Quantity takeoff arithmetic

A quantity takeoff is the systematic measurement of every material and item of work shown on the drawings and described in the specifications. It is the foundation of the estimate, the source of purchase orders and a baseline for tracking progress and changes. Lessons 3 to 5 covered areas, volumes and earthwork; this lesson applies that geometry to the materials that are counted rather than poured: framing lumber, sheet goods such as drywall, reinforcing steel, masonry units and tile. Each has its own units of sale, standard sizes and counting rules, and each rewards a careful, tabulated method. The full estimating process, pricing and software are covered in the construction estimating course; here the focus is on the arithmetic that makes quantities right.

Principles of a good takeoff

• Work in an organized order, usually by specification division and then by floor, area or system, so that nothing is missed and nothing is counted twice.
• Measure net quantities from the drawings, then apply waste, laps and allowances separately and visibly, so that others can check them.
• Use the unit of measure in which the item is bought or priced: m³ or yd³ for concrete, t or tons for rebar and aggregates, m² or ft² for drywall, pieces for doors and fixtures.
• Record dimensions, not just results, in a takeoff sheet or software, with references to drawing numbers and details.
• Mark up the drawings as items are measured, so that what has been counted is visible.
• Round only at the end, and round up to the units in which materials are sold.

Counting rules matter as much as formulas. When items are spaced along a length, the number of items is the number of spaces plus one if there is an item at each end. Forgetting the extra one, called the fence-post error, is one of the most frequent small errors in takeoffs of studs, joists, bars and anchors.

Here L is the length over which items are spaced, s is the spacing, and the brackets mean 'round up to the next whole number'. A wall 3.0 m long with studs at 400 mm needs ⌈3,000 ÷ 400⌉ + 1 = ⌈7.5⌉ + 1 = 9 studs, before any extras for corners, openings and connections.

Framing lumber

US lumber is sold under nominal names such as 2×6 and priced per piece, per linear foot or per thousand board feet (MBF). Precut studs in standard lengths, such as 92 5/8 in for 8 ft walls and 104 5/8 in for 9 ft walls, reduce cutting and waste. Standard lumber lengths run in 2 ft increments, typically from 8 to 20 ft.

A board foot is a volume of wood equal to a board 1 inch thick, 12 inches wide and 1 foot long, or 144 cubic inches. Board feet are calculated from nominal, not actual, dimensions. The metric equivalent volume is the cubic meter; one cubic meter of nominal dimensions is about 424 board feet.

Sheet goods: drywall and sheathing

Drywall, plywood, OSB and rigid insulation are sold in sheets. The simplest takeoff divides the net area by the sheet area and adds waste, then rounds up to whole sheets. More careful takeoffs lay out sheets wall by wall, choosing lengths that minimize joints and waste: a 2.7 m high wall may be boarded horizontally with sheets 1.22 m wide, and longer sheets (3.66 m or 12 ft) reduce butt joints on long walls.

Drywall takeoffs also generate quantities for screws, tape, joint compound and corner bead, usually by applying rates per square meter or square foot from manufacturers' data, and for the labor of hanging and finishing, which is often priced per unit area at a specified level of finish.

Reinforcing steel

Reinforcing bars are bought by mass and placed by count and length. The takeoff counts the bars of each size and length from the drawings and bar schedules, adds laps where bars are spliced, and converts total length to mass using the mass per unit length of each bar size. Detailing and lap lengths are set by the structural engineer and the governing concrete standard; the construction manager's role is to check quantities and understand how they were produced.

US bars are sized by numbers under ASTM A615 and A706, where the number is the diameter in eighths of an inch (a #4 bar is 4/8 = 1/2 in). Common stock lengths are 20, 40 and 60 ft. Bar weights are fixed by the standard:

To count bars in a mat, find the length available for spacing (the slab dimension less the cover at each edge), divide by the spacing, round up and add one. Each bar's length is the other slab dimension less the cover at both ends. If a bar is longer than the stock length, it must be spliced, and each lap adds the lap length to the total.

Masonry units

Masonry is taken off by wall area, net of openings, and converted to units using the number of units per square meter or square foot. That number depends on the unit size plus one mortar joint in each direction, because each unit effectively occupies its own face plus half a joint all round.

US masonry uses modular units in inches. A modular brick (7 5/8 × 2 1/4 in face) with 3/8 in joints occupies 8 × 2 2/3 in, so about 6.75 bricks cover a square foot. A standard concrete block (15 5/8 × 7 5/8 in face) with 3/8 in joints occupies 16 × 8 in, so 1.125 blocks cover a square foot.

Tile and other boxed materials

Tile, flooring planks, shingles and many finishes are sold in boxes or bundles that cover a stated area. Divide the area including waste by the coverage per box and round up to whole boxes. Owners often require attic stock, extra material from the same production lot kept for future repairs, usually stated as a percentage or a number of boxes in the specification. Because color and shade vary between production lots, all the tile for one area, including attic stock, should be ordered at the same time.

Units of measure