Nominal Sizes, Land Measure and Setting Out

Nominal is not actual, and the gap is large

Sawn timber is named by the size it was before it was dried and planed. A piece called two by four inches finishes at about one and a half by three and a half — so the NAME describes a rough-sawn ancestor and the piece in your hand is around thirty per cent smaller in section.

The consequences run through every calculation that touches framing. A stud wall built from two-by-fours is three and a half inches thick, not four; a cavity for insulation is the actual depth, not the nominal one; and a section modulus computed on nominal dimensions overstates a joist's bending capacity substantially, because depth is squared.

The gap is not a constant percentage either. It is a fixed allowance per dimension, so it matters proportionally more on small sections than on large ones — a nominal one-by-two loses a much greater share than a nominal eight-by-ten.

Metric practice mostly avoids the problem by quoting the finished size, but not entirely: timber sold as a target size after planing, and sheet materials whose nominal thickness differs from the measured one, both behave the same way. The general rule is that a size in a product name is a description and a size on a drawing is a dimension, and only one of them can be used in arithmetic.

A board foot is a trading unit, not a volume

Lumber is priced by the board foot, defined as a nominal one inch by twelve inches by one foot. The definition uses NOMINAL thickness and width with ACTUAL length, which makes it internally inconsistent — and that inconsistency is the convention rather than an error in it.

So the wood in a board foot of planed two-by-four is meaningfully less than a twelfth of a cubic foot, and two suppliers quoting the same price per board foot for rough-sawn and surfaced stock are quoting different amounts of timber. Comparing prices means knowing which the quote is for.

Thickness has its own vocabulary in the hardwood trade, quoted in quarters of an inch of ROUGH thickness — four-quarter, eight-quarter and so on — again before surfacing. A four-quarter board finishes around thirteen-sixteenths, and a project drawn at a finished three-quarters of an inch needs four-quarter stock rather than the nominal match the numbers suggest.

None of this is a trap to be fixed; it is a convention to be respected. The calculators here state which dimensions they are using, because the same physical piece of timber has a nominal size, a finished size and a board-foot count, and all three are correct answers to different questions.

A cord is wood and air, and nobody has agreed the ratio

A cord of firewood is a STACKED volume — a hundred and twenty-eight cubic feet, conventionally four feet by four feet by eight feet — and stacked wood is mostly wood with a substantial fraction of air between the pieces.

How much of it is wood depends on the pieces: straight round split billets of uniform length stack tightly, while crooked, knotty or irregular pieces leave far more void. Reported solid-wood fractions across ordinary firewood span roughly two thirds down to under half, which means two honestly-measured cords can differ by a third in the fuel they contain.

The derived units are worse. A face cord, rick or run is a stack four feet high and eight feet long of whatever length the pieces happen to be — so it is a fraction of a full cord equal to the piece length over four feet, and it is meaningless without that length. A face cord of sixteen-inch pieces is a third of a cord; of twenty-four-inch pieces, a half.

Moisture is the third variable and it affects value more than volume does. Freshly cut wood can be half water by mass, and that water absorbs energy as it boils off rather than releasing any, so seasoned and green wood of identical volume deliver substantially different heat. A volume calculation is the start of a fuel comparison, not the end of one.

Land measure: the acre is historical, and the area is a plan area

An acre is forty-three thousand five hundred and sixty square feet, which is an odd number because it is a historical one: a chain by a furlong, the area a team could plough in a day. It survives because land records are written in it, not because it is convenient.

The estimating point that matters is subtler and catches people on sloping sites. A title deed, a land registry entry and a map all state a PLAN area — the area of the projection onto a horizontal surface. The ground itself has more surface than that wherever it slopes.

So a sloping site has less land than its surface suggests for the purposes of title, and more surface than its title suggests for the purposes of seeding, spraying, membrane, fencing or earthworks. The slope-and-true-area paper's factor converts between them, and on steep ground the difference is large enough to change an order.

Slope itself is quoted three incompatible ways, and the conversions are not linear. A one-in-two slope is fifty per cent and about twenty-six point six degrees; a hundred per cent is forty-five degrees, not vertical. The ratio form is the most ambiguous of the three, because different trades write it rise-over-run and run-over-rise — so a stated ratio without a stated convention is a number that could mean either of two very different slopes, and the pages here say which they use.

A plot that is not a rectangle is measured by decomposition rather than by averaging its sides, which over-reads. Offsets taken square off a straight baseline at a fixed interval sum as trapezoids, or as Simpson's curved strips over an even number of intervals, and a surveyed polygon closes in one pass by the shoelace formula on its corner coordinates.

Setting out: the diagonals find what the sides cannot

Measuring the four sides of a rectangle proves nothing about its corners. A parallelogram has equal opposite sides at any angle, so a frame can be exactly the right size in both directions and still be a rhombus.

Equal DIAGONALS are what make it a rectangle, and this is why every setting-out procedure compares them. The check is also far more sensitive than it looks: a small angular error produces a diagonal difference several times larger than the perpendicular offset it corresponds to, so the diagonal comparison detects an error the eye and the tape along the sides would both miss.

The other classical method is the three-four-five triangle, which relies on the same theorem from the other direction: a triangle with sides in that ratio has a right angle between the two shorter ones. Larger multiples give better accuracy for the same measuring error, which is why six-eight-ten is preferred on a building and why the check is worth doing at the largest scale the site allows.

Curves are set out by the same logic with a different relationship. A chord across an arc and the perpendicular offset at its midpoint determine the radius, so a curve can be established from two straightforward tape measurements without ever locating its centre. The sensitivity runs the other way from the diagonal check, though: for a shallow curve the offset is small and the derived radius is extremely sensitive to an error in it, which is why measuring a large radius in the field from a short chord is unreliable and why a longer chord is used wherever there is room.

Stacked storage: the cube is not the capacity

Working out how much a building holds by dividing its volume by a pallet's volume produces a number no warehouse has ever achieved, for several reasons at once.

Access takes most of it. Aisles wide enough for the handling equipment, cross aisles, pick faces, staging and dock areas consume a large share of the floor, and the share rises as the aisles widen — which is the trade a wide-aisle layout makes for cheaper, more flexible equipment.

Height is limited before the building's clear height is reached. Sprinkler clearance below the heads, flue spaces between and behind pallets in racking, the beam and deck thickness at every level, and the lift height of the truck all subtract, and they subtract at every tier rather than once.

And the load itself sets a limit the rack does not. How high a pallet can be stacked block-fashion depends on what is being crushed at the bottom, not on what the floor can carry — so a light crushable product reaches its stacking limit far below a dense robust one. Between that and rack beam capacity, a storage calculation is a series of independent limits of which the smallest governs, and a cube-based figure is an upper bound that none of them respects.