Why You Must Subtract the Post Volume from the Hole Volume

The basic idea: two solids can’t occupy the same space

A hole’s total volume is fixed by its width and depth. Once a post goes into that hole, part of that volume is now wood (or metal, or vinyl) — not empty space waiting for concrete. Calculating “hole volume” and buying that much concrete means calculating for a hole that no longer exists in that form, because the post is already taking up part of it.

How much this actually matters, by hole size

The post’s share of the hole’s volume depends entirely on the hole’s diameter — the wider the hole relative to the post, the smaller a percentage the post represents. Depth doesn’t change this ratio at all, since both the hole and the post scale together with depth.

At the tightest, minimum-recommended hole size for each post, the post occupies roughly a quarter of the total volume — genuinely significant. At a generously oversized hole, it drops to under 5%, where the subtraction barely moves the final number.

Why it matters most at exactly the hole size people actually use

This is the part that makes the subtraction genuinely important rather than a rounding footnote: the standard “3 times the post’s width” rule — the size most people actually dig — lands right in the range where the post fills 20-27% of the hole. It’s not an edge case. It’s the default, recommended hole size for both 4×4 and 6×6 posts.

The formula

Use the post’s actual dimensions (3.5×3.5 in for a “4×4”), and only the depth that’s actually buried, not the full post length.

What you need to calculate the subtraction

• Post’s actual cross-sectionIts real width, not the nominal lumber name.
• Embedded depthHow far below ground the post actually sits — not its total length.
• Hole diameterNeeded for the hole’s own volume before subtraction.
• Post shapeSquare posts use width², round posts use the circle formula.

Worked examples: does it actually change the bag count?

Example 1 — tight 8 in hole, 4×4 post, 2 ft deep

Here, the subtraction changes the actual bag count — a real, practical difference, not just a technicality.

Example 2 — standard 10 in hole, 4×4 post, 2 ft deep

At this size, both numbers round up to the same 2 bags for a single post — but the underlying volume difference is still real, and it compounds across multiple posts (see Example 3).

Example 3 — the same 10 in hole, across 10 posts

The per-post volume difference from Example 2 is about 0.19 cubic feet. Across 10 posts, that’s nearly 2 cubic feet — over 3 extra bags bought for concrete that was never actually going to fit, simply because the individual per-post rounding hid the difference until it was added up across the whole project.

Edge cases worth knowing about

• Round postsUse the circle formula for the post’s own volume too, not the square one — a round post displaces less than a square post of the same nominal width.
• Tapered postsSome vinyl and fiberglass posts are wider at the base than the top — use the average cross-section, or calculate the embedded taper separately if precision matters.
• Posts with an attached base bracketA metal post base or anchor bracket takes up its own space too — factor its rough dimensions in alongside the post itself.
• Very deep, narrow holesThe percentage stays the same regardless of depth, but the absolute volume difference in cubic feet grows larger the deeper the hole goes.

Mistakes with the subtraction step

• Skipping it entirelyOver-orders material on every single hole, most noticeably at minimum-recommended hole sizes.
• Using nominal post size instead of actualA “4×4” measured as a full 4 inches overstates the post’s own volume slightly, partially offsetting the error in the other direction.
• Subtracting the post’s full length instead of just the embedded depthOnly the buried portion displaces concrete — the above-ground section doesn’t.
• Assuming it never matters because “it’s just one post”The effect compounds fast across a multi-post project, even when a single post’s rounding absorbs the difference.
• Applying the subtraction to a freestanding column with nothing inside itIf there’s no post, there’s nothing to subtract — see Concrete Bags for a Small Column or Post for that distinction.

Quick reference: overestimate if you skip this step

What determines how much the subtraction matters

• Hole diameter relative to post sizeThe single biggest factor — tighter holes mean the subtraction matters more.
• Post sizeA 6×6 displaces more absolute volume than a 4×4 at the same hole diameter.
• Number of postsSmall per-post effects compound into a real number across a multi-post project.
• Post shapeRound posts displace less than square posts of the same nominal width.

Apply the subtraction in five steps

1. Calculate the hole’s full volume using its diameter and depth.
2. Calculate the post’s own volume, using actual dimensions and embedded depth only.
3. Subtract the post’s volume from the hole’s volume.
4. Add your waste allowance to the net result.
5. Divide by bag yield and round up for the final count.

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