag yields about 0.6 ft³, so you need 2.1 ÷ 0.6 = 3.5, so 4 bags. With a 10% waste factor, 4 bags is still enough, but 5 is safer.

Should I subtract the post volume from the hole volume?
Yes, always. The post occupies space inside the hole, so the concrete fills only the remaining volume. For a 4″ post in a 12″ hole, the post takes up about 11% of the hole volume – that is a meaningful amount.

What if my hole is not round?
Measure the width at the top and bottom, average them, and use that as the diameter. For a very irregular hole, you can fill it with water and measure the water volume, but that is impractical for most people. The average diameter method is accurate enough for ordering concrete.

How deep should a post hole be?
The depth depends on the frost line and the load. In general, fence posts should be set at least 2 feet deep, and deck posts often 3–4 feet. The calculator does not determine depth; it only computes volume once you know the depth.

Can I use this calculator for deck footings that are wider at the bottom?
Yes, but use the average diameter. If the bottom is 18″ and the top is 12″, use 15″ as the diameter. For a bell‑shaped footing, the average is a good approximation, but for very flared footings, you may need a more complex calculation.

Does the concrete volume change if I use a square post?
Yes. For a square post, use the area of the square (side²) instead of π/4 × d². For example, a 4″×4″ post has an area of 16 in², while a 4″ round post has an area of 12.57 in². The difference is about 27%, so it matters.

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in d | Hole diameter | in | 12 | 0
in h | Hole depth | ft | 3 | 0
in n | Number of posts | - | 1 | 1
in pd | Post diameter | in | 4 | 0
out yd3 | Concrete volume | yd³ | n * (pi/4 * ((d/12)^2 - (pd/12)^2) * h) / 27 | 2
out ft3 | Concrete volume | ft³ | n * (pi/4 * ((d/12)^2 - (pd/12)^2) * h) | 1
out m3 | Concrete volume | m³ | n * (pi/4 * ((d*0.0254)^2 - (pd*0.0254)^2) * (h*0.3048)) | 2