Trades & Construction formula solvers

Stair Riser Count from Total Rise

N = \frac{H}{r}

Trades & ConstructionDivides the total rise, finished floor to finished floor, by the target riser height to give the number of risers a stair needs.

Stair Comfort Rule (2R + T)

2R + T = C

Trades & ConstructionThe stride rule that keeps a stair comfortable: twice the riser plus one tread should land near 25 inches, or 630 mm in metric practice.

Stair Total Run from Risers and Tread Depth

R_t = (N - 1)\,T

Trades & ConstructionThe floor space a straight flight consumes: one fewer tread than there are risers, because the upper floor serves as the last tread.

Stair Stringer Length

L = \sqrt{H^2 + R_t^2}

Trades & ConstructionGeometryThe straight-line length of the stringer board, the hypotenuse of the total rise and the total run.

Roof Pitch to Slope Angle

\theta = \arctan\!\left(\frac{p}{12}\right)

Trades & ConstructionGeometryConverts a roof pitch quoted the framing way, p inches of rise per 12 inches of level run, into the slope angle from horizontal, and back.

Common Rafter Length from Run and Pitch

L = R\sqrt{1 + \left(\frac{p}{12}\right)^2}

Trades & ConstructionGeometryThe line length of a common rafter: the level run from ridge to wall plate, stretched by the slope factor for a pitch of p in 12.

Roof Area from Footprint and Pitch

A_r = A_f\sqrt{1 + \left(\frac{p}{12}\right)^2}

Trades & ConstructionGeometryTurns the plan area a roof covers into the sloping area you actually have to shingle, using the pitch multiplier for a pitch of p in 12.

Board Feet of Lumber

BF = \frac{t \, w \, L}{12}

Trades & ConstructionThe lumberyard's volume unit: thickness in inches times width in inches times length in feet, divided by twelve. One board foot is 144 cubic inches.

Pieces from a Stock Length (with Saw Kerf)

N = \frac{L_s + k}{L_p + k}

Trades & ConstructionHow many finished pieces come out of one stock length once every cut eats a kerf of saw blade. The last piece needs no trailing kerf, which is where the +k on top comes from.

Sheets or Tiles Needed (with Waste Allowance)

N = \frac{A\left(1 + \frac{w}{100}\right)}{a}

Trades & ConstructionCounts the sheets, tiles or planks a surface takes: the area to cover, padded by a percent waste allowance for cuts and breakage, divided by the area one unit covers.

Studs on a Wall at a Given Spacing

N = \frac{L}{s} + 1

Trades & ConstructionCounts the studs, joists or fence posts along a run at a fixed on-centre spacing, including the one that closes the far end.

Paint Quantity from Coverage Rate

N = \frac{A \, c}{a}

Trades & ConstructionContainers of paint needed: the surface area times the number of coats, divided by the area one container covers at the manufacturer's spread rate.

Concrete Bags from Volume and Bag Yield

N = \frac{V}{y}

Trades & ConstructionCounts bags of premixed concrete: the volume of the pour divided by the yield printed on the bag, typically 0.6 ft³ for an 80 lb bag or 13.5 L for a 30 kg bag.

Truck Loads from Bank Volume and Swell

N = \frac{V_B\left(1 + \frac{S}{100}\right)}{C}

Trades & ConstructionTurns an in-place excavation quantity into truck loads: bank volume swelled to its loose volume, divided by the capacity of one truck box.

Drain Line Fall from Slope and Run

F = S L

Trades & ConstructionThe vertical drop a drain gains over a measured run, from a slope quoted as a plain ratio such as 1:40 or a quarter inch per foot.

Ladder Setback and Angle (4-to-1 Rule)

\theta = \arctan\!\left(\frac{H}{B}\right)

Trades & ConstructionGeometryRelates the height a ladder reaches, the distance its feet sit out from the wall, and the resulting angle. The 4-to-1 rule sets the setback at a quarter of the height, which lands at about 75.5°.