Perimeter Runs, Stock Lengths and Mitres

Area does not determine perimeter

This is the fact the whole family rests on and it is worth stating before anything else: two spaces with the same floor area can have very different perimeters. A square room of a hundred square metres has a perimeter of forty metres; a two-by-fifty corridor of the same area has a perimeter of a hundred and four.

So there is no such thing as a metres-of-skirting-per-square-metre rule, and any estimate that starts from an area is guessing at a shape. The perimeter has to be MEASURED, or derived from dimensions that describe the shape rather than its size.

The square is the minimum: for a given area, no rectangle has a shorter perimeter, and the figure rises without bound as the room gets longer and thinner. That is why corridors, galleries and L-shaped rooms are disproportionately expensive to trim, and why a plan rearranged for the same floor area can change the finishing order substantially.

The same reasoning runs through everything measured along an edge — skirting, casing, coving, gutter, edging, furring, ridge, flashing. Each is a length, each is set by shape, and none of them can be recovered from an area.

Openings cut both ways, and one of them adds

A door opening removes skirting across its width, and that is the deduction everyone makes. It also ADDS casing up both jambs and across the head, on both faces of the wall, plus the architrave returns and — where the wall is thick — a lining all the way round the reveal.

Count it through and a doorway frequently adds more linear metres of trim than it removes. The net effect of adding a door to a room is usually an INCREASE in the finishing order, which is the opposite of the intuition that an opening is a deduction.

Windows do not touch the skirting at all but carry their own casing, sill and apron, and a bay or a splayed reveal adds returns at every change of direction. Each return is a short piece with two mitres, which is where the labour goes even though the length is trivial.

The general rule that comes out of it is to measure deductions and additions as separate lists rather than netting them mentally. They are different products, cut differently, and a net length in the right total can still order the wrong things.

Stock lengths turn a total into a packing problem

Trim, gutter, edging and furring are sold in fixed lengths, and a wall does not care what those lengths are. A four-and-a-half metre run from three-metre stock takes two lengths and leaves one and a half metres over, whether or not another run can use it.

So the order is not the total divided by the stock length. It is a bin-packing problem — the same one the cut-list paper describes — and the answer depends on how the individual runs are distributed rather than on their sum. Several medium runs can waste more than one long one, and a total that divides neatly into stock lengths can still need an extra piece.

Where a run exceeds the stock length it has to be JOINED, and the joint is a decision rather than an accident. A scarf — two long opposing bevels rather than two square ends — holds a tighter line as the timber moves and is far less visible; and joints are positioned away from the sight line from the door, which is a setting-out choice that the length calculation cannot make.

Where the lengths LAP or slot into each other rather than butting into a connector, every joint costs the overlap. Pieces of length L lapped by o cover nL − (n − 1)o on a run with two ends and n(L − o) on a closed loop, a bed or a tree ring, where the last piece also laps the first. So the count is the run less one overlap, divided by L − o and rounded up, on an open run, and the whole run divided by L − o and rounded up on a loop — and on short lengths with a generous lap that can be a whole piece more than the run divided by the length.

Long profiles add a constraint the arithmetic does not see: stock has to fit through the building. A five-metre length that cannot turn the stairwell is not available at that length however the packing works out, which is why refurbishment work sometimes orders shorter stock deliberately and accepts the extra joints.

Mitres: the angle is half the corner, until the moulding leans

For flat trim lying against one surface — skirting, casing, flat edging — the mitre is half the corner angle. A ninety-degree corner takes two forty-five-degree cuts, and a corner that is not ninety takes half of whatever it actually is.

CROWN MOULDING breaks this, and it is the case that catches people. A crown does not lie flat: it bridges wall and ceiling at a SPRING ANGLE, tilted away from both. Cutting it flat on the saw therefore needs a compound cut — a mitre AND a bevel — and neither setting is forty-five nor half the corner.

Both settings are functions of the corner angle and the spring angle together. For the common case of a ninety-degree corner with a thirty-eight degree spring, the settings are close to 31.6 degrees mitre and 33.9 degrees bevel — numbers that look arbitrary and are not, and that change entirely if the spring angle is forty-five instead.

The alternative is to cut the moulding NESTED: held against the saw fence at its spring angle, upside down, so the fence and table stand in for the wall and ceiling. Then the mitre really is half the corner angle and no bevel is needed. It is simpler arithmetic and harder holding, which is the trade, and it only works while the moulding is small enough to be held that way.

The corner is not ninety degrees, and the mitre doubles the error

Rooms are not square. Walls bow, plaster builds up in corners, and a corner that measures ninety on the drawing is regularly a degree or two off in the building.

The consequence is amplified by the joint. Two pieces each cut at half the assumed angle meet with DOUBLE the error between them, so a corner two degrees out produces a gap that would need a two-degree correction split across both cuts — and a gap of that size at the top of a skirting is plainly visible from across the room.

So the practical method is to measure the actual angle at every corner rather than assume it, halve it, and cut to that. Where the angle cannot be measured, the traditional answer for internal corners is to COPE one piece — cut the second to the profile of the first rather than mitre it — which tolerates an out-of-square corner and does not open as the timber shrinks.

External corners have no equivalent and stay mitred, which is why they are the joints that open first. Glue and a pin across the mitre resist the movement that would otherwise separate it, and the resulting order needs a little more length than the geometry implies.

Curves become segments, and the segment count comes from a tolerance

A curved edge trimmed with straight stock is approximated by a polygon, and the question is how many segments. It is not a matter of taste: each chord sits a measurable distance inside its arc, and that distance is the visible flat spot.

The deviation falls with the SQUARE of the segment count, so doubling the number of pieces quarters the flat. That is a fast return at first and a poor one later — going from four segments to eight transforms the curve, and going from twenty to forty is invisible while doubling the cuts and joints.

So the count is chosen from an allowable deviation rather than from the radius, and a tight radius needs more segments than a gentle one for the same visual result. Pre-formed or kerfed sections avoid the question entirely by bending, at the cost of a limited minimum radius and a different material.

Each segment also adds two mitred joints whose angles are set by the included angle between adjacent chords rather than by anything on the plan. This is the one place in the family where the fabrication cost rises much faster than the length, and a length-only estimate misses almost all of it.

Rainwater goods: the run is not the only length

Gutter length follows the eaves, which is a straightforward perimeter measurement, and then diverges from it in two ways. The gutter runs to a FALL, so its length along the slope slightly exceeds the horizontal eaves — negligible on a domestic run, real on a long commercial one — and it is interrupted by outlets, stop ends, angles and unions, each of which is a component rather than a length.

Downspout length is the part most often under-ordered. It is the vertical drop from the outlet to the discharge, plus any offset needed to clear an overhang — and an offset is two bends and a short raking piece rather than a straight addition. A building with deep eaves needs an offset at every downspout and a plain vertical measurement misses all of them.

Fixings follow their own spacing rule rather than the run: brackets at a stated maximum centre, closer where the fall is greater or the gutter deeper, and an extra bracket beside every joint and outlet. That is a count over a line with a plus one, which is the arithmetic the fastener paper describes.

None of which is answered by the roof area, and this is where the two halves of measurement meet. The roof area sizes the gutter's CAPACITY and the outlet spacing; the eaves perimeter sizes the QUANTITY. They are different calculations from different measurements, and using either for the other is the standard mistake on this family of pages.