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Woodworking Math

Fence calculator

Enter each straight run of the fence and its height. You get the posts, rails and pickets, the concrete for every post hole in bags of the mix you buy, and a lumber list in board feet.

Fence runs (ft)

Traditional rule, stated by This Old House and Long Fence

Picket style
0 for a privacy fence.
Post holes and concrete
Blank: 10 1/2 in, three times the post.

Traditional rule, stated by Quikrete and Sakrete

Blank: 36 in, a third of the post in the ground.

Traditional rule, stated by Quikrete, Sakrete and Long Fence

Quikrete and This Old House say 6 in; Long Fence 3–4 in.

Posts

14

14 × 4x4 at 10 ft (108 in each: height plus depth)

Pickets
219
Rails
39
Sections
13
Concrete bags
49

3.44 bags a post (1.291 ft³), 18.07 ft³ in all, of Quikrete Fast-Setting, 50 lb.

One source: Quikrete, the maker of that bag

Where the ground freezes, posts that carry a gate or a structure go below the frost line, and your local building department sets that depth. Fence height limits are local too (zoning and HOA rules).

Why: 100 ft of fence at 8 ft spacing is 13 sections and 14 posts; 14 holes of concrete take 49 bags.

Lumber list

ForPiecesSizeBoard feet
posts144x4 × 10 ft186.67
rails392x4 × 8 ft208
pickets2191x6 × 6 ft657
Total1,051.67

Board feet are counted at nominal size (a 2x4 as 2 × 4 in) on the stock length; a picket is 5 1/2 in wide when dressed (PS 20). Rails are 8 ft stock for 8 ft spacing. No waste allowance is added.

Why these numbers?
  1. The situation

    100 ft of fence, posts 8 ft apart, holes 10 1/2 in wide and 36 in deep.

    From your input: the fence and its posts

  2. What that means

    Posts go 6–8 ft apart on centre; closer at corners, gates and in wind.

    Traditional rule: This Old House and Long Fence , sources [1, 2]

  3. What that means

    About a third of the post’s length goes in the ground, in a hole about three times the post’s width, over a gravel base.

    Traditional rule: Quikrete, Sakrete and Long Fence , sources [3, 4, 2, 3, 4]

  4. So

    Concrete per post = (π × 5.25² − 3.5²) × the depth above the gravel ÷ 1,728 = 1.291 ft³; × 14 posts = 18.07 ft³.

    Arithmetic: exact by definition

  5. The number

    Quikrete rates Quikrete Fast-Setting, 50 lb at 0.375 ft³ a bag: 18.07 ÷ 0.375 = 48.18, so 49 bags.

    One source: Quikrete, the maker of that bag , sources [5]

  6. The number

    Where the ground freezes, posts that carry a gate or a structure go below the frost line, and your local building department sets that depth. Fence height limits are local too (zoning and HOA rules).

    From your input: where you build

How we source these numbers

How the materials are worked out

Each run is divided into sections no longer than the post spacing, and needs one more post than sections. Runs that turn a corner share the corner post. Posts usually go 6 to 8 feet apart on centre, closer at gates and in windy places; 8 feet suits the common 8 foot rail.

Pickets set side by side must cover the run with a gap between each pair, so the count is the run plus one gap, divided by a picket plus a gap, rounded up. Board on board alternates a back and a front layer, each front board lapping its neighbours, so every board starts the board's width less the overlap after the last. A 1x6 picket is 5 1/2 inches wide once dried and planed under the softwood lumber standard.

Quikrete and Sakrete both say to dig a hole about three times the post's width and deep enough to bury a third of the post, over a gravel base. The concrete is the hole's volume above the gravel less the post, divided by the yield the maker prints on that bag. The calculator rounds the total up to whole bags and adds no waste. Sakrete's own table for a 10 inch hole agrees with this method within a fifth of a bag at every depth it lists.

Frost depth and fence height limits are set locally, so ask your building department before you dig. The board foot calculator prices a lumber list, and the 4x4 actual size page has the post's dressed size.

Sources

  1. This Old House, Fence post installation: spacing, hole depth, gravel base, read 2026-11-07
  2. Long Fence, How to build a wood fence: post spacing and hole depth, read 2026-11-07
  3. Quikrete, Setting Posts project sheet: hole 3 times the post, 1/3 of its length deep, plus 6 in of gravel, read 2026-11-07
  4. Quikrete, Quikrete Fast-Setting Concrete Mix (No. 1004-50) data sheet: yield per bag; method for setting posts, read 2026-11-07
  5. Quikrete, Quikrete Concrete Mix (No. 1101) data sheet: yield per bag; method for setting fence posts, read 2026-11-07
  6. Sakrete, Sakrete Fast Setting Concrete Mix technical data sheet (rev. 04/16): yield, post setting, read 2026-11-07
  7. NIST, PS 20-25 American Softwood Lumber Standard, Table 3: minimum dressed sizes, read 2026-11-07

How we source these numbers