
These equations are some of the most frequently used on a
typical jobsite.
Pythagoras Theorum
This equation is the root of most construction mathematics. It uses
are virtually unlimited. It is commonly used to square a layout via
the 3 4 5 method, and roof framing would be nothing but guessing without
this equation.
A^{2}+B^{2}= C^{2}
It is also common to see the equation wrote like this:
Hypotenus (C) = SquareRoot(A^{2} + B^{2})
Radius Equation
This formula can be used to find the radius of any simple arch.
It is a common occurrance for homes we build to have arched cased openings,
arched windows, or arched ceilings.
Radius = ((1/2S)^{2}+R^{2})/2R
Octagon side formula
This equation is commonly used to calculate the octagonal sides
of trey ceilings or to find the chamfer length on a cabinet.
H = squrt((1/2R)^{2}+(1/2R)^{2})
O = R  H
S = squrt(O^{2}+O^{2})
Angle of Departure
This equation is used to find the departure angle for rafters and
other structures built on an angle. The formula is quite simple but
having a scientific calculator on hand is necessary.
Angle of departure from horizontal = arctan(Rise/Run)
Angle of departure from vertical = arctan(Run/Rise)

