Tool List - Framing Square (Carpenter's Square)

The framing square is used by the carpenter in a variety of framing operations. The spacing of studs and rafters, marking of angular cuts in roof rafters, and layout of stair stringers are some of its main uses.
The framing square is available in a variety of types and makes. The better makes contain the tables and scales which will be described. The chief difference in the tables of comparable squares will be found in the rafter table; most tables are based on the unit length of rafters for the desired pitch of the roof.

The framing square consists of a wider and longer member called the blade and a narrower and shorter member called the tongue; the tongue forms a right angle (90°) with the blade (or body) at the heel. The face of the square has the manufacturer's name stamped on it and is the side viewed as the square is held in the left hand with the blade vertical and with the tongue pointing to the right. The blade is 2A" long and 2" wide and the tongue is 16" long and 1½" wide when measured from the heel. It should be noted that the illustration (Figure 7) identifies scales on the back of the square for special uses.

The twelfth scale is commonly used for right triangle solutions without computation. The chief purpose of the twelfth scale is to provide shortcuts in problem solving with the framing square. Since the inch is divided into 12 parts, it allows the carpenter to reduce a problem to 1/12 size by allowing the graduations on tie scale to represent 1", i. e., 7 5/12" may be taken to represent 7 feet, 5 inches.

Although the twelfth scale can be used to find the overall length, or hypotenuse, of a rafter by the stepoff method, most carpenters use the line length method. The computation can be verified by using the twelfth scale of the framing square.

Brace Table

The brace table (Figure 8) appears directly below the twelfth scale. The brace table allows the carpenter to determine the hypotenuse length (length of brace) of the right triangle for the vertically placed numbers by direct reading. The number placed between and to the right of these vertically placed numbers is the hypotenuse length. These three numbers form a group which indicates the legs and hypotenuse of a right triangle (Figure 9). The use of the brace table could be expanded by multiplying each of the numbers in the group by the same value; i. e., to find the hypotenuse of a right triangle with legs of 15", take each number of any group which is a multiple of 15, such as 60 84.85 and multiply by ¼: 60/ 4 = 15, 84.85/4 =
21.2125. 21.212 is the desired hypotenuse length. The decimal fraction could then be converted to sixteenths of an inch by computation or by direct measure using the hundredths scale and a pair of dividers. Only the more expensive squares contain the hundredths scale (Figure 9). This scale divides the inch into 100 equal parts and allows a direct conversion of a decimal fraction into sixteenths or other fractional divisions of the inch by comparison with another scale of the framing square. The number which is used as a multiplier with the group may be any fraction, decimal fraction or whole number.

Essex Board Measure

The back (blade section) of the square (Figure 10) allows the carpenter to determine board feet measure with a minimum of computation.
Lumber is cut and sold in even foot lengths. The thickness and width are used to compute the board feet (B. F.) in order to determine the cost.
A board foot is a piece of lumber 1" thick by 12" wide by 12" (1 ft.) long.
When the essex board measure table is used the board measure of a piece of stock is read directly from the table by either of the two methods which are explained as follows.

Example:
Determine the board feet contained in a piece of stock 1" x 8" x 10'.
(1) Find the 12-inch mark on the twelfth scale. All computations will begin at this point. Under the number 12 you will note the numbers 8, 9, 10, 11, 13, 14 and 15 which represents the width of the stock.
(2) Locate the number 8, which is the stock width for the example.
(3) Move along the horizontal line to the left and locate the number 6 | 8 which appears under the 10-inch mark, the length of the stock, on the twelfth scale.
(4) The number 6 | 8 is the desired amount and is read as 6 8/12 or 6 2/3 board feet.
The essex board measure table will allow you to determine the board measure of any size stock by doubling or taking multiples of stock whose thickness is greater than 1".

Example:
Determine the board feet contained in a 4" x 4" x 10' post.
(1) On the twelfth scale locate the number 10 under the 12-inch mark. Note that the number 4 does not appear in this column. The table allows you to find board measure by using the stock length in this column instead of the board width as previously described.
(2) Move horizontally to the left to the number 3 | 4 under the 4-inch mark on the twelfth scale. This is the stock width.
(3) This represents the number of board feet in a piece of stock 1" thick. Multiply this amount by 4 to determine the board feet in a piece of stock 4" thick. 3 4/12 x 4 = 13 4/12 = 13 1/3 board feet.

The essex board measure table will allow you to use either of the two methods indicated by the examples for the measurement of board feet by direct reading. The method which best adapts to the stock size whose board footage you need to determine can be used; i. e., if the stock width appears under the 12-inch mark, the board footage of stock lengths up to 24' can be determined. If the stock width does not appear under the 12-inch mark, the length of the stock could be used in this column with the width read directly under the appropriate inch mark on the twelfth scale.
Again it should be noted that the direct measurement gives the board measure of stock whose thickness is one inch. The desired board footage can be obtained by multiplying the number read directly from the table by the thickness of the stock. For stock lengths which are beyond the range of the table, a similar method could be used; i. e., board measure of stock which is 36' in length could be determined by finding the board footage of a 12' piece and tripling this answer, or by finding the board measure of two values whose sum equals 36'.

Roof Cutting Terms

The use of the unit-length rafter table requires an understanding of some basic terms which are noted in Figure 11.

The slope of a roof is identified as pitch and will vary from the flattest pitch of Y2" of rise to each 12" of run to 24" of rise to each 12" of run. 24" of rise to 12" of run is identified as full pitch.

The illustration shows a commonly used pitch for house roofs which is identified as 1/6 pitch. The numbers which are used on the framing square are the 4-inch mark on the tongue and the 12-inch mark on the blade when measured from the heel of the square. Blue prints which identify roof slope showing the triangle with the numbers 4 and 12 are for use by the carpenter and sometimes are mistakenly called 4 and 12 pitch. By definition, the pitch of a roof is the rise divided by the span, i. e., 4 / 12+12 = 4/24 = 1/6 pitch. The numbers 4 and 12 are used by the carpenter to layout the angular cuts that are made for fitting the rafter to the top plate and ridge.

Unit-Length, Total Length Rafter Table

The unit-length rafter table (Figure 12) allows the carpenter to compute the theoretical length of a common rafter; the hypotenuse of the right triangle. The table does not make allowances for thickness of ridge or overhang on the building. These allowances must be added to or subtracted from the computed length to allow use of correct rafter stock length.

Example:
Find the length of a common rafter for 1/6 pitch when the span of the building is 20 feet.
(1) Move horizontally along the line marked "length of main rafter per foot of run" to the number 4 on the upper scale of the framing square and locate the number 12 65 which is read as 12.65. This value indicates that the hypotenuse of the right triangle with a rise of 4 units and a run of 12 units has a length of 12.65 units.
(2) Multiply 12.65 by 10 to determine the common rafter length of a building whose span is 20 feet; one half of the span equals 10 feet which is the run of the building.
(3) The common rafter length equals 126.5" or 126½" or 10' 6½".

Example:
Find the length of the hip rafter for 1/6 pitch for a building whose span is 20 feet.
The hip rafters are members which slope up from the corner of the building and meet at the end of the ridge with a pair of common rafters. They represent the hypotenuse length of right triangles whose legs are the run of the building and the length of the common rafter.
(1) Move horizontally along the line marked "length of hip or valley rafter per foot of run" to the number 4 on the upper scale of the framing square and locate the number 17 44 which is read as 17.44.
(2) Multiply 17.44 by 10 = 174.4". Convert .4" to sixteenths by direct measurement using the hundredths scale:
.4" = 6/16" (to nearest sixteenth); 174.4" as 174 6/16" = 14'-6 3/8".

Valley rafters, where required, would be measured in the same manner as hip rafters.
A jack rafter occurs in any roof containing a hip or a valley rafter. They can best be described as common rafters which have been cut short by their intersection with a hip rafter or a valley rafter. The lengths of the jack rafters can be determined by using the "difference in lengths of jacks—16 inch centers" or "difference in length of jacks—2 feet centers" table. Roof rafters are normally spaced on 24" centers or on 16" centers. The numbers indicated horizontally on these tables under the desired rise of the roof can be used to shorten each jack rafter the amount indicated. Under the number 4 of the table locate the value 25 30 which is read as 25.3" or 25 5/16". The jack rafters fill a triangular space in the roof area. The first jack rafter will be 25 5/16" shorter than the common rafter. Each succeeding jack rafter will be progressively shorter by the same amount when the rafter spacing is set at 24" on centers.

The jack rafters, where required, must have an angular cut on the stock thickness to fit against the hip or valley rafter. This angular cut is determined by the use of the "side cut of jacks" table. Using this table, locate the number 11 3/8 along the horizontal line and directly under the number 4 on the outer scale of the framing square.
Hold the framing square as indicated in Figure 13 to determine the angular cut. In the unit-length rafter table which was previously illustrated, the number 12 is always used with a number from the "side cut of jacks" table to determine the angular cut. Although the tables on all framing squares are not made up in the same manner, the side cut can be determined by noting that as the pitch of the roof increases the angular cut decreases.

Use the table in figure 12 to determine the angular cut of a rafter rise of 2 and 12; use the number 11 13/16 from the "side cut of jacks" and note that the number of degrees given in the "angle table for the square" is more than 44° and less than 45°. Follow the same procedure for a rafter rise of 4 and 12. Use the number closest to 11% from the "side cut of jacks" table (11½) under the 4-inch mark on the outer rafter scale. The number of degrees listed for the number 11½ (which is the number closest to 11%) on the "angle table for the square" is 43%°. Follow the same procedure for a rafter rise of 16 and 12 and it will be noted that the angular cut has decreased to 31°.

The side cuts for hip and valley rafters are determined in the same manner as the side cuts for jacks. It should be noted that the cutting of angular cuts on jack, hip and valley rafters at the jobsite can best be performed with a radial-type saw. Angular cuts can be made with a portable electric saw up to 45°.

The "total length common rafter" table (Figure 14) is found on some squares. Its use is limited to roofs which have standard pitches, such as 1/6, 1/4, 1/3, etc., and whose run does not exceed 24'.