Roofing Materials Estimating
Roofing Materials Estimating
A square is used to describe an area of roofing that covers 100 square feet or
an area that measures 10' by 10'.
If we are able to calculate total roof area, we can find the number of squares of
roofing needed simply by multiplying the total area by the unity fraction:
1 SQUARE
100 ft
2
Roof Slope
The roof slope symbol is the symbol placed on a profile view of the roof
which shows roof slope in relation to its rise and run. The rise is always
given in relation to a run of 12 units.
The symbol below represents a 4/12 slope, the rise being 4 units and the run
being 12 units. This means that the line that is drawn to represent the roof
rises 4 units for every 12 units that is travels horizontally.
Rafter
The rafter is that structural roof member that extends from the ridge board to
the fascia board.
Looking perpendicular to the side of a gable roof it represents the width of the
rectangle that is formed by the roof surface on that side of the house. It,
therefore will be used, along with the roof length, to calculate roof area.
By using the Pythagorean
theorem we can figure out the
rafter length.
Pythagorean Theorem
The Pythagorean theorem states that the square of the hypotenuse of a right
triangle is equal to the sum of the squares of the other two sides. Where c
represents the hypotenuse and a and b represent the other two sides, the
equation would read c 2 = a 2 + b 2
This equation coupled with the
roof slope symbol and the
theory of similar triangles can
be used to find rafter length.
Theory of Similar Triangles
The theory of similar triangles states that if, in two triangles, the corresponding angles
are equal then the ratio of corresponding sides are proportional. In the similar
triangles below a/b = A/B similarly c/a = C/A. The ratios of any other combination of
corresponding sides would also e equal.
=
Building Dimensions
Looking at the figure below we can see a roof slope triangle showing a slope of 4/12.
We can see a building width of 30'-0”. When we add the two 2'-0” overhangs to the
building width, we can see that the total distance between fascia boards is 34'-0”.
We can also see that the length of the roof is equal to the building length of 65'-0” plus
the two 1'-0” overhangs for a total roof length of 67'-0”.
Step 1
Step 2
Lets now compare the roof slope triangle to the triangle formed by the roof rafter
and its rise and run. We know the roof rafter run to be half of the total distance
between fascia boards (which we previously determined to be 34'-0”). One half of
34' is 17'. Comparing the rafter triangle formed by the rafter and its rise and run,
and the roof slope triangle we have the two figures below.
We've labeled the hypotenuse of the rafter triangle “WIDTH” since it represents the
width of the rectangular shape of the roof surface.
Step 3
Substituting into the theory of similar triangles we can see that, from the slope
triangle, the ratio of hypotenuse to base or 12.65/12 is equal to, the hypotenuse of
the rafter triangle over its base or WIDTH/17'. Setting this up in ratio proportion
form:
12.65
12
WIDTH
=
17'
Step 4
12.65
12
WIDTH
=
17'
Solving for WIDTH by multiplying both sides of the equation by 17' and canceling
where possible we arrive at the equation.
(17')( 12.65
12
)=
WIDTH = 17.92'
Step 5
(17')( 12.65
12
)=
WIDTH = 17.92'
The 17.92' just calculated, is the rafter length and is also the width of the rectangular
roof surface on one side of the gable roof.
Step 6
Substituting the WIDTH value of 17.92' and the length of the roof, previously
determined to the 67', into the area equation we arrive at the equation”
A=LW
=
A=(67')(17.92')
=
A=1200.6ft 2
2
Since the gable roof has two sides we multiply 1200.62 ft x 2 to arrive at a total
roof area of 2401.2 ft 2 .
Step 7
To determine the number of squares of roofing needed to cover the roof we
multiply our total roof area by the unity fraction 1 SQUARE/100 ft 2.
Our total number of squares = 2401.2 ft 2
THE NUMBER OF
SQUARES
1 SQUARE
= 2401.2 ft x 100 ft 2
= 24.01
SQUARES
2