M A T H
F O R
C A B I N E T M A K E R S
Chapter
13
MATH FOR CABINETMAKERS
Cabinetmaking carry out mathematical calculations, conversions and measurements on every
project they build.
For example, architectural plans, in 1/4" scale, give the dimensions of the room and basic cabinet
dimensions in feet and inches, but because of the small scale and the fact that architects aren’t
cabinetmakers, more detailed drawings are necessary. So the cabinetmaker makes shop drawings
at a larger 1″ scale with dimensions converted to inches and/or millimeters. The shop drawings
include - a plan view showing how all the cabinets relate to the room or wall(s), elevations (front
& side views) showing what the cabinets look like, and individual cabinet drawings giving
specific dimensions and construction details. These drawings are usually submitted back to the
architect or designer for approval.
Cabinetmakers also have a different precision tolerance than carpenters. Where a framing
carpenter will work within a 1/8" to 1/4" tolerance a cabinetmaker will hold his/her tolerance to
1/32″ or .5 millimeter. So, cabinetmakers use precise measuring instruments like calipers,
digitally controlled power tools, folding rulers and short 10′ to 12′ steel metric and/or imperial
tape measures.
With the shop drawings completed and approved, materials must be ordered. Panel products
and cabinet doors are bought by the square foot or by the sheet, and solid stock is bought by the
board foot.
Imperial linear and square measurement conversions are covered in chapters 1 through 4. So,
let’s take a look at the metric system followed by the calculation of hardwood board footage and
square footage of panel products
The Metric System
Most cabinetmakers are ahead of the curve when it comes to mathematics because they use the
metric system. No fractions, no feet to inch conversions; just a simple decimal-based system of
units. There is one hitch though – designers and architects still express their designs in feet and
inches, so it is necessary to convert their measurements into metrics, and the conversion factors
can make the metric system seem complicated. But of course it isn’t, and after mastering this
chapter you will never want to go back. to those pesky fractions.
M A T H
F O R
C A B I N E T M A K E R S
DEFINITION – Originally the meter was defined as one ten-millionth the distance between
the Equator to the North Pole. Later it was defined as the length of an actual object kept at the
International Bureau of Weights and Measures in Paris. Today it is defined as that distance that
makes the speed of light in a vacuum equal to exactly 299,792,458 meters per second. The speed
of light in a vacuum is one of the fundamental constants of nature.
The American Heritage Dictionary defines the metric system as a decimal system of units based
on the meter as a unit length, the kilogram as a unit mass, and the second as a unit time. We will
limit our discussion to the metric system as it relates to linear measurements.
In plain English and in terms we can all understand one-meter measures approximately 39 3/8".
When we use the metric system for defining long distances we use kilometers and for short
distances centimeters and millimeters. Let me explain. The metric system is a decimal system
with a base of 10.
1 kilometer = one-thousand meters
1 decimeter = one-tenth of a meter (rarely used)
1 centimeter = one-hundredth of a meter
1 millimeter = one-thousandth of a meter (used most often by cabinetmakers)
One of the reasons many American cabinetmakers have made the leap to the metric system is
because of the machinery they use, much of which was developed in Europe where the metric
system rules. They have adopted a cabinetmaking system called the 32 millimeter system. You
have seen the hole boring patterns inside cabinets haven’t you? The holes which support
shelves, hinge mounting plates and drawer guides are 32 mm center to center measuring
vertically, hence the name 32 mm System.
So, cabinetmakers typically work in millimeters. European cabinets are built as modular
components, with widths usually in 76mm (3″) increments starting with 229mm (9″) and going
up to 1219mm (48″).
Abbreviations and some equivalencies:
S.F. = Square Feet
S.I. = Square Inches
CM = Centimeters
M.M. = Millimeters
1 meter = 1000 mm = 100cm
1"= 25.4mm or 2.54 cm
1 S.F. = 144 Square Inches
1 S.F.= 92,903.04 Square Millimeters
M A T H
F O R
C A B I N E T M A K E R S
Examples:
Convert 5″ to millimeters. We know there are 25.4 mm in one-inch so simply multiply 5 times
25.4
5″ x 25.4mm = 127mm
If you want the answer in centimeters or meters, simply move the decimal point to the left
127mm =12.7 cm = 1.27m
Convert 343mm to inches. Now the reverse - dividing the quantity of millimeters (343) by 25.4
(the number of millimeters in one-inch)
343mm ÷ 25.4mm = 13 1/2″
Now it’s your turn:
Round the answers to the following problems to the nearest .00 (Example- .94382 = .94)
Convert the following numbers and fractions to millimeters:
1. 12 5/16"=_______ mm = _______cm
3. 3 1/2" = __________mm= _______cm
2. 122 3/8"= _______mm =_______cm
4. 31 ¼ "=__________mm=________cm
Convert the following metric measurements to inches (express decimals as fractions and
round to nearest 1/16") See chapter 2 for decimal to fraction conversion
5. 752 mm=__________"
7. 510 mm=__________"
6. 32 mm=___________"
8. 37 mm= ___________"
Cabinetmakers often order their cabinet doors from a door company. Most cabinet
door companies price their cabinet doors by the square foot. If the cabinetmakers
works in millimeters then square millimeters will have to be converted to square
feet to obtain a cost. Let’s look at an example:
SQUARE MILLIMETER-SQUARE FOOT CONVERSIONS
The Quality Door Company sells their oak raised panel door for $12.00/SF.
Cabinetmaker A needs a door constructed that measures 350mm x 560mm. How
much will the door cost?
M A T H
F O R
C A B I N E T M A K E R S
Step 1: Calculate the number of square millimeters in one square foot.
1″ = 25.4mm
12″ x 25.4 = 304.8mm
1 SF = 304.8mm x 304.8mm = 92,903.04sq.mm
Step 2: Divide the answer from step 1 into the square millimeters of the door.
350mm x 560mm = 196,000sq.mm
196000 ÷ 92,903.04 = 2.1097 SF
Step3. Multiply the square footage of the door times the cost
2.1097SF x $12.00 = $25.32
Note:
Do not round until the price is obtained. For example the answer in step 3 was $25.3164. If there is only
one door then round to $25.32, but if there are 20 doors don’t round until you multiply times twenty.
Now it’s your turn:
You are outsourcing cabinet doors for a vanity you are building. You have measured the
cabinet for doors and drawer fronts and determine the following:
Doors
2 @ 371mm x 537mm
Drawer fronts
1 @ 746mm x 140mm
1 @ 394mm x 140mm
3 @ 394mm x 176mm
Note:
Most cabinet door companies have a 2 SF minimum. This means that if you order a door or drawer front
that measures 1.8SF, the door company will charge you for two square feet. This is because the labor is
essentially the same for a small or a large door. It takes the same number of steps to construct it. In fact
some small doors/drawer fronts are actually more difficult to construct. Consequently each door and/or
drawer front must be calculated individually to see if it meets the minimum size.
9. Calculate the # of S.F. in each piece. Use a 2 square foot minimum for doors and
drawer fronts. Calculate the number of square millimeters, then convert to square feet,
check to see if your door or drawer front is 2 SF or more and the multiply times the cost.
Doors:
371mm x 537mm =_________sq. mm = _________ SF X $14.45/sq. ft.= $__________
290mm x 520mm =_________sq. mm = _________ SF X $14.45/sq.ft. = $__________
M A T H
F O R
C A B I N E T M A K E R S
Drawer Fronts:
746mm x 140mm =_________sq. mm =__________ SF X $8.25/sq.ft. = $___________
394mm x 140mm =_________ sq. mm = _________SF X $8.25/sq.ft. = $___________
480mm x 390mm =_________sq. mm = _________ SF X $8.25/sq.ft. = $___________
480mm x 390mm =_________sq. mm = ________ SF X $8.25/sq.ft. = $___________
394mm x 276mm =________ sq. mm = __________SF X $8.25/sq.ft. = $___________
Total
= $___________
BOARD FOOTAGE FOR HARDWOODS
Hardwood lumber is measured and sold by the board foot, but in a slightly different way
from dimensional lumber. Everything is done the same as in chapter 5 except that board
thickness is measured in ¼ fractions. For example 1″ thick lumber is measured as 4/4
(pronounced four quarter) and 2″ lumber is 8/4 (pronounced eight quarter). Check out the
chart below.
HARDWOOD THICKNESS CHART
Board Thickness
1″
1 1/ 4"
1 1/ 2"
1 3/ 4"
2″
Rough
4/4
5/4
6/4
7/4
8/4
Surfaced
13/
16"
1 1/16"
1 5/16"
1 1/ 2"
2″
AWI
3/
4"
1″
1 1/ 4"
1 3/ 8"
1 1/ 2"
Column 1 = Board Thickness given in inches
Column 2 = Board thickness given in quarters.
Column 3 = Board thickness after mill surfaces face and back.
Column 4 = Architectural Woodworking Institute (AWI) minimum thickness of finished
product.
Explanation:
Let’s say you need a piece of cherry lumber that is 1″ thick. It can be
bought several ways. You can buy it rough, meaning you will need to surface the face and
back with your planer, or you can buy it surfaced, which means the lumber mill has planed
it to a thickness of approximately 13/16". In either case, more sanding will be required to
smooth it and prepare it for finish. AWI Standards, outline the minimum thickness
allowed in the finished product, and in the case of 4/4 stock the minimum thickness is
3/ ".
4
M A T H
F O R
C A B I N E T M A K E R S
You can see how important this is to know. If you want to make a chair leg that is 1 1/2"
thick you wouldn’t buy 6/4 stock would you? Even though you are buying it 1 1/2" (6/4)
thick, that measurement is in the rough. After it is surfaced your chair leg will only be
1 5/16" at best, and more likely 1 1/4". A better choice for your 1 1/2" leg would be 2″
stock.
Note:
Whether you buy the wood rough or surfaced you will pay for the rough thickness. Hardwoods are never
sold less than 4/4 even if what you are buying is less. If you buy material that is ½” thick it will still be
sold as 4/4.
Let’s apply this to a board footage problem:
Board Footage =
thickness " xwidth " xlength ' x # pieces
x cos t
12
Remember this formula from Chapter 5? Nothing has changed except you need to convert
the thickness to its decimal equivalent if your calculator won’t handle fractions.
This is done by dividing the numerator by the denominator.
4/4 = 1″
5/4 = 1.25″
6/4 = 1.5″
7/4 = 1.75″
8/4 = 2″
BOARD FOOT COST FOR HARDWOODS
When calculating the cost of hardwood lumber use the cost per board foot, which is
usually derived from the cost per thousand board feet.
Example:
Cherry lumber cost $6,400 per thousand board feet. (I made that number up)
Your hardwood salesperson would say it cost’s $6400.00 per thousand board feet and
would write it as – 6400M (M is the Roman Numeral representing one-thousand)
To convert the cost per thousand to the cost per 1 board foot, simply move the decimal
three places to the left.
$6400.00 per thousand board feet = $6.40 per one board foot
Let’s try a problem:
You need 15 pieces of 5/4 cherry, 6 inches in width, and 10 feet in length and the cost is
$6400.00M. How much will your order cost?
1.25 x6 x10 x15
x6.40 = $600.00
12
M A T H
F O R
C A B I N E T M A K E R S
Now you try a few:
10. You have estimated that in order to complete a kitchen cabinet project you will need
the following hardwoods:
6 pcs. - 4/4 Red Oak 6 1/2″ wide and 8′ in length cost = 1600M
4 pcs. - 7/4 Maple, 6″ wide and 6’ in length
cost = 1200M
10 pcs. - 5/4 Walnut 4″ wide x 12′ in length
cost = 4800M
Red Oak __________ BF
Maple ___________ BF
Walnut ___________ BF
Cost
Cost
Cost
Total Cost
$___________
$___________
$___________
$___________
SQUARE FOOT COST FOR PANEL PRODUCTS
Panel products like plywood, particle board and melamine are sold by the square foot or
by the sheet, and unlike solid wood, thickness is not considered. The price per square foot
or per sheet is adjusted up or down depending on the thickness, the substrate and/or the
wood species.
Panel Product Facts
Common Panel/Plywood Sizes:
ƒ 4 x 8 (most common)
ƒ 4 x12 (typically special order)
ƒ 4 x10 (typically special order)
ƒ 8 x 4 (grain runs perpendicular to long dim.)
Panel/Plywood Substrates:
Veneer core (3,5,7,9 ply)
MDF core
Lumber core
Particleboard core
Panel/Plywood Thickness:
1/4", 3/8", 1/2", 5/8", 3/4"
Example:
You are ordering panel products for a bathroom vanity. You need 10 sheets of
4x8 birch plywood and the cost is 3500M. What will the materials cost?
Step 1: Calculate the square footage for one sheet
4′ x 8′ = 32SF
Step 2: Multiply the square footage of one sheet times the cost per sheet.
3500M
= $3.50/BF.
32SF x 3.50 = $112.00
1 sheet
= $112.00
Step 3: Multiply the cost per sheet times the number of sheets needed.
$112.00 x 10 = $1120.00
M A T H
F O R
C A B I N E T M A K E R S
Try these:
11. You have estimated that in order to complete a kitchen cabinet project you will need
the following panel products: Calculate the square footage of each item and the cost.
10 pcs.
5 pcs.
12 pcs.
6 pcs.
3/
3/4x4x12 sheets Red Oak Plywood
1/4x4x8 sheets Red Oak Plywood
3/4x 4x8 sheets
White Melamine
3/4x4x8 sheets White Melamine
4"
Red Oak Plywood = ___________ SF
4" Red Oak Plywood = ___________ SF
3/ " White Melamine = ___________ SF
4
1/ " White Melamine = ___________ SF
4
1/
Cost = 1500M
Cost = 890/M
Cost = 780/M
Cost = 490/M
Cost
Cost
Cost
Cost
Total Cost
$________
$________
$________
$________
$________
CALCULATING ANGLED CABINET MEASUREMENTS
For planning purposes it is often necessary to calculate the lengths of corner cabinet parts
such as the back wall or the diagonal. In order to use the method outlined below two
things must be known. First, you must know the cabinet depth of the adjacent cabinets or
if different, the depth of the corner cabinet. Second, the angle must be 45°.
For the following problems assume that the inside wall corners are 90° and all diagonal
angles are 45°. Remember, the sine of a 45° angle = .7071
12"
22"
10"
45°
1
10"
4
1
/
8
"
45°
14 1/8" x .7071 =10"
10/.7071 = 14 1/8"
To find the back wall length of the corner cabinet above, multiply the sine of 45° (.7071)
times the diagonal length and add the remaining cabinet depth.
In the example above 14 1/8″ x .7071 = 10″.
M A T H
F O R
C A B I N E T M A K E R S
Add 10″ to the remaining cabinet depth of 12″ and a back wall measurement of 22″ is
obtained.
If you know the back wall measurement and want to know the length of the diagonal
simply subtract the cabinet depth (12″) from the back wall measurement.
22″-12″ = 10″
Now divide .7071 into 10″
10″/.7071 = 14 1/8″
Try these:
12. What is the back wall measurement on the base angle cabinet below? ____________
13. What is the diagonal (x) measurement on the base angle cabinet below? ___________
39"
24"
39"
2
1
1
/4
x
"
24"
M A T H
F O R
C A B I N E T M A K E R S
14. What is the diagonal (x) measurement on the wall angle cabinet below?
24"
12"
24"
1
7
"
x
12"
15. What is the diagonal (x) measurement on the wall angle cabinet below? ___________
22 5/8"
12"
X
1
5
"
12"
FINDING THE RADIUS
Here is a way to determine the radius of an existing curved such as a curved wall. Place a
straight edge (6′ level is ideal) horizontally against the curved wall. The straight edge
should only be touching at its ends. The length of the straight edge will be called the chord
length.
Next, measure the perpendicular distance from the center of the straight edge to the
curved wall. This measurement is called the rise.
M A T H
F O R
C A B I N E T M A K E R S
RISE
LEVEL (CHORD)
That’s all the information you need. Use these two values in the formula which will give
you the diameter. Divide by 2 for the radius.
(1/ 2Chord 2 ) + rise 2
DIAMETER =
rise
Example:
You are trying to determine the radius of a curved kitchen wall that will receive new
cabinets. You place an 8′ level horizontally against the inside of the wall, so that only the
ends are touching. You have your assistant measure the distance from the center of the
level to the wall (measured at 90° to the level). That measurement is 3″. What is the radius
of the wall? Make sure use like units(i.e feet or inches) for the chord and rise.
(1/ 2Chord 2 ) + rise 2 482 + 32
=
= 771 Diameter
rise
3
771
= 385.5" Radius
2
1
32′-1 /2" Radius
Try this:
16. You encounter a curved wall with an unknown radius. You must calculate the radius in order to build
cabinets against the wall, which approximate the same curve. What is the radius length? ________in
2
2
4"
Diameter = (1/2 Chord) + Rise
Rise
72"
If you build curved cabinets to fit the wall above, and they are 22 1/2” deep what radius length will you use for
the cabinet fronts? ______________ ft.
M A T H
Notes:
F O R
C A B I N E T M A K E R S
GLOSSARY
Acute angle : An angle less than 90° and greater than 0°.1
Addend : A number that is added.1
Addition : The process of combining two or more numbers to form one number.1
Altitude : The perpendicular height or distance between a point and lower base.1
Angle : The figure formed by the intersection of two lines, which extend from the same
point1
Area : The measurement of a surface, expressed in square units.
Arc : A curved line whose points are equal distance from a single point. 5
Average : The result obtained by dividing the total of two or more quantities by the number
of quantities. 1
Baluster : One of the supporting posts of a handrail or guardrail. 2
Balustrade : A rail and the row of balusters or posts that support it. 2
Board Foot : A piece of lumber 12″ wide, 12″ long and 1″ thick or a piece of material
measuring 144 cubic inches. 1
Capacity : Content by volume. 1
Chord : A straight line from one point on a circle to another point on a circle. The longest
chord is the diameter of a circle. 5
Circle : A curved figure with all points an equal distance from the center point. 1
Circumference : The perimeter of, or linear distance around a circle. 1
Common Rafter : A rafter that extends at 90° from the top plate to the parallel ridge.
Compass : A tool used to draw circles or curves. 5
Complex fraction : A fraction having one or more fractions in its numerator and/or
denominator. 1
Complimentary angles : two angles whose sum is 90°.
Cone : A solid object whose base is a circle and whose sides taper evenly to a point. 1
Constant : The number in a formula whose value does not change. 1
Cosine : In right triangle trigonometry, the ratio of the adjacent side of a reference angle to
the hypotenuse.
Corner brace: A piece of material placed diagonally at a corner to reinforce the structure. 1
Cornice : The part of the roof that extends out from the wall also called the eave. 3
Cube : object with equal sides, width, height and depth. 1
Cubic foot : A measurement 1′thick, 1′ wide and 1′ long. or 1,728 cubic inches. 1
Cubic inch : A measurement 1″ thick, 1″ wide, 1″ long. 1
Cubic yard : a measurement 3′ thick, 3′ wide and 3′ long or 27 cubic feet. 1
Cylinder : A three-dimensional object with a curved surface and two circular bases such that
the height is perpendicular to the bases.
Decimal : A proper fraction with a denominator which is a power of 10 and which is placed
to the right of a decimal point. 1
Degree ( ° ) : A unit of measurement for angles. 5
Denominator : The number in a fraction which is written below the division line and which
represents the number of portions to which the whole has been divided.
Diameter : The straight line segment from a point on the circle through the center to
another point on the circle.
Difference : The result or answer in subtraction. 1
Division : a process of finding the missing factor when one of the two factors are known. 1
Eave : The overhang of a rafter over an existing wall. 1
13
Equilateral triangle : A triangle with three angles equal in size. 1
Equivalent : An expression of like value. 1
Factor : One number used in a process to obtain another number. 1
Footing : The base of a foundation system, column or pier designed to spread the loads of
the structure across supporting soil. 3
Formula : A symbolic statements that indicates a relationship among numbers. 2
Foundation : A system used to support and distribute a building’s loads to the ground on
which it is located. 3
Fraction : In math, a part of a whole. 1
Frustum : Formed by cutting off the top of a cone-shaped solid with a plane parallel to the
base. 1
Gable roof : A type of roof with two sloping surfaces that intersect at the ridge of the
structure. 3
Gallon : A unit of liquid measure, equals four quarts. 1
Geometry : a branch of math dealing with the measurement, relationship and properties of
figures, points, lines and solids. 1
Girder : A horizontal support member at the foundation level. 3
Hip : The exterior edge formed by two sloping roof surfaces. 3
Hip rafter : A rafter which extends from the corner of the building diagonally to the ridge. 3
Hip roof : The roof with four sloping sides. 3
Horizontal : Parallel to the horizon. 1
Hypotenuse : The side opposite the 90° angle of a right triangle and also the longest side of
a right triangle.
Improper fraction : A fraction with numerator the same or greater than the denominator.
Inch : A fractional portion of one foot. 1
Interest : An amount usually expressed as a percentage, which is added to a borrowed sum.
Isosceles triangle : A triangle with two equal sides.
Joist : Framing members used to support floor surfaces or ceiling surfaces.
Linear : A measurement of length.
Metric system : a decimal system of measurement.
Minuend : A number from which another number is subtracted. 1
Minute : A measure of time equaling 60 seconds. 1
Mixed decimal : A number comprising of a whole number and decimal. 1
Mixed number : A number comprising of a whole number and fraction. 1
Multiplicand : A number being multiplied. 1
Multiplication : The process of adding a number to itself a specified number of times. 1
Multiplier : The number in multiplication by which the multiplicand is multiplied. 1
Notation : In math, the expression of numbers in symbols. 1
Numerator : The number in a fraction that is written above the division line. 1
Obtuse angle : An angle greater than 90° and less than 180°.1
On-center : A term used to define the distance from the center of one structural member to
the center of the next. 4
Overhang : The horizontal distance that a rafter projects beyond a wall. A general term
describing the portion of the lower roof that projects beyond the wall. 3
Parallelogram : A four sided polygon with opposite sides equal in length and parallel.
Percent (%) : Next to a number, indicates the number of hundredths expressed. 1
Perimeter : The distance around an object.
Pi : The circumference of a circle with a diameter of 1, or 3.1416…..
Pier : A concrete or masonry foundation support. 3
14
Pitch (Roof) : The incline of a roof expressed as rise divided by span. 1
Plane : A flat, two dimensional surface.
Polygon : A plane figure bound by three or more sides. 1
Product : The result of multiplication. 1
Proper fraction : A in which the numerator is smaller than the denominator. (I.e. ¾ )1
Proportion : An expression of equality between two ratios. 2
Radius : One-half the diameter of a circle, measured from the center to a point along the
circumference. 1
Ratio : The relation between two quantities expressed as the quotient of one divided by the
other. 2
Rectangle : A four sided polygon with four 90° angles.
Reference angle : An angle being referred to in a given problem.
Reflex angle : An angle greater than 180° and less than 360°.1
Right angle : An angle equaling 90°
Rise: The altitude of a right triangle representing the vertical distance between stair risers or
the vertical height of a roof.
Riser : The vertical member, either solid or open, of stairs between the treads.
Run : The base of a right triangle representing the horizontal length of a staircase or roof.
Sine : In right triangle trigonometry, the ratio of the opposite side of a reference angle to the
hypotenuse.
Slab : A concrete floor system typically poured at ground level. 3
Span : The total width of a building. 1
Sphere : A globular object, such as a ball. 1
Square : A polygon with equal sides and four 90° angles. To multiply a number times itself.
A term used in roofing to represent 100 square feet.
Square root : A divisor of a quantity that when squared gives the quantity. 2
Square yard : A measurement of 3′ by 3′ or 9 square feet.
Stringer : The inclined support member of a staircase that supports the treads and risers,
also known the carriage. 3
Subtraction : The process of taking one number or quantity away from another number or
quantity.
Tangent : In right triangle trigonometry, the ratio of the adjacent side of a reference angle
to the opposite side of the same angle.
Trapezoid : A four sided polygon with only two sides parallel.
Tread : The horizontal surface of a staircase on which one steps
Triangle : A three sided polygon.
Trigonometry : The study of the relationship between the angles and sides of a triangle.
Trigonometric functions : factors derived from the relationship of two sides of a triangle.
Vertex : The point where two lines meet making an angle.
Volume : The product obtained by multiplying the width, length and depth of an object.
1 Mathematics
for C arpenters by Robert Bradford, Copyright © 1975 by Delmar Publishers
Inc.
2
The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2000 by
Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.
3 Architectural
Drafting & Design, Second Edition, By Alan Jefferis and David Madsen,
Copyright © 1991 by Delmar Publishers.
15
Practical Problems in Mathematics for Carpenters by Harry C. Huth, Copyright © 1985 by
Delmar Publishers
5 Math to Build On, A Book For Those Who Build by Johnny and Margaret Hamilton,
Construction Trade Press PO Box 953 Clinton, NC 28328-0953
4
16
ANSWER KEY
Chapter 1
17. 3 5/16"
18. 3 3/16"
19.
20.
21.
22.
23.
24.
25.
26.
2 19/32"
5"
1 1/8"
4 5/16"
2 3/16"
4"
5/
8"
3 5/16"
Chapter 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
.375
.1875
.625
.3125
.9375
.6875
.875
.8125
.4375
.1563
16; 16/16
12, 12/12
8, 8/16, 1/2
2
/16
10
/16
12
/16
14
/16
6
/16
61 1/2″
4 15/16″
55 1/8″
91 3/8″
50 3/4″
31 3/4″
17 3/8″
33 9/16″
5 3/8″
36 1/16″
38 7/8″
11 3/8″
.375″
.1875″
.625″
.3125″
.9375″
Your Chart
37.
38.
39.
40.
41.
42.
43.
44.
/16″
/8″
3
/16″
1
/4″
5
/16″
1
1
15/
16"
/16″
1
/2″
45. 9/16″
46. 3/4″
47. 125 15/16″
48. 38 15/16″
49. 13′-6 5/16″
50. 28′-1111/16″
51. 2′-4 5/8″
52. 15’-3 9/16″
53. 4 3/4″
54. 150′-4 1/16″
55. 12′-8 5/16″
56. 4′-2 3/8″
57. 59′-13/16"
58. 27′-101/8″
59. 38′-3 13/16"
60. 62′-5 7/8″
61. 10′-3 5/16″
62. 1′-4 9/16″
63. 11′-11 ½″
64. 1′-1 3/16″
65. 6′-5 7/16”
66. 2′-5 15/16″
67. 19′-9 7/8″
68. 39′-10 3/8″
69. 1′-10 15/16"
70. 6′-9 11/16″
5
Chapter 3
1.
2.
3.
b,c,d,e,f,g
b,h,i,j
g =360°,h = 540°
I=720°, J=1080°
4. 15′-2″
5. 61′-2″
6. 93′-4″
7. 78’1″
8. 40′-6″
9. 31′-3 7/8″
10. 39′-3 1/4″
11. 76′-11 5/8″
12. 14′-3 3/4″
17
13. 15′-8½″, 6′-3 3/8″
14. 15′-6 7/8″
15. A. 197′-6″
B. 166′-1″
Chapter 4
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
16.39 SF
5.39 SF
5.49 SF
151.98 SF
203.85 SF
474.46 SF
959.63 SF
471.44 SF
95.49 SF
361.36 SF
312 SF
1,116.80 SF
124.09 SY
1314.49 SF
41.0778 or 42
13.42 squares
105.55 SF
Chapter 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
.6667
1
1.333
1.667
2
10.6667
20
4.6667
3.3333
4
106.67
160
480
34.6667
1045.3333
504
40 BF, $14.00
410.67 BF,
$242.29
19. 480 BF, $350.40
20. 640 BD, $307.20
21. 380 BF, $231.80
22. 176 BF, $100.32
23. 480 BF, $283.20
24. 64 BF, $37.76
25. 213.33 BF,
$168.53
26. 16 BF, $7.81
27. $149.76
28. $140.70
29. $235.76
30. $840.00
31. $694.32
32. $192.00
33. $153.60
34. $806.40
35. 8431.38 LF
5620.92 BF
$5508.50
36. 4032 LF
2016 BF
$3719.52
Chapter 6
1.
2.
3.
4.
5.
6.
7.
8.
9.
12
30 or 31
46
48
32′-0″
24
45
45,36
8′-2 5/16″, 90 5/16″,
91 9/16”, 5 1/4″, 17,
3 13/16″
10. 12, 3 ¾ ″
11. 15, 3 13/16"
12. 16, 3 15/16+″
Chapter 7
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
73.62CF
258 CF
120 CF
265.07 CF
3675 CF
2.72CY
9.56 CY
4.44 CY
9.82 CY
236.93 CF, 8.78 CY
301.59 CF
226.20 CF
19.54 CF
14. 1031.33 CY; 52 loads
15. 1261 CF 105 CFM
6. 71/4", 431/2″
Chapter 8
Chapter 10
1.
2.
3.
4.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Factor = .667, 9′-0″
Factor = .333, 5′-5″
Factor = .75, 10′-1 1/2″
Factor = 1.167,
10′-119/16″
5. Factor = .25, 15′-8″
6. Factor = .9367x10
7. 3.75
8. $306.67
9. 21
10. 208.05
11. .25′
12. 2266.85′
13. 7
14. 1694.12
15.
2.1875
= .3977
5.5
2 3/4″, 3 5/8″, 4 7/16″
16. 3.6 hours
17. 16.67 Squares
18.
PART 1
6
= 1.304
4.6
Slow contractor = x
1.304 x + 1x = 2050
x = 889.7569′
2050-889.76′ = 1160.24
PART 2
1160.24 6
=
x
60
x = 193.37 Hours
Chapter 9
99 13/16″
106 1/4″
14, 71/8″, 13, 143″
4. 15, 71/16″, 14, 143 1/2″
5. 10, 71/4″, 9, 105/8″,
95 5/8″
1.
2.
3.
18
19′-2 1/2″
34′-6″
27′-7 5/16″
56′-8 3/8″
No
27′-6 3/8″
9′-4 1/16″
9′-73/8″
60°
75°
96°
1800
Label diagram
14. Rise factor=.3333
Total run=16′, Line
Length = 16′-103/8″
L.L. factor = 1.0541
Total rise = 5′-4″
15. Span = 34′-10″
Rise Factor =.6667
L.L.=20′-113/16″ Unit
L.L. factor = 1.2019
Total rise=11′-75/16″
16. Rise factor = .75
Total run=14′-8″
Total rise = 11′-0″
L.L. Factor = 1.25
L.L. Factor = 1.25
L.L.=18′-4″
17. 4′-8″
14′-91/16″
1′-7″
16′-41/16″
1
/4″
4′-11/2″
18. 9′-21/4″,
18′-213/16″
1′-6 1/2″
19′-9 5/16″
19. 5′-8 3/16″