Why Fence Quotes Go Wrong: The Concrete Math Almost Everyone Gets Wrong

Ask someone to estimate the concrete for a 100 ft fence with posts every 8 ft and you’ll almost always get the same answer: “100 divided by 8, so about 12 posts, maybe 13 with rounding.” That number is wrong, and it’s wrong in a way that compounds with a second, sneakier mistake about hole size — the two together are why so many fence quotes run over budget on the one material line item that should be the easiest to get right: bags of concrete mix.

Mistake #1: posts are spacing + 1, not length ÷ spacing

Picture a fence line as a series of spans between posts, not a series of posts spread along a length. A 100 ft fence with 8 ft spacing has 100 ÷ 8 = 12.5 spans, which rounds up to 13 spans. But 13 spans require 14 posts — one at the start, one at the end, and one at every division in between. Think of a fence with a single 8 ft span: that’s one span, but it obviously takes two posts (start and end), not one.

The correct formula is:

numberOfPosts = ceil(fenceLength / postSpacing) + 1

Skip that “+1” and you undercount by one post on every fence, which sounds trivial until you realize that one missing post is also one missing hole’s worth of concrete, one missing bag (or several, depending on hole size), and — if the crew shows up short — a second trip to the supply yard. On a small job that’s an annoying delay. On a contractor’s bid across a dozen jobs a year, it’s a line item that never quite balances, and everyone assumes it’s waste or spillage when it’s actually just arithmetic.

Run the numbers for our 100 ft / 8 ft example: ceil(100/8) = ceil(12.5) = 13, plus 1 = 14 posts. Not 12, not 13 — 14.

Mistake #2: hole volume doesn’t scale the way it looks like it should

The second error is subtler and costs more per mistake. A post hole is a cylinder, and a cylinder’s volume is:

V = π × r² × depth

where r is the radius (half the diameter). The critical detail is that r is squared. That means if you bump the hole diameter up by 20% — say from 10 in to 12 in — you might expect roughly 20% more concrete. You’d be wrong by more than double the error: because the radius term is squared, a 20% increase in diameter produces roughly a 44% increase in volume, not 20%.

Do the actual arithmetic to see why. A 10 in diameter hole has a radius of 5 in; a 12 in diameter hole has a radius of 6 in. Volume scales with r², so the ratio is (6/5)² = 1.44 — a 44% jump in concrete needed for a hole that only “looks” 20% bigger. This is exactly the kind of error that turns a builder’s on-site judgment call (“eh, let’s just go a bit bigger for a sturdier post”) into a real cost surprise, because the intuition for “20% bigger hole” and the reality of “44% more concrete” are worlds apart.

This is also why the rule of thumb for hole diameter — roughly 3x the width of the post, so a 4x4 post gets a 10–12 in hole — matters more than it looks. Going from a “generous” 12 in hole back down to a code-typical 10 in hole isn’t a minor trim; it’s the difference between needing 44% more bags or not.

Worked example: 100 ft fence, 8 ft spacing, 10 in × 24 in holes

Let’s put both corrections together with real numbers, matching the defaults in the Fence Post Concrete & Spacing Calculator.

Step 1 — count posts correctly.

numberOfPosts = ceil(100 / 8) + 1 = ceil(12.5) + 1 = 13 + 1 = 14 posts

Step 2 — find the volume of one hole. A 10 in diameter, 24 in deep hole has a radius of 5 in:

holeVolume (cu in) = π × 5² × 24 = π × 25 × 24 ≈ 1,885 cu in
holeVolume (cu ft) = 1,885 / 1,728 ≈ 1.09 cu ft

Step 3 — multiply by the post count.

totalConcreteVolume = 1.09 × 14 ≈ 15.3 cu ft

Step 4 — convert to bags. A standard 50 lb bag of concrete mix yields about 0.375 cu ft once mixed. So:

bagsNeeded = ceil(15.3 / 0.375) = ceil(40.8) = 41 bags

At $6 a bag, that’s roughly $246 in concrete alone — and that number only holds up if both the post count and the hole volume were calculated correctly. Undercount posts by one (using the naive 100/8 = 12.5 → 13 approach) and you’re short almost 3 bags’ worth of concrete on the last post before anyone notices. Round the hole diameter up “just to be safe” from 10 in to 12 in without redoing the math, and the volume per hole jumps from about 1.09 cu ft to roughly 1.57 cu ft — pushing total bags from 41 to around 59, an increase most people would never predict from what looks like a small change to a drill bit or auger size.

What this calculator doesn’t decide for you

Bag count and cost are a mechanical calculation once you know three things: how many posts, how big each hole is, and how deep it goes. But hole depth is a judgment call this tool deliberately leaves to you. The standard guidance is that a hole should be roughly 1/3 to 1/2 of the post’s total length in the ground, or dug below your local frost line — whichever is deeper. In a warm climate with a 6 ft post, that might mean a 24 in hole. In a region with a 42 in frost line, you need to dig to at least 42 in regardless of what the post-length rule suggests, or the post will heave when the ground freezes and thaws. Check your local building code or frost-depth map before you lock in a depth — this calculator only does the volume and bag math once you’ve decided.

Do the math once, not twice

The pattern behind both mistakes is the same: fence concrete estimates go wrong when people eyeball a formula instead of running it. “Length divided by spacing” feels like the obvious post count, but it silently drops the last post. “A slightly bigger hole” feels like a small adjustment, but squaring the radius turns a modest increase in diameter into a much larger jump in concrete. Neither error is caused by bad measuring — they’re caused by intuition standing in for arithmetic.

Plug your fence length, post spacing, hole diameter and depth, and bag size into the Fence Post Concrete & Spacing Calculator and it will run the post-count-plus-one and radius-squared math for you every time, along with the total bags and total cost. If you’re pouring a slab, footing, or a handful of individual columns instead of a fence line, the Concrete Volume & Bags Calculator handles those shapes with the same bag-yield logic.