Reference/Glossary
43 terms behind jobsite calculations, each defined plainly, with its formula where it has one and a link to the calculator that does the maths.
How steep a roof is, written as inches of rise per 12 inches of horizontal run. A 6/12 roof climbs 6 inches for every foot it travels horizontally. It is a ratio, not an angle.
The same steepness expressed in degrees. A 6/12 roof is about 26.57°, and 12/12 is exactly 45°.
angle = arctan(rise ÷ 12)
Steepness as rise over run times 100. A 6/12 roof is a 50% grade. More common for site work and drainage than for roofs.
grade % = rise ÷ run × 100
The number that converts a horizontal distance into the true distance along the slope. Multiply a rafter's run by it to get the rafter's length, or a roof's footprint by it to get its real surface area. At 6/12 it is about 1.118; at 12/12 it is √2, about 1.414.
slope factor = √(1 + (rise ÷ 12)²)
The horizontal distance a rafter covers — for a common rafter on a symmetrical gable, half the building width. Always measured level, never along the slope.
The shortening that allows for the thickness of the ridge board. Half the ridge thickness comes off each rafter's horizontal run before the slope factor is applied, so each side stops at the face of the ridge rather than its centreline.
run = building width ÷ 2 − ridge thickness ÷ 2
The part of the rafter that extends past the wall to form the overhang. Its length along the rafter is the horizontal overhang multiplied by the slope factor.
tail length = overhang × slope factor
The rafter running diagonally from a building corner up to the ridge, where two roof planes meet on an outside corner. On a regular hip, with equal pitch both sides, it runs at 45° in plan, so it travels √2 times as far horizontally as the common rafter does.
hip plan run = common run × √2; hip length = √(plan run² + total rise²)
The same geometry as a hip rafter, but where two roof planes meet on an inside corner and water runs toward it rather than away. On equal pitches the length calculation is identical.
A regular hip travels 12 × √2, about 16.97 inches, of plan run for every 12 inches the common rafter travels. The hip scale on a framing square rounds that to 17. Calculators use the exact value.
A shortened common rafter that runs from the wall plate up to a hip, or from a valley up to the ridge. Successive jacks step down in length by the same amount each time.
The amount each successive jack rafter is shorter than the one before it. It depends only on the spacing and the pitch: at 16 inches on centre on a 6/12 roof it is about 17.89 inches.
common difference = rafter spacing × slope factor
A unit of roof area equal to 100 square feet of roof surface — measured on the slope, not on the footprint.
A package of shingles. Standard asphalt shingles are commonly packed three bundles to the square, but that is a manufacturer convention rather than a rule — the wrapper states the coverage, and it governs.
The true surface area of a roof, larger than its footprint because the roof is sloped. For a simple roof, multiply the plan area by the slope factor.
roof area = footprint area × slope factor
The vertical distance a stair climbs, from finished floor to finished floor. Measured to finished surfaces — flooring added later changes the first and last riser.
The vertical height of one step. Every riser in a flight should be equal, so the total rise is divided by the number of risers rather than using a fixed height. Many jurisdictions follow the IRC maximum of 7¾ inches for residential stairs, but local code governs.
riser height = total rise ÷ number of risers
The horizontal depth of one step, where the foot lands. The IRC residential minimum is 10 inches; local code governs. A straight flight usually has one fewer tread than risers.
The horizontal distance a flight covers from the first riser to the last.
total run = number of treads × tread depth
The inclined board, usually cut from a 2×12, that carries the treads and risers. Its length is the diagonal of the total rise and total run.
A comfort check, known as Blondel's rule: twice the riser height plus the tread depth. Comfortable stairs land near 24 to 25 inches. It is a guide to how a stair feels to walk, not a code requirement.
2 × riser + tread ≈ 24–25 in
The name of a lumber size, such as 2×4, which refers to its rough-sawn dimensions before drying and planing. It is not what the board measures.
What a surfaced, dry board really measures. A 2×4 is 1½ by 3½ inches. The full table is on the lumber dimensions reference page.
A unit of lumber volume equal to 144 cubic inches — a board 1 inch thick, 12 inches wide and 12 inches long. Board feet are conventionally calculated from nominal, not actual, dimensions. A 2×6 ten feet long is 10 board feet.
board feet = thickness (in) × width (in) × length (ft) ÷ 12
A measure of length only, regardless of the board's width or thickness. Trim and moulding are sold by the linear foot; hardwood lumber usually by the board foot.
The spacing of framing members measured from the centre of one to the centre of the next. Walls are most often framed at 16 or 24 inches on centre, because both divide evenly into 48-inch sheet goods.
For a straight wall, the number of bays the length divides into at the chosen spacing, plus one stud to close the far end. A 16-foot wall at 16 inches on centre is 192 ÷ 16 = 12 bays, so 13 studs — before corners, openings and blocking, which are added separately.
studs = (wall length in inches ÷ spacing) + 1
The horizontal members a wall's studs are nailed between. Bearing walls usually carry a doubled top plate, so plate linear footage is the wall length times the number of plates.
The unit ready-mix concrete is ordered in, equal to 27 cubic feet. A 10 by 10 foot slab 4 inches thick is about 33.3 cubic feet, or 1.23 cubic yards, before a waste allowance.
cubic yards = length (ft) × width (ft) × thickness (ft) ÷ 27
Reinforcing bar is named by number. For #3 through #8, the number is the nominal diameter in eighths of an inch, so #4 is ½ inch and #5 is ⅝ inch. #4 bar weighs about 0.668 pounds per foot. Larger sizes do not follow the eighths rule exactly.
A grid of bars running both ways across a slab at a set spacing, tied at the crossings. Bar count in each direction is the covered dimension divided by the spacing, plus one.
The distance from the surface of the rebar to the surface of the concrete. It protects the steel from corrosion and fire. Minimums are set by code and drawings — for example ACI 318 calls for 3 inches where concrete is cast against and permanently exposed to earth.
The angle between the wall and the back of a crown moulding as it sits installed. The two common crown profiles are 38° and 45°. It is what makes crown a compound cut when it is laid flat on the saw.
A cut made with both the saw's miter and bevel set at once, used to cut sprung moulding lying flat. For 38° crown in a square corner the settings are about 31.6° miter and 33.9° bevel; for 45° crown, about 35.3° miter and exactly 30° bevel.
half = (180 − corner) ÷ 2; miter = arctan(sin spring × tan half); bevel = arcsin(cos spring × cos half)
The angle between the two walls the moulding turns across — 90° for a square corner, 135° for an octagon corner. The moulding turns through 180° minus that angle, and each piece takes half, which is why the corner angle cannot be used directly as a saw setting.
Two equal bends in opposite directions that move a run of conduit sideways to clear an obstruction while keeping it parallel to its original line.
The number that converts the depth of an offset into the distance between its two bends. It is the cosecant of the bend angle: 2 at 30°, about 1.414 at 45°, about 2.613 at 22.5°, about 5.76 at 10°.
multiplier = 1 ÷ sin(angle); distance between bends = offset × multiplier
How much shorter the conduit run becomes because of an offset — the angled section travels farther than the straight line it replaced. It has to be added to the measurement to the obstruction. At 30° it is about 0.27 inch per inch of offset.
shrink = travel − run = offset × tan(angle ÷ 2)
An offset where the pipe moves both vertically and horizontally at the same time. The two movements combine into a single true offset, which is then treated like an ordinary offset.
The actual diagonal distance a rolling offset moves the pipe — the hypotenuse of the vertical rise and horizontal roll. A 9-inch rise with a 12-inch roll is a 15-inch true offset.
true offset = √(rise² + roll²)
The centre-to-centre length of pipe along the angled section of an offset, between the two fittings. At 45° fittings it is the true offset times about 1.414.
travel = true offset ÷ sin(fitting angle)
The total vertical drop of a drain line over its length. A 20-foot run at ¼ inch per foot falls 5 inches.
fall = run (ft) × slope (in per ft)
The steepness a drain line is laid at, most often given in inches per foot. A quarter inch per foot — 1:48, about 2.08% — is the common minimum for smaller lines, and an eighth is often permitted for larger diameters. The governing plumbing code sets the figure.
Code figures quoted here — riser and tread limits, drain slopes, concrete cover — are common references, not the rule where you are working. The governing document is your approved drawings and your local code.
Check it against the job. Building codes, span tables and product specifications vary by jurisdiction and manufacturer. Your approved drawings and your local code govern, not this page.