Trades & Construction formula solvers

Categories — 73 of them, 1787 solvers in all

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B C D L P R S T

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.

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.

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.

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°.

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.

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.

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.

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.

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.

Snow Gun Output Rate

\dot{V}_s = \dot{V}_w \, \frac{\rho_w}{\rho_s}

Snow & IceHVAC & HydronicsTrades & ConstructionSnow production rate from the water flow a gun is fed and the density of the snow it makes. Guns are specified in gallons or litres per minute of water and hills are planned in cubic metres or acre-feet of snow, and this is the conversion between the two.

Snow Made in a Wet-Bulb Window

V_s = \dot{V}_w \, t \, (1 - f) \, \frac{\rho_w}{\rho_s}

Snow & IceHVAC & HydronicsTrades & ConstructionHow much snow a given water flow actually puts on the ground over a night, once the water lost to evaporation and drift is taken off. THE FACT THIS PAGE EXISTS TO TEACH: snowmaking is gated on WET-BULB temperature, not on the thermometer. You can make snow at +2 °C if the air is dry enough, and you cannot make it at −1 °C if the air is damp.

Snow Volume from Water Volume

V_s = V_w \, \frac{\rho_w}{\rho_s}

Snow & IceHVAC & HydronicsTrades & ConstructionHow much snow a given volume of water becomes, at whatever density the snow is made to. It is a mass balance and nothing more — the water does not change amount, only how much space it occupies — which is why the snow density on the bottom is the only interesting number in it.

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 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 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.

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.

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.

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.