CONSTRUCTION GEOMETRY
What types of construction tasks require an understanding of geometry? The answer is just about every
type. From construction surveying to cabinetmaking, geometry plays an integral part in defining property
boundaries; squaring building corners, cutting roof rafters, and building cabinets that are square.
What is geometry? Geometry can be defined as a branch of math dealing with the measurement,
relationship, and properties of figures, points, lines, and solids. In the previous chapter on surface
measurements we looked at, defined, and learned area formulas for polygons and circles. This chapter will
take a closer look at the properties of these objects.
Geometry has been used to solve building construction problems for thousands of years. The Egyptians
used geometry to build the great pyramids.
An age-old problem, encountered by the builders through out time is laying out a square corner. In figure 9A an interior wall is to be constructed to intersect with an existing exterior wall at a right angle (90).
Drawing the right angle in figure 9-A was easy. I simply pressed the shift key while I clicked and dragged
the mouse. On the construction site it’s a different story. How did the Egyptians do it?
They used a rope with knots tied in strategic locations. They would place the rope in the corner and bend it
into the shape of a right triangle, with the knots at each vertex. Smart, because one of the three angles of a
right triangle is of course 90.
right triangle
interior wall
exterior wall
90
Figure 9-A
Egyptian builders knew from experience where to tie the knots in the rope and how to bend it into a right
triangle but they didn’t know why it worked mathematically. Some of the pyramids indicate an accurate
understanding of Pi, but the mathematical knowledge of the Egyptians did not include the ability to arrive
at this by calculation. It is possible that this could have been arrived at "accidentally" through a means such
as counting the revolutions of a drum. Their lack of mathematical understanding should take nothing away
from their accomplishments, many of which are not completely understood 4000 years later.
Around 500 BC the great thinkers of the ancient Greek civilization began to confirm these field proven
techniques through mathematics. One of the greatest Greek philosopher-mathematicians was Pythagoras
who was no doubt inspired after living in Egypt. Today we particularly remember Pythagoras for his
famous geometry theorem. Although the theorem, now known as the Pythagorean theorem, was known to
the Babylonians 1000 years earlier, he may have been the first to prove it.
The Pythagorean Theorem explains why the Egyptian rope method worked. The theorem of Pythagoras
states that for a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the
other two sides. It should be pointed out that to Pythagoras, the square on the hypotenuse would certainly
not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the
side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut
up and reassembled to form a square identical to the third square.
Figure 9-C illustrates how Pythagoras saw the theorem. The triangle in Figure 9-B is made up of three
sides, one side four feet in length, a second side three feet in length and the third side five feet in length.
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If each side is made into a square, the area of the 4 foot square plus the area of the three foot square equal
the area of the five foot square as seen in figure 9-C
44 = 16
33 = + 9
55 = 25
55 = 25
4
5
44 = 16
Figure 9-B
Figure 9-C
3
33 = 9
Today we write the Pythagorean theorem in a mathematical formula - a2 + b2 = c2
In this formula c represents the side opposite the right angle called and is called the hypotenuse. See figure
9-D. The other sides of the triangle are represented by a and b. It is important to note that in the formula
above the outcome of adding a2 and b2 is c2.
Lets substitute the values of the triangle in figure 9-B into the formula.
42 + 32 = 52
16 + 9 = 25
However what you want to know is c. Therefore the formula can be written in a different form, which
solves for c as below.
Angle A
Pythagorean Theorem  a2 + b2 = c
The hypotenuse of a right triangle
equals the square root of the sum of
the squares of the other two sides.
Hypotenuse
side c
side b
Angle B
90 Angle C
side a
Solve for the hypotenuse of figure 9-B
42 + 32 = c
16 + 9 = c 25 = 5
Figure 9-D
Right Triangle
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THE 3-4-5 SQUARING METHOD
Today we still use the same techniques employed by the Egyptians to square a corner, except we use our
Mylar tape measures instead of a rope. Carpenters call the method the three four five method. Here is how
it works.
As in figure 10-1 we know that a triangle with sides measuring three feet and four feet, and hypotenuse
measuring five feet is a right triangle. Consequently carpenters measure three feet along an existing wall
from the point where the intersecting wall will be constructed (called the point of beginning) and make a
pencil mark. Next from the point of beginning the tape measure is extended four feet at an approximate
right angle to the existing wall. Another tape is then extended diagonally from the pencil mark to the
extended tape. They are then aligned so that the five-foot mark on the diagonal tape touches the four-foot
mark on the perpendicular tape. Another pencil mark is made on the floor at this point. A chalk line is now
extended and snapped from the point of beginning to the pencil mark. Presto, a right angle is formed!
In reality to increase the accuracy of the procedure the lengths of the sides of the triangle can be doubled.
The same procedure would be carried out except that the triangle sides would measure six feet and eight
feet, and the hypotenuse would measure ten feet.
Try these:
Where appropriate express answers in feet and inches
1. Solve for the hypotenuse of the right triangle
12
Answer ___________
15
2. Solve for the hypotenuse of the right triangle.
10 4
Answer ____________
32 11
3. Solve for the hypotenuse of the right triangle.
25 7 7/8
Answer ___________
10 2 7/16
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4. Solve for the hypotenuse of the right triangle.
3 4 11/16
56 7 3/16
Answer _________
5. You are to construct a tall cabinet measuring 93 in height, 48 in width and 24 in depth. The cabinet
will be assembled in the shop and delivered to the job site. It must be carried through a doorway, stood up
in the room and slid against the wall where it will be secured. The ceiling height is 96. Will the cabinet
clear the ceiling when tilted up?
Answer ______
How do you solve for one of the sides when you know the length of the hypotenuse and the other side as in
this example? Substitute the values into the formula and solve.
a2 + 92 = 172
a2 + 81 = 289
a2 = 208 (to isolate a2 on one side of the equation,
a = 208 subtract 81 from both sides)
a = 14.42 or 14 5 1/16
17
a
9
Try these:
6. Solve for side b of the right triangle
30 2
12 4
Answer ______________
b
7. Solve for side a of the right triangle
a
16 5
Answer _________________
13 6
8. Solve for side b of the right triangle
33
Answer ________
120
b
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SQUARING BUILDING CORNERS
As a carpenter you will be checking various squares and rectangles for squareness. That is, checking to
make sure that all of the interior angles are 90. For example when foundation forms are set it is essential to
check for square before concrete is poured. Figure 10-4 illustrates a rectangular building measuring 24 0
by 10 0. If squareness were not checked the building in figure 9-E could easily wind up looking like
figure 9-F.
10 0
24 0
Figure 9-E
Figure 9-F
In figure 9-F the linear measurements are still the same, the problem is the interior angles are no longer
right angles. It’s pretty obvious that the corners in figure 9-F are not square but think about what it would
actually look like out in the field. Being out of square is not that easily detected, when you consider the
scale.
Luckily we can fall back on the Pythagorean theorem to insure the corners are square. Drawing an
imaginary diagonal across the rectangle makes two identical right triangles. See figure 9-G
26 0
10 0
24 0
Figure 9-G
Using the Pythagorean Theorem, the length of the diagonal can be easily calculated. 242 + 102 = 26 0
Squaring Corners: - After calculating the length of the hypotenuse extend the tape diagonally across the
foundation forms. If the diagonal measures 26 0 Your forms are probably square. Measure the diagonal in
the opposite direction and check the length. See figure 9-H
Figure 9-H
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What if one diagonal measures exactly 26 0 and the other does not. Is it possible? It is possible, so what
does it mean? It means that one side of the rectangle is longer or shorter than its counterpart. For example
one side of the rectangle is 24 0 and the opposite side is 24 1.
If both diagonals are of equal length the object is square. Calculating the length of the hypotenuse is not
always necessary. For example if you want to know whether a piece of plywood is square, measure the
diagonals. If they are not equal the plywood is not square.
INTERIOR ANGLE REVIEW
You will remember from a previous chapter that the sum of interior angles of any closed polygon equal the
number of sides minus two, times one hundred and eighty.
Sum of interior angles = ( n – 2 ) 180
Therefore the sum of interior angles of a triangle are 180. In a right triangle one angle is 90.
Consequently the sum of the other two angles is 90.
Try these: ∡ is the symbol for angle
9. What is angle A in the right triangle
B
∡ C = 90
∡B = 30
∡C = _______
C
A
10. What is angle B of the triangle
∡ C = 90
B
∡ A = 15
∡ B = _________
C
A
11. What is angle C in the non-right angle triangle.
C
∡ A = 32
∡ B = 52
∡ C = ________
A
B
12. What is the sum of the interior angles of the polygon.
Answer ___________
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ROOF FRAMING
Roofs come in many different shapes and styles but by in large they are nothing more than right triangles.
Figure 9-I illustrates the simplest roof form the shed roof. Figure 9-J illustrates the right triangle hiding
under the roof.
Figure 9-I
Shed Roof
Figure 9-J
Right Triangle
The gable roof (figure 11-10) is made up of two right triangles. Sketch them next to figure 9-K.
Figure 9-K
Gable Roof
Your Sketch
All roof systems share a common terminology as seen in figure 9-L
Span - The total width of the structure
line length
Run - One half the span (base of the roof triangle)
Rise - The height or altitude of the roof triangle
unit run – the unit of measurement given in inches (12”)
unit rise – the amount of rise per foot of run
Run
Slope* -The incline of a roof expressed as a ratio
of rise to run. i.e. 4/12
Pitch* – The slope of a roof expressed as rise divided
by span
Line length – the hypotenuse of the triangle
unit run
unit rise
Rise
Span
Figure 9-L
*Note: The words slope and pitch have different meanings as noted above, however you will commonly
hear well meaning carpenters incorrectly say the roof pitch is 6/12 when they actually mean the roof slope
is 6/12. Gently make them aware of the error of their ways. We will not speak in terms of roof pitch in this
book because it is something rarely used. Later we will talk about slope angle and how it may be
calculated.
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13. Write in the roof properties listed below in the appropriate locations on figure 9-M.
Properties
Span = 24 0
Run = 12 0
Rise = 6 0
unit run = 12
unit rise = 6”
Slope = 6/12*
Pitch = 6/24 0r .25*
Line Length = 13 5
* do not include in diagram
Figure 9-M
Next let’s look at how the roof properties are calculated. Consider figure 9-N
Typically roof span along with unit rise and run can be found on your plans. The line length and rise
usually must be calculated.
In order to cut the rafters for this roof you need to know three additional measurements.

Total Run (total is added to distinguish from unit run)

Total Rise (total is added to distinguish from unit rise)

Line Length
12
5
A
B
30 0
Figure 9-N
Figure 9-O
Triangle A is the same as triangle B. Therefore we only need to concern ourselves with one side of the
house as in figure 9-O
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Step by Step Procedure for Calculating Total Rise and Line Length
Step 1: Find Total Run (one half the span)
Total Run = 15 0
30  2 = 15 0
Step 2: Find Total Rise. Hopefully you remember doing this in the Ratio Chapter.
The unit rise over unit run or the ratio of unit rise to unit run is 5/12 in inches or
.4167/1in feet.
5 = ”
or
12 180
 = 75= 6.25 = 6 3
.4167 = 
1
15
 = 6.25 =6 3 = 75
An easier method may be employed by simply multiplying the total run in feet by the
unit rise in inches.
15  5 = 75
Total Rise = 6 3
Step 3: Find the line length. Pythagoras would be proud of you!
152 + 6.252 =
16.25
16.25
6.25
15
Summary: Total run = 15 0
Total Rise = 6.25
Line Length = 16.25
Try these:
Where appropriate express answers in feet and inches
14. The span of a structure is 32 0  and the slope is 4/12. Fill in the blanks below.
Unit run ____________
Total run ___________
Unit rise ____________
Total rise ____________
Line length __________
15. The total run of a building is 17 5 and the slope is 8/12. Fill in the blanks below.
Span ________
Unit rise _______
Unit run ______
Total rise ______
Line length _________
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16. Fill in the blanks based on the information given in illustration.
28 Rafters
12
9
29 4
Elevation
Plan View
Unit run _____
Total run ___________
Unit rise _____
Total rise ___________
Line Length __________
A CLOSER LOOK AT RAFTER CALCULATIONS
Until now we have been looking at simple wire frame models of framed roofs but in reality rafters have
thickness and height so lets take a closer look. Figure 11-15 introduces us to some new terminology.
See Detail A
Center Line
of Ridge
Line Length
Common Rafter
Layout Line
of Rafter
Tail
Total Run
Double
Top Plate
See Detail A
Span
Overhang
Figure 9-P
In the previous examples you solved the theoretical line length and theoretical total rise. It is important to
note where the theoretical triangle is in relation to the actual rafter. Notice in figure 9-P the theoretical line
length or layout line is not measured at the top or bottom edge of the rafter. The exploded view of the ridge
and rafter in detail 9-1 clearly shows the point to which total rise is measured.
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If you look carefully at figure 9-P you can see the overhang extends the rafter beyond the wall plate. Note
also that the rafter must be shortened at the ridge because the ridge board has thickness.
Terminology

The Rafter Tail – The line length of the rafter does not include the tail. The length of the tail
is a separate calculation, based on the overhang dimension. See figure 9-P.

Overhang – The overhang is always given as a horizontal measurement. If the plan states that
the overhang is 24. That means 24 horizontally from the vertical plan of the wall. See figure
9-P

Bird’s Mouth – This is a notch cut into a rafter to provide a bearing surface where the rafter
intersects the top plate of the wall. The bird’s mouth notch is comprised of two cuts in the
rafter. A seat cut which is the horizontal cut where the rafter bears on the top wall plate. The
plumb cut as the name implies is the vertical cut of the bird’s mouth. See Detail 9-1

Height at Plate (HAP) –The distance measured vertically from the intersection of the seat cut
and plumb cut, to the top edge of the rafter. See detail 9-1 .
The HAP measurement is a variable determined by the carpenter on the job. Generally
speaking it should be no less than 2 . Notice that the HAP measurement can also be seen at
the ridge end of the rafter.

Ridge – The horizontal framing member that rafters are aligned against to resist their
downward force. The minimum thickness allowed by CABO Code is 1 nominal, however 2
members are more typically used. Notice that the ridge has been lowered so that its top edges
align with the top edge of the rafter. Beveling the ridge to match the angle of the rafter would
eliminate the need to lower it, however this is rarely done because of the labor-intensive
nature of such a procedure.
Total rise is measured
to this point
Ridge
?
HAP
HAP
Seat Cut
Plumb Cut
DETAIL 9-1
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Let’s look at an example that will build meaning into all of the facts just discussed.
You must construct a roof with a slope of 8/12, a span of 25 0, and an overhang of 24 .
The plan calls for 2 8 rafters a 210 ridge board and a 4 HAP.




To what length will the rafter be cut, including the tail?
What is the total rise?
How far will the ridge be dropped?
You must cut a 24 brace, running from the top plate to the bottom of the ridge, to
temporarily support the ridge until the rafters are in place. What will its length measure?
Step 1: Make a sketch of the roof showing what you know. This is a good idea until you become
very comfortable with these calculations.
Your Sketch
Step 2: Calculate the total run.
Formula: Span  2 = Total run
25  2 = 12.5 or 12 6
Total run 12 6
Step 3: Calculate total rise.
Formula: Total run  unit rise = Total rise
12.5  8 = 100
100  12 = 8.33 or 8 4
Total Rise = 8 4 
Step 4: Calculate line length
Formula: Total run2 Total rise2 = Line length
12.52 + 8.332 = 15.02 or 15 0
Rafter line length = 15 0
Step 5: Calculate the line length of the rafter tail.
Formula: Same as in Step 4
Total Run is 2 therefore Total rise is 2  8 = 16 or 1.33 or 1 4
22 + 1.332 = 2.40 or 2 4 7/8
Line length of rafter tail = 2 4 7/8
Step 6: Add the two line lengths together.
15 0 1/4
+ 2 4 7/8”
17 5 1/8
Total length of rafter = 17 5 1/8
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Step 7: Calculate ridge drop. Look at the small black triangle at the top of the ridge, labeled
triangle A in figure 9-Q Triangle A is proportional to the large roof triangle made by the rise, run
and line length. Therefore, we can set up a proportion. The base of triangle A is 1/2 the width of
the ridge.
1 1/2(width of ridge)  2 = .75 or 3/4
Proportion:
8 = X
12 .75
X = .5 or 1/2
Ridge Drop = 1/2
Triangle A
1/2
Rafter
9 1/4
Ridge
1 1/2
Figure 9-Q
Step 8: Calculate the length of the 2  4 that will temporarily support the ridge board.
Remember the support extends from the top plate to the bottom of the ridge board.
Also remember that the total rise extends from the top plate to the point where the layout
line intersects with the center-line of the ridge. To solve for the brace we must add the
height at plate (HAP) measurement to the total rise, subtract the ridge drop and finally
subtract the height of the ridge board.
We already have gathered the information needed to answer this question .
Total rise
HAP
Total.Rise + HAP
Ridge Drop
Ridge Height
8 4
+ 4
8 8
- 0 1/2
8 7 1/2
- 9 1/4
Length of 24 support = 7 10 1/4
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Note: Hopefully working several of these problems will bring all of this into focus. There is much more
involved in actually laying out and cutting common rafters. The purpose of this chapter is to focusing on
the theory behind roof framing. An understanding of this theory will make the job of laying out and cutting
rafters much easier and fun.
Are you ready to try some on your own? Use the previous example to guide you through the next three
problems.
17. Situation:
 Gable roof
 Span = 28 0
 Slope = 4/12
 HAP = 5
 Overhang = 18
 Rafters = 2X10
 Ridge = 212
 Ridge to have temp. support off
of top plate of wall
Fill in the blanks:
18. Situation:
 Shed roof
 Total run = 15 9
 Slope = 7/12
 HAP = 3 1/2
 Overhang = 16
 Rafters = 2X8
 Ridge = 2X10
 No temp. support necessary
Fill in the blanks:
19. Situation:
 Gable roof
 Span = 22 8 5/8
 Slope = 6/12
 HAP = 3
 Overhang = 18
 Rafters = 2X8
 Ridge = 210
 Ridge to have temp. support off
of top plate of wall
Fill in the blanks:
20. Situation: Hint – find a proportion to solve total run
 Gable roof
 Span unknown
 Total run unknown
 Slope = 10/12
 Total rise = 9 5
 HAP = 4
 Overhang = 28
 Rafters = 2X12
 Ridge = 2X14
 Ridge to have temp. support off
of top plate of wall.
Fill in the blanks:
Total rise ___________
Line Length _________
Overhang line length ____
Common rafter length _______
Ridge drop ________
Support length _____________
Total rise ___________
Line length __________
Overhang line length __________
Common rafter length ___________
Total rise ___________
Line Length _________
Overhang line length __________
Common rafter length _____________
Ridge drop ________
Support length _____________
Total run ___________
Line Length _________
Overhang line length __________
Common rafter length _____________
Ridge drop ________
Support length _____________
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HIP ROOF – A roof shape with four sloping sides. The most basic form of hip roof is a four-sided
pyramid figure 9-R. Typically hip roofs look like figure 9-S.
Figure 9-R
Pyramid
Figure 9-S
Hip Roof
The rafter layout of a hip roof is illustrated in plan view in figure 9-T. Notice that the run of the hip rafter is
the diagonal of a square, having sides equal to the total run.
Let’s take the roof apart and look at the individual components. The isometric view in figure 9-U shows the
common rafters and ridge. Notice the common rafters that are parallel with, and intersecting with the ridge.
Because of the squares made by the hip rafters, they are exactly the same length as the common rafters
perpendicular to the ridge. Given the span, you could calculate their length.
Figure 9-T and 9-V show the hip rafters that are diagonals of squares measuring one half the span. We will
come back to this later. Figure 9-W shows the hip rafters and common rafters together.
Finally in figure 9-X the jack rafters have been added to complete the roof frame. Notice that the jacks are
simply common rafters that, because of their intersection with the diagonal hip rafter, get progressively
shorter in length.
Hip Rafter
Jack Rafters
Ridge
Ridge
Figure 9-T
Plan View of Hip Roof
Figure 9-V
Ridge w/ Hip Rafters
Common Rafters
Figure 9-U
Ridge w/ Common Rafters
Figure 9-W
Roof w/Ridge Hip and Common Rafters
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Figure 9-X
Framed Hip Roof
Let’s look at a hip roof example. Figure 9-Y illustrates a plan view of a hip roof with a slope of 6/12.To
simplify the problem the roof has no roof overhang.
Rafters 24 o.c. typ.
12
6
6 0
12 0
6 0
6 0
10 0
22 0
6 0
Figure 9-Y
Roof Framing Plan
First lets look at what we need to calculate.




Ridge Length
Common Rafter Length
Hip Rafter Length
Jack Rafter Length
Step by Step Procedure
The following steps use figure 9-Y as the example problem
Step 1: Calculate the ridge length. If each corner of the structure is thought of as a square with sides
measuring ½ the span or the total run , the ridge measurement would measure 10 0.
Ridge length = Building length - Span
Span = 12 0
Total Run 12  2 = 6 0
Ridge = 22 0 - 12 0 = 10 0
Ridge length = 10 0
89
Step 2: Calculate the roof total rise.
Total Rise = unit rise  total run
Total Run = 6 0
Unit Rise = 6
Total rise = 6 6= 36 or 3 0
Total Rise = 3 0
Step 3: Calculate the common rafter line length.
Line length = total run 2 + total rise 2
Total run = 6 0
Total rise = 3 0
Line length = 62 + 32 = 6 8 1/2
Common rafter line length = 6 8 1/2
Step 4: Calculate the line length of the Hip Rafter.
First, lets isolate one of the 6 X 6  squares in which the hip rafter cuts a diagonal, see figure 9-Y.
If the hip were lying flat (horizontal), as it would seem in plan view, the line length would be easy
to calculate.
62 + 62 = 8 5 13/16
But it is not lying horizontally, it is rising from the wall plate to the ridge. Now this may be a hard
concept to grasp but bear with me. In figure 9-Z you can see that the hip and common rafters are
on the same plane, making a triangle with a base equaling the total run, an altitude equaling the
line length of a common rafter and a hypotenuse equaling the line length of the hip rafter
Common rafter
6 8 1/2
Figure 9-Z
Run 6 0
To calculate the line length of the hip rafter, employ the Pythagorean Theorem.
total run2 + common rafter length2 = line length of hip rafter
62 + 6.70822 = 9 0
Hip Rafter line length = 9 0
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Another way to solve for the line length of the hip rafter is to solve for a different triangle. Look at figure
9-AA and notice that the hip is the hypotenuse of two triangles. The one just discussed and one where its
base is the diagonal of the 6 square and the altitude is the total rise. The hip and the common rafter both
gain 6 vertical feet but the hip rafter must cover a longer distance to get there.
Once again the Pythagorian Theorem can be used to calculate the length of the hip run.
6 2 + 62 = 8.4853 or 8 5 13/16
Now the Pythagorian Theorem can be used again to find the line length of the hip rafter.
 32 + 8.48532 = 9 0
Hip Rafter line length = 9 0
Total Rise
Common
Rafter
Common
Rafter
Hip
Total Run
Total Run
16.97*
Hip Run
12
12
figure 9-AA
*Remember: For every foot of run, the hip rafter run is 17.
Solve for Jack Rafters
As stated earlier jack rafters are simply shortened common rafters. Shortened because of their intersection
with the hip rafter. Look at figure 9-BB. As we have studied, rafters are repetitive members usually spaces
16 to 24 inches on center. Therefore, as a jack rafter shortens, it shortens the same amount each time. The
amount the jack rafter is shortened is called the common difference.
Common Difference – In our example the rafters are laid out 2 on center. So we need to know the length
of a common rafter with a run of 2 and a total rise of 1 (unit rise times two).
Pythagorean Theorem  22 + 12 = 2 2 13/16
2 2 13/16
1
2
6 8 1/2(common rafter)
4 5 11/16 (1st jack rafter)
2 2 13/16 (2nd jack rafter)
Common difference = 2 2 13/16
Figure 9-BB
As you can see in figure 11-28, The length of the common rafter is 6 8 1/2 as we previously calculated.
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The first jack rafter is 2 2 13/16 shorter. The next jack rafter is 2  2 13/16 less than the previous and so
on.
Common Rafter:
Common difference:
1st Jack Rafter
Common difference:
2nd Jack Rafter:
6 8 1/2
- 2 2 13/16
4 5 11/16
- 2 2 13/16
2 2 13/16
We have now calculated all of the roof members we set out to solve. It is now your turn to run through the
calculations. Use the problem just solved as a model for your calculations.
21. Calculate the following dimensions of the framing members in the roof illustrated below:
Note: the number of rafters shown in the illustration are not necessarily the actual number that would
be present in a roof with the given dimensions. Your calculations will not be affected by this
inconsistency.
Rafters 24 o.c.
12
8
15 0
Total run ___________
25 0
Total rise _____________
Ridge length ___________
L. L. of common rafters _____________
L.L. of hip rafters ______________
Common difference of jack rafters ______________
Show your calculations below:
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22. Situation:
 Hip roof with
 Span = 19 5 3/16
 Slope = 9/12
 HAP = 3
 Roof over hang = 16
 Repetitive spacing = 16 o.c.
 Common rafter size = 2 X 8
 Ridge = 2 X 10
 Hip Rafters = 2 X 10
Fill in the blanks:
Total run = ____________
Total rise = ____________
Line length of common rafter = ___________
Total length of rafter including overhang = _____________
Length of temporary ridge support extending from top plate to bottom of ridge= ______________
Line length of hip = _______________
Total length of hip = _______________
Jack rafter 1 = _________
Jack rafter 2 = _________
Jack rafter 3 = _________
Jack rafter 4 = _________
Show work below
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