Framing or Carpenter's Square and Rafter Square

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History

The square as a building tool dates back many centuries.  It is illustrated in English wood-cuts from the 16th century.  Wooden versions were used to layout the Egyptian pyramids. The modern framing (steel) square was patented in the U.S. by in 1819 by Silas Hawes, a blacksmith from South Shaftsbury, Vermont.   Rafter squares (also called a speed or triangle square) were invented by Albert J. Swanson in 1925 as a carpenter's layout tool. He later founded the Swanson Tool Company to mass produce his invention.

Framing Square vs. Rafter Square

 Both tools provide a right angle and can determine angles for roof framing but have different utility.   The rafter square is the simpler tool that is smaller and easily carried in a carpenter's nail bag.  It also makes an excellent saw guide for cutting square cuts on lumber less than 6" wide.  The framing square is a more versatile tool that can be used to layout stairs, rafters, determine board feet, and layout octagon (8 sided) shapes (ex. a post). 

 

Framing Square	Rafter Square

Using the Framing Square

The modern framing square is right angle with a 2" "body" and a 1 1/2" "tongue". The body is 24" long and the tongue is 16" long.  A good quality framing square has the following tables stamped on the square:

• Rafter Table
• Octagon Scale
• Essex Board Foot Table
• Brace Measure

Note that not all squares have all the tables.  Trivia:Some squares have a hole on the tongue near 3 1/2".   When hung on a wall using this hole the square will hang straight.

Hanging Hole

Determining Board Feet using the Essex Board Foot Table

This table found on the body of the square is likely named for Jeremiah Essex an early manufacturer of steel squares.  The table will determine the board feet (bf) of 1" thick board.   To determine the board feet of a piece of lumber you start with the numbers under the 12" mark.   These are the length of the board (by definition a board foot is 1" thick x 12" wide x 1' long so these numbers also represent the bf of a 1 x 12.  From the 12" column choose the row that indicates the length of your board.   Now choose a column that is the width of your board.  The number at the intersection of the column and row (length) is the bf of a 1" think board.   If the board is a 2 by then double the number.   You can do this type of adjustment for length as well.  For example if you have a 2 x 6 x 16 then you would take the number under 6" and the 8' row (4-0) double it for the 2" thickness and double again for the 16' length (16 bf).

Determining Length and Cutting Braces using Brace Measure

Located on the tongue of the square this table is simply the length to cut a 45o brace given the length of the side.   The two small numbers are the side length. The large number is the brace length.   For example to cut a brace for 36" side you would layout a length of 50.91 inches.  This is the LONG side of the brace.  Some squares have 100th scale.  To use the 100th scale find the decimal value (in this case .91) on the 100th scale then read to the closest 16th inch.  Since these braces are a 45o on the ends.  Layout the 45o angle using the square and any convenient pair of inch measurements (ex. 10 and 10).   The angle must taper toward the middle. 

Brace Table

100th Scale (Not found on all squares)

Layout of Octagons using the Octagon Scale

This scale is found on the tongue and is used to determine the side length of an octagon.  Start with a square shape.   Measure the side of the square.  Read this length on the scale. Then read the corresponding distance (inches) on the square.   For example if the side of the square is 12"  the reading would be 4 1/2".  This is 1/2 of the side length of the octagon.   To layout find the center of each side and then measure toward the corner from that mark using the reading and mark that point.  Finally connect the marks to finish the octagon shape.   Note that larger octagons can be constructed by using multiples.  For example if you want to form an octagon slab that will be 8' (96") across.  Read 48" on the scale and double the reading (12"). 

Cutting a Common Rafter

A common rafter on a gable roof spans 1/2 of the building width. 

1. Determine the rise (vertical) and run (horizontal) of the roof.    Typically these are expressed as rise/12" of run.  For example a common roof might be a "6/12" which means the rise is 6" for every foot of run.   If the gable roof of a building is 16' wide and 32" tall the rise would be 32" and run (1/2 of the width) would be 96".  Rise/Run (sometime called slope) would be 32"/96" normally expressed as 4"/12".   Note:while rise/run is commonly called the "pitch" the pitch is actually rise over span.  In this example the pitch is 32"/192" or 1/6th. 
2. Use the square to determine the angle.   Place the square on the lumber.  For the 4/12 roof align the outside 4" on the tongue to the edge of the board.  Align the  outside 12" mark on the body to two the edge of the board.  The angle created by the tongue is the "plumb" or vertical cut for the rafter.  Important:  You must read both reading on the same side of the square. 
    
   Square positioned with 6" on the tongue and 12" on the body.  Plumb is marked on the tongue (right).  Note: Top of rafter is down. 
   
3. To determine the length you can use the rafter table or more simply use the square.
   1. Using the rafter table on the square:   Choose the row for the type of rafter. Choose the column under the number that represents the rise.  Multiply the resulting value by the total run of the rafter.   For example for a common rafter the rise/run is 6/12 and the total run is 12' then the length would be 13.42 x 12' = 161.04".  The same calculation can be used to calculate the tail length
      .
      
      Rafter Length Tables
   2. The simpler method is to simply use the square.   No math needed.  On the square find the rise on one leg and the run on the opposite leg.  The slope distance is simply the distance between these two points.   Note:  These are the same two point used to determine the angle of the plumb cut.   Now use that distance to mark out the rafter.   For example for a common rafter the rise/run is 6/12 and the total run is 12' then mark out the distance 12 times.   Use the same method to determine the length of the tail.   Hint:  If the tail run is 2 1/2 feet.  Mark out two full lengths then divide rise/run by 2 (3/6) and use that distance on the square.
      
      Square used to mark length.  12" on the body and 6" on the tongue. Distance between 12" and 6" is the "slant" distance of 12" of run.
4. Once the rafter is laid out it needs to be marked for th the bird's mouth.  Simply lay the square on the plumb cut line and slide it up to width of the plate.  Note: this cut should not exceed 1/3-1/2 of the rafter width (check building codes). 
   
   Square used to mark bird's mouth.   Bottom of the rafter is down.  The square is aligned with the lower plumb cut. Bird's mouth is sized for a 3 1/2" plate in this photo.
5. Finally the rafter needs to be trimmed for the width of the ridge board.  Ridge boards are commonly 1 1/2" thick so we shorten the length by 3/4" .  Using the measure back (at right angle) from the plumb cut at the end of the rafter 1/2 the thickness and draw a parallel cut line. 
   
   Square used to locate the trim for the ridge board from the top plumb cut.  Top of rafter is up. 
6. Once you have cut (and checked) the first rafter you can use it as a template for the rest.  A power miter saw can be used to cut the ends. 

Finished Layout.   Top of the rafter is down.  In this example the slope is 6/12, the total run is 3' and the tail is 6". 

Cutting a Shed Roof Rafter

A shed roof simply spans the two outside walls.  The difference in wall height determines the slope.  A shed roof rafter has two bird's mouths. 

1. Lay a uncut rafter on the building.  Set the square against the wall the mark the plumb angle on the rafter for both walls.  This determine the angle as well as the length. 
2. For the lower bird's mouth layout as a common rafter for a gable roof. 
3. For the upper bird's mouth using a square measure in (towards the middle) the width of the seat cut and draw a parallel plumb line.   Then using that like layout the bird's mouth.
4. Add tails to both ends.  
5. Note: You can use a rafter square to determine the angle of the plumb cuts for using a power miter saw to cut the rafter or align the saw with the plumb cut line. 

Layout of Stair Jacks (Stringers)

Stair jacks support the stairs and typically 2 or three are used for normal width stairs.   They are easily laid out using the square.

1. First determine the rise of the stair and the depth of tread. 
   1. The tread depth is determined by several factors.  The width of the tread, the amount the tread overhangs, and if solid riser (toe plate) is used. 
   2. The tread height should be less that 8" and is determine by the total rise of the stair.  Measure the total rise.  Divide by 8" or less to determine the number of stairs.  For example if the rise is 38"  and a 7" rise is desired then 38" / 7 = 5.42 stairs.   Now round up to the nearest even number (6).   Finaly to determine the actual rise of the stairs divide the total rise by the number of stairs 38" / 6 = 6.33"  (6 5/16).  . 
2. Starting at the top of the jack lay the square on the board in the same orientation as the notch will be.  Align the square so the rise is measured on one leg and the run (depth) on the other.  Mark the notch on the board.  Repeat for each stair.  Note in most cases there will be one less actual tread than you calculated since the landing will be the floor.   In some case you may want a tread at the upper floor level so add an additional stair to the jack.
3. At the top of the jack the first plumb cut will be the full width of the board so extend that line. 
4. At the bottom of the stair you need to subtract the tread thickness.

From: https://xiiowt.unveriumenflue.com

Finding the Center of a Circle

The center of a can easily be determined with a framing square. 

1. Place the square inside the circle with the outside angle corner touching the edge.   Draw a line down each outside leg to intersect the edge of the circle.  Connect the points where the lines insect the circle (a line across the diameter).
2. Rotate the square about 90^o and repeat the process.  
3. Where the two diameter lines intersect is the center.

Using the Rafter Square

The rafter square is a flat triangular square with a T stop on one leg. 

From: https://www.anikasdiylife.com/speed-square-beginners-guide/

Finding the rafter plumb cut angle

The rafter square can be used to determine the angle of the plumb cuts.  Place the pivot on the edge of the board.  Pivot the square until the rise is aligned with the number on the square.  For example if the rise/run is 6/12 and you want the angle for a common rafter then align the edge with the 6 on the common scale.   Note:  You can also use the square to determine the angle of the plumb cut by aligning the square then reading the angle scale at the edge of the board.  This is useful in setting a miter saw angle for repetitive cuts.

Square is positioned for 4/12 slope of a common rafter.  The plumb cut is the angle on the right side of the square.

Determining Length

The rafter square cannot be used to determine the length of a rafter. Most rafter scales come with a table like the one shown below.  Find the rise in the table then multiply the number buy the run.   For example for a common rafter the rise/run is 6/12 and the total run is 12' then the length would be 13.42 x 12' = 161.04".  The same calculation can be used to calculate the tail length.

Marking an Angle

The rafter square has a built in 45^o angle.   To mark another angle (< 45o) place the pivot against the edge of the board and rotate the square until the edge of the board is aligned with the degree marking on the outer edge of the square.

Square is set to 25o angle.  The angle is marked on the right side of the square.

Saw Fence

By placing the T edge of the square against the edge of the board the other leg can be used to guide a circular saw to make a clean straight cut.  Hint.  Mark the edge of the board to be cut then align the saw blade with the mark and move the square against the saw base plate.

Check Saw Blades for Square

The rafter square is an ideal square to check the blade for square on a circular saw or table saw.   It is recommended that you check a circular saw every time the angle is changed.  Simply place the square against the base plate and blade (between the teeth)

As a marking gauge

Some rafter squares have groves in the inner part of the square.  To mark a thin strip on a board place square tightly against the board and place a pencil in the appropriate groove.  Now slide the square along the board to make a line parallel to the edge of the board.   Pushing the pencil is best.

To Mark Both Sides of a Board

To cut a board that is thicker than a circular saw will cut you need to mark both sides of the board.  The rafter square makes quick work of this task.

1. Mark the length to be cut.
2. Use the square and draw a line on the board.
3. Rotate the board 90^o and use the square to draw a line that is aligned with the previous line.
4. Again rotate the board 90^o and use the square to draw a line that is aligned with the previous line.
5. Cut on the first line then turn the board over and cut on the third line.

Other Related Tools

Sliding T Bevel

Once the angle is determined  using square a sliding T bevel can be used to quickly reproduce the angle.

Stair Gauges

Stair gauges are attached to a square like a fence to allow quick reproduction of the angle.  They can be used on framing squares and rafter squares. 

Terms

The following terms are used to describe the framing square and common building framing.

STEM Connections

Their is a good deal of math behind the tasks listed above.   In some cases the square itself removes the need for math as in the determination of slope distance.  However there is still many opportunities to introduce and practice common problems in carpentry using math. 

Worksheet

References

Swanson Speed Square

Stanley Rafter Square

Stanley Framing Square

ABC of the Steel Square and its Uses  (an historical reference published in 1908)