Building Up a Unit Rate: What One Square Metre Has to Carry

The constant, and whose hour it is measured in

The labour half of any rate begins as a constant: hours per unit. The first question to ask of any constant, before its value, is whose hour it counts. Gang-hours per square metre and man-hours per square metre are the same work described two ways, and they differ by the size of the gang — a factor of five on a gang of five. A constant lifted from one source and multiplied by a rate that assumed the other is not slightly wrong, it is wrong by a whole crew.

Price the gang as the people who are actually in it. Three layers and two labourers is not five layers and it is not five labourers; the gang costs three times one all-in hourly figure plus two times another, per gang-hour, and dividing that by the square metres the gang lays in an hour gives the labour line of the rate directly. Take the man-hour route instead and the same answer requires the weighted average of the two trades, not the layer's rate applied to all five, which is the commonest single overstatement in a hand-built rate. What sits on top of a wage to turn it into the cost of employing somebody — the taxes, the cover, the holiday accrual — is a separate stack and is worked through on the guide to pricing your own work.

Constants come from three places and they are not equal. Your own recorded outputs, elevation by elevation, on jobs you finished and were paid for, are the only ones that describe your gang. Published price books — Spon's Architects' and Builders' Price Book, Laxton's, RSMeans Building Construction Cost Data, and the BCIS data behind a good deal of British cost planning — describe somebody else's gang on somebody else's job, and are worth having for the sanity check rather than for the number. The CIOB Code of Estimating Practice describes the method rather than supplying figures, which is what makes it the one worth owning.

What moves a constant is mostly physical and mostly visible on the drawing before anybody starts. Height, because a gang working off the third lift of a scaffold stops every time the lift changes and the material has to arrive by hoist rather than by hand — NASC TG20 governs how the scaffold is put up, not how fast anyone works off it, but the number of lifts is knowable at tender. Unit weight, because a block that has to be handled two-handed is laid more slowly than one that does not; the Manual Handling Operations Regulations 1992 with HSE guidance L23, and NIOSH Publication 94-110 in the United States, set out how a lift is assessed rather than how many go up in an hour, but a wall of heavy units is a slower wall and the rate has to say so. Then repetition, which reduces the constant across a long run of identical bays and does nothing on a wall of eleven different details, and cutting content, which is why a gable is not a rate you can lift from an elevation.

One last property of a constant, and it is the one that explains most disagreements between two of them: what it includes. Some carry setting-out, scaffold moves, cleaning down, material handling and breaks; some count only the hour with a trowel in it. Two constants that appear to differ by a third often differ only about that, and neither is wrong. Write down which yours is, on the sheet, next to the figure.

1. Take a finished elevation whose cost you can actually reconcile, not a whole job — one elevation, one gang, one period.
2. Recover the quantity as it was measured in the bill, not as it was built, so the constant comes out on the denominator you will use it against.
3. Recover the hours from timesheets or allocation sheets rather than from the programme, and note the crew that was standing there rather than the crew that was planned.
4. Divide, and label the answer gang-hours per unit or man-hours per unit in words. An unlabelled constant is a factor-of-crew-size error waiting for its next user.
5. Write beside it what the hours included: setting-out, handling, scaffold moves, breaks, or none of them.
6. Record the conditions that will not repeat — the weather, the lift height, the number of details, whether the gang had a labourer — because those are what you adjust when you use it on the next job.

Ten blocks a square metre is already one and a quarter per cent

The material constant starts as pure module geometry and it is worth doing exactly once rather than believing the round number. A 440 by 215 mm block with a 10 mm joint occupies 450 by 225 mm of wall face, which is 0.10125 square metres, which is 9.877 blocks per square metre. A 215 by 65 mm brick with the same joint occupies 225 by 75 mm, or 0.016875 square metres, which is 59.26 bricks per square metre in a half-brick skin. The trade says ten and sixty, and both of those round-ups are the same 1.25 per cent, because ten of the first module and sixty of the second both come to 1.0125 square metres. A small allowance, entirely defensible — but it is inside the constant before anybody has said the word waste, and unwritten it gets added again by somebody who assumes the figure was net.

After that, the word waste needs testing rather than defining, and the test is a single question: does this quantity scale with the wall? Cutting to a module does — reveals, returns, rakes and snapped headers create part-units in proportion to how much work there is, and the opening schedule computes it with a pencil rather than a percentage. Damage and residue do — what breaks at the pallet and the saw, what stiffens in the tub, what is left in the bottom of a bag, all rise with throughput. A pallet round-up does not. Neither does a minimum load, a part-load charge, or the 3 m length bought because the run is 2.6 and it is not sold shorter.

That question is what decides where each one goes, and getting it wrong is expensive in a way that hides. What scales may be divided by the bill quantity and survives a remeasure intact. What does not scale is a step, and a step divided by a quantity gets charged once per unit instead of once: fold a pallet round-up into a rate, build twice the wall, and the rate collects two round-ups against one pallet actually bought. That is a windfall until the quantity halves instead, at which point it is a shortfall with your name against it. Round-ups, minimum loads and part-load charges belong on the order, where the rounding is done line by line at the point the merchant's ladder forces it — an ordering exercise with its own arithmetic, and not a rate decision at all.

Two things are settled elsewhere and are not settled again here. Whether the allowance sits in the quantity or on the price is a decision, and most of the quantity calculators on this site have already made it for you inside the quantity — the buyer's-side version of that double-count is on the renovation-budget guide. And mortar consumption is its own piece of arithmetic, worked through on the masonry-mortar guide: BS EN 998-2 specifies what the mortar has to be, not how much of it a thousand units will drink, and the consumption figure comes from the manufacturer's data sheet for the specific product.

Bought by the cubic yard, sold by the square metre

Every unit rate contains at least one conversion between a purchase unit and a bill unit, and that conversion is where a decimal goes missing. Mortar is bought by volume and laid over an area. Fill is bought by volume or by mass and placed to a depth over an area. Concrete is bought and measured in the same units, which sounds safe and is not, because the volume you buy and the volume you are paid for are two different quantities separated by over-break, spillage, what stays in the truck and what goes into the test cubes.

The figure that belongs in a rate is the delivered cost per unit of volume, and the quoted price per unit of volume is only the first line of it. Sitting between the two are part-load charges below a full load, waiting time beyond the discharge allowance — ASTM C94/C94M sets out the discharge and revolution limits that turn a wait into a chargeable event rather than an argument on the gate — washout, out-of-hours delivery, and the small-load surcharge that lands on the last pour of every phase. BS EN 206 with BS 8500-1 and 8500-2, or ACI 301 on the American side, tell you what the concrete has to be; none of them tells you what it costs to get it into the wall, and that is the number the rate needs.

How many yards a truck can legally carry, and how a tonne of anything becomes a yard of it, is settled on the bulk-materials guide and is not repeated here. The step that belongs here is the last one: take the all-in delivered figure per unit of volume, multiply it by the volume constant per unit of wall, and you have one line of a rate in the bill's units rather than the merchant's.

The lines that run along the wall, not across it

Damp-proof course, cavity tray, movement joint filler, wall plate, sole plate, edge trim, cill: their quantity is a length, and the wall's quantity is an area. Folding one into the other is a conversion whose factor lives in the shape of the wall, and the shape of the wall appears in neither number. The arithmetic is short and it is decisive. Twelve hundred and forty square metres of wall at 2.4 m high is about 517 metres of base course. The same 1,240 square metres at 8 m high is 155 metres. Identical area, a third of the damp-proof course, and a composite rate carrying a DPC allowance per square metre is out by a factor of more than three between those two walls without a single price having changed. The same applies to every trim, closer and tray that runs along an edge, which is why the honest treatment is to measure the length, price it per metre, and convert it onto the area only at the moment you need one number — knowing what height that number is true at.

Enumerated items behave worse still, because they do not scale with either. A lintel is one lintel per opening. A wall with four windows has four lintels whether it is 400 square metres or 900, so anything counted rather than measured has exactly the property of a pallet round-up and needs the same treatment: its own line, priced per item, kept out of the rate that gets remeasured. Three denominators on one wall — a number, a length and an area — and the only rate anybody will ever check is the one expressed in the third.

Seven rates over one square metre

One square metre of cavity wall is not one rate. It is an outer leaf, a cavity insulation, a tie density, an inner leaf, a damp-proof course at the base, a lintel at every opening and a pointed face — seven quantities in at least three units, each of which has to be converted onto the same denominator before any of them can be added. Building the composite is the blockwork exercise repeated six more times and totalled, and it is the point at which a unit mismatch stops being an error in one line and becomes an error in a number somebody quotes.

So run it backwards as soon as it exists. Take an elevation you have already finished, divide its reconciled total cost by the area you were paid for, and set that beside the composite you have just built from constants. They should agree to something you can explain in one sentence. Where they do not, the prices are almost never the culprit, because prices sit on invoices; it is the constant or the denominator, which are assumptions wearing the same typeface. ASTM E1557, the UNIFORMAT II elemental classification, is worth having to hand purely to keep the two figures at the same level: an element rate against a trade rate is two different quantities agreeing by accident.

This is narrower than whether the job made money, which is a different division with different inputs and is handled on the guide to pricing your own work. What the back-check settles is only this: whether the constant you are about to use again next month is the one your gang actually achieves.