Building & materials

These all start the same way — an area multiplied by a depth — and differ in the unit the answer needs to be in, because that is set by how the material is sold rather than by the maths.

• Asphalt Tonnage for a driveway or car park, by area and compacted depth.
• Concrete bags How many bags of pre-mixed concrete a pour takes, in 40, 50, 60 or 80lb bags.
• Concrete slab Work out how much concrete a slab needs, in cubic yards, cubic metres or bags.
• Footings & columns Concrete for a strip footing or a set of round piers, by the yard and by the bag.
• Gravel How much gravel or crushed stone an area needs, by the ton and by the yard.
• Sand How much sand a paver base, sandbox or bedding layer needs, by weight and volume.

The mistake running through this whole category is confusing wall area with floor area. A twelve by ten room has 120 square feet of floor and 352 square feet of wall, so working from the floor figure gives you about a third of the paint you need.

• Baseboard & trim How many lengths of skirting, coving or picture rail a room takes.
• Drywall Sheets, screws, compound and tape for a room, with the openings taken off.
• Flooring Square footage for a room, plus how many boxes it takes with waste allowed for.
• Insulation Batts or rolls for a wall or ceiling, with the framing taken out.
• Paint Work out how much paint a room needs, with the doors and windows taken off.
• Tile How many tiles a floor or wall takes, with the grout gap and waste counted in.
• Wallpaper Rolls needed, counted in drops, with the pattern repeat allowed for.

These are counting problems rather than area problems, and they go wrong in two specific ways. The first is the fencepost problem: a 24-foot run at 8-foot spacing has three bays but four posts, because both ends get one. Dividing the run by the spacing leaves you a post short.

• Board foot Board feet and the cost of them, worked out on the nominal size the yard bills.
• Decking Board rows, linear feet, joists and screws for a deck.
• Fencing Posts, rails, pickets and concrete for a run of fence.
• Plywood & sheet goods How many sheets a floor, roof or wall takes, in any sheet size.
• Roofing Roof area, squares and shingle bundles, with the pitch properly accounted for.
• Stairs Risers, treads, total run and stringer length from your floor-to-floor height.

Depth is the decision that matters, and more is not better. Two to three inches of mulch suppresses weeds and holds moisture; deeper than four sheds light rain before it reaches the soil. Topdressing a lawn wants an inch or two at most.

• Mulch How much mulch a bed needs, in cubic yards or two cubic foot bags.
• Pool volume How many gallons a pool holds — rectangle, round, oval or kidney.
• Sod & grass seed Rolls and pallets of turf for a lawn, or the seed to do it the slow way.
• Topsoil How much topsoil a bed or lawn needs, in cubic yards, bags and tons.

Masonry counts the way tiling does, and for the same reason. A brick does not occupy its own size on the wall — it occupies its size plus the mortar joint around it, so the joint thickness changes how many bricks a wall takes. Quoting a fixed number of bricks per square foot works for one brick at one joint and is wrong everywhere else.

• Brick How many bricks a wall takes, worked out from the brick size and the mortar joint.
• Concrete block Block counts, courses and mortar for a CMU wall, with openings taken off.

These size a machine to a load rather than counting material, and they all share one trap: bigger is not better. An oversized air conditioner cools the air quickly, shuts off, and never runs long enough to pull the humidity out, so the room ends up cold and clammy and the compressor wears out short-cycling.

• Air conditioner size What size of unit a room needs, with ceiling height, sun and occupancy allowed for.
• Solar array size How large an array your electricity use needs, in kilowatts and in panels.
• Water heater size What size tank a household needs, sized on its busiest hour rather than its day.