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How to use a framing square.
A framing square is a lot more than a simple square-cut saw guide. This simple device is crammed with tables, data and tricks that allow a carpenter to lay out roof rafters, stairs, or other building features.
A carpenter's framing square includes tables stamped right into the tool itself. This article explains how to make quick use of a framing square and its imprinted data to get some basic roof measurement data like roof pitch or slope, rafter lengths, and end cuts, stair stringer cuts, lengths of braces and other construction measurements.
Roof measurement methods: these articles explain various methods for measuring all roof data: roof slope or pitch, rise, run, area, and other features. This article series gives clear examples just about every possible way to figure out any or all roof dimensions and measurements expressing the roof area, width, length, slope, rise, run, and unit rise in inches per foot.
We also provide a MASTER INDEX to this topic, or you can try the page top or bottom SEARCH BOX as a quick way to find information you need.
Here we explain just how to use a framing square and its etched-on tables to figure out roof slope & rafter lengths, rafter cuts, brace lengths & cuts, stair stringer layout & cuts and other construction & framing layouts & saw cuts.
We link to a separate page where we explain how to use the framing square to lay out and construct stairs.
The standard two-foot framing square is an L-shaped tool that is used to mark angles for cuts used in building framing, particularly roof rafters, stair stringers, and many other cuts or angles other than 90°.
On both the long and short arms of the framing square are marked various framing tables giving rafter lengths, roof slopes and the proper angle of cuts for various roofing connections such as a rafter end abutting the ridbe board, the birds' mouth cut at the rafter segment that rests atop a wall plate, hip and valley rafter cuts and other information.
[Click to enlarge any image]
Other tables include conversions of inches of rise/run to slope in degrees, conversion of fractions of an inch (1/32, 1/16, 1/8 etc. ) to decimal fractions, conversion of inches to decimal fractions of a foot, numbers of joists, studs, rafters, and even pilot hole size recommendations for wood screws.
The parts and faces of the framing square labelled in the framing square photograph above, and are referred to as follows:
Below our photo shows the front or face side of the heel of a framing square. You'll see that the manufacturer's name (Empire) and the framing square model number (e1190) appear on the framing square's heel face.
We will discuss the inch-divisions shown on the heel face of the framing square in just a bit further along in this article at FRAMING SQUARE DIVISION WARNINGS 8ths 10ths 16ths.
Here we'll list all of the tables found on a decent quality framing square, then we'll explain how each of them is used.
Seen from the top edge of the framing square blade then moving downwards, on the front of the blade when you hold the framing square with the tongue or shorter arm to your right and pointing down you'll see inches marked in 16ths on the blade top edge, then the tables we give below, and finally inches marked in 8ths on the bottom edge of the blade.
When you hold the framing square with the tongue or shorter arm to your right and pointing down, on the outer edge of the framing square tongue are inches marked in 8ths, then the table I cite below, and finally inches marked in 16ths on the inner edge of the tongue.
Here we describe how to use the rafter tables found on the front blade on a framing square.
[Click to enlarge any image]
The rafter tables allow you to calculate the length of a rafter by choosing a "full scale" number that matches the unit rise (slope or angle) of the roof.
The table will provide full scal
The full scale number will be the length of the rafter in inches for each foot of horizontal run distance.
Our sketch above illustrates the concepts of run (horizontal distance) and rise (vertical distance) along the length of a rafter. Normally roof slopes are expressed as inches of rise per foot of run.
To use the rafter length tables on the framing square blade front you need first to understand the type of rafter you are cutting.
For a common rafter, or for each of the other rafter types, these tables give the length of the rafter per foot of horizontal run.
Above we see the key to the lines in the rafter length table.
This key is at the left end of the front of the framing square blade. Here is the identification of each line of numbers on the blade front:
COMMON RAFTER LENGTH PER FOOT RUN
HIP OR VALLEY RAFTER LENGTH PER FOOT RUN
DIFF. IN LENGTH OF JACKS 16 INCH ...
DIFF. IN LENGTH OF JACKS 24 INCH ...
SIDE CUT LENGTH OF JACK ...
SIDE CUT OF HIP...
To the rifght of these line names are columns of numbers under each inch number along the blade's upper edge. Each number gives the unit length in inches of the rafter type for the corresponding particular roof slope also as inches of rise per foot of run.
Let's look again at the drawing above and review some definitions of basic rafter and roof framing terms.
[click to enlarge any image].
Definition of Rafter Run: You can see that for any rafter, the rafter's RUN is the horizontal distance spanned by the rafter from the center of the ridge to the outer edge of the top plate of the wall.
Definition of Rafter Span: the rafter span is the same as the rafter's run: the total horizontal distance (parallel to the ground) below the rafter.
Definition of Rafter Line Length: Typical carpentry texts refer to the rafter's actual length from the rafter's plumb-cut face abutting the ridge board to the rafter's bird's mouth plumb cut as the rafter line length.
Definition of Rafter Total Length: When we add the additional rafter length necessary to include the roof overhang I call that the rafter total length. Some texts may also call this the rafter line length so one needs to take care.
Definition of Roof Span: In a symmetrical roof such as the gable roof shown above, the total building width between the outer faces of the walls or wall top plates is the total area spanned by the roof or total horizontal span.
Definition of Rafter Rise or Roof Rise: a rafter's rise or the roof's rise is the total increase in vertical height over the rafter run or rafter span - the vertical distance shown in the center of our sketch above.
Definition of Roof slope: the slope of a roof or rafter is its angle off of dead flat or horizontal, expressed as the number of inches of rise or increase in height per foot or 12" of horizontal run or distance. An 18-in-12 slope roof is one whose height above horizontal increases 18 inches up for every 12 inches of horizontal distance.
Let's figure the rafter length for an 18 in 12 roof.
On the framing square blade face, using the COMMON RAFTER LENGTH PER FOOT RUN line in the table, look along the blade under the inch number 18 we see 21.63. I marked it in red to make it easier to spot.
[Click to enlarge any image]
That tells us that for a common rafter on an 18/12 sloped roof, the rafter length will be 21.63" per horizontal foot of run.
If in our building the rafter span is 10 feet (the building, would thus be 20 feet wide), we calculate the required rafter length from ridge to the outer face of teh wall top plate as follows:
Common Rafter Table No. = 21.63 = inches of rafter length per unit (one foot) of run
Rafter Run Distance = 10 ft or 10 units
Rafter Length = 10 units x 21.63" per unit
Rafter Length = 216.3" or we can divide by 12 to get feet and fractions
Rafter Line Length ridge to top plate outer face = 216.3 / 12 = 18.025 ft.
And to be very precise we could convert the fraction of a foot ( .025) back to inches.
12" /ft. x 0.025 ft = 0.3 " or 3/10 of an inch.
Or if you want to convert this to 8ths 16ths or 32nds or 64ths, multiply 0.3 x 8 (for example to get eights) to get 2.4 eighths - or about 2/8 or about 1/4 " since unlike furniture makers, roof framers won't measure accuracy to more than an eighth.
Rafter Length = 18 ft 1/4"
Really? No. Not really. We haven't yet considered the roof overhang past the face of the building wall.
Watch out: take a second look at our roof sketch shown earlier.
Rafter Length = 18 ft 1/4" is the length froom the ridge centerline to the outer edge of the wall top plate.
You need to increase the run length to account for the amount of roof overhang or eaves out past the wall.
For example on a 10 ft. run, if we want the roof overhang to extend two feet horizontally past the wall front, we need to increase the run length by two feet.
Our new rafter run will be 12 ft. not 10 ft. (before allowing for thickness of siding and trim).
New with overhang Rafter Length = 12 units x 21.63" per unit = 259.56"
Rafter Line Length to End of Roof Overhang = 259.56"
Really? is this really the final rafter line length? No. Not really.
The final total rafter line length including roof overhange will need one final adjustment for half the thickness of the ridge board.
The rafter run, distance specified as the horizontal distance (parallel to the ground) from the center of the ridge line to the outer face of the wall top plate OR to the outer face of the rafter plumb cut after we add additional run length to give a roof eaves or overhang.
Using the framing square guide we calculated a final rafter length of 259.56" that I would have
rounded down to 258".
More precisely, if we are using a ridge board against which the
rafter upper-end plumb-cuts will be nailed, the ridge board is 1 1/2"
thick, so if we were being very precise we could have considered that
thickness (or half of it, 3/4") when figuring the rafter's true
run distance and ultimately its cut length.
Ignoring this adjustment means that the excact
final roof outside dimensions and overhang may be "off" by 3/4" and worse, yur bird's mouth cut for the wall top plate connection may end at the wrong location.
The answer is none at all, provided that you remember to square up the starting end (I use the ridge-board end) of the rafter with a squaring-cut if necessary, before making your rafter layout and length measurements.
True Final Rafter Total Line Length = (259.56" minus 3/4" (half the thickness of a 2x ridge board) ) = (259.56" - 0.75") = 258.81".
If this were my roof, I'd round either down to 258" (which in feet and inches = 21' 6" - a nice even number on my measuring tape).
Really? is this really the final rafter line length? Yes, finally.
Let's look at a 6/12 roof for some rafter lengths
Above my pencil is pointing to the 6-inch mark. Using the rafter length table below, this significes that we are looking at rafter lengths for the various types of rafters on a 6/12 slope roof.
That is, on this roof there will be a 6-inch rise in 12-inches of horizontal run.
Now let's put those line names together with the numbers we read
under the 6-inch mark on the same blade surface
Finally let's look at a common rafter length for a very low slope roof
Here is another example of common rafter length for a very low slope roof.
In the top line of the rafter table shown above near the heel of a framing square, look under the 3-inch mark where you find the 3" on the top edge of the framing square blade.
There in the top of the column of numbers you'll see 12.37.
This tells us that the length of a common rafter for each 12" of run will be 12.37" long if the roof rise is 3" in 12.
So if our rafter run or span is 10 feet we calculatethe rafter length from ridge to outer wall face as
12.37" / foot of span x 10' of span = 123.7" of total rafter line length (before adding for roof overhang and before subtracting half the thickness of the ridge board.)
This discussion now has its own page at FRAMING SQUARE for BIRDS MOUTH CUT
The octagon scale on the front of the tongue of some framing squares (including the Empire Level framing square illustrated here) is used to lay out an eight sided shape or figure. You will recognize this scale, if it's on your framing square, by noticing that it counts up in multiples of 5 with dots between the octagon scale markings.
Our photo below shows the unit-5 octagon scale on an Empire Level framing square.
Both entire homes and more-often towers or turrets are sometimes framed in an octagon shape while other structures use octoganally-shaped timbers and beams that were cut out of square stock. Interestingly Empire's own "Rafter Book" is silent on using the octagon scale. We did find an explanation of using the octagon scale at free-ed.net from which we excerpt and paraphrase below. See REFERENCES for the full citation.
To use the octagon scale to lay out an octagon we start working from a rectangle whose equal sides are of length L.
Measure to the center of each side of the rectangle and place a center-mark there.
[Click to enlarge any image]
Draw a straight line through each pair of opposing center marks on your rectangle so that you have a cross dividing the large retangle into four smaller squares.
To use the octagon scale on the framing square to cut stock into an octagon, use a pair of dividers whose ends are set apart a distance equal to the number of dots on the octagon scale that corresponds to the original length of the side of your starting rectangle. One leg of the dividers is placed on the starting line on the octagon scale and the other leg of the dividers is placed on the nth dot that corresponds to the original rectangle side length.
Because the octagon scale on the framing square does not extend past 16" (the length of the gongue), what good is it? It's used to mark the cut lines on square stock that you want to trim into an octagonal shape. Examples of octagonal stock appear as decorative posts and beams.
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This framing square table converts inch measurements into decimal fractions of a foot.
For example:
This table provided on the back of the framing square blade helps you convert inches of rise to slope expressed in degrees.
For example:
See ROOF SLOPE TABLE, TYPES, WALKABILITY for a detailed table of roof slopes in rise & degrees as well as comments about woor slope walkability
The table below, found near the end of the back of our framing square blade converts all of the common inch-fractions into decimal fractions.
Examples:
Making use of the last bit of free space on the back of the framing square blade, Empire includes a table of recommended pilot hole diameter for wood screws of various sizes.
For example, in the table shown above, if you are using a #10 wood screw the pilot hole should be 0.109"
On the back of the framing square tongue you'll find a brace measuring table giving the lengths of common braces in sets of three numbers, two equal numbers and a third fractional number stamped to the right of the equal number pair.
For example, looking at the back of the tongue of your framing square find at the triplet 33 33 46.67. The "67" appears as a superscript in a smaller character size to the right of the "46".
This scale is used for knee bracing or for post bracing in timber framing, and is also referred to as the Diagonal Scale on the Framing Square because the scale is telling us the length of the diagonal of a right triangle whose short arms are of equal length, for example 33" in the example I give below.
This brace measurement number triplet tells us that for a 33" brace the hypotenuse of that trianglular member will be 46.67" long on its outer or longer side. Now I know that no carpenter has a tape that measures in hundredths of inches. A rough carpenter will round these decimal fractions off to something she can understand.
The framing square engineers considered this problem and gave us a pretty good solution - the Conversion Table of Inch Fractions in 32nds, 16ths, & 8ths into Decimal Frctions on a Framing Square Blade Back discussed next.
We listed this inch fraction to decimal fraction conversion table earlier in this article.
A savvy carpenter will use the table given on the right end of the back side of the framing square body to find common (close enough) conversions of fractions of an inch to 8ths, 16ths, or 32ds. That table is shown just below.
Let's use the decimal to inch conversion table above to find the length of our brace hypotenuse in the 33 33 46.67 example given above.
We want to convert 46.67" to something in eights or sixteenths of an inch. Look into the table and find the decimal fraction closest to .67.
I see that the entry for 5/8" = .625" and the next bigger entry is for 11/16" = .687". Without a lot of thought I think figure that .687 is the closest number to my target of .67" so I'll measure my cut to 46 11/16". Let's see just how close this table gets us to spot-on by calculating the numbers instead of using the table above.
Whip out your cellphone, turn on its calculator and multiply the number of sixteenths in an inch (that's 16 of course) by .67 (the fraction of an inch given in the table) and you'll get 10.72 sixteenths.
That tells me that if I'm measuring my cut to the nearest 16th of an inch I'll measure out 46" and another 10 1/2 sixteenths inches or 46 10/16" plus a hair as we say in the trade.
And you can see that the table gave us 46 11/16" while the calculation gave us 46 10/16" plus a hair. In other words either approach gives us something between 46 5/8 (that's the same as 46 10/16) inches and 46 11/16 inches.
What's nice about these brace length numbers is that if you measure the hypotenuse length carefully to match the numbers in the brace table you can just slap your speed-square or try-square onto the length measurement point and with your square set at 45 degrees, mark your cut. For my example, your trianglular layout of the brace, measured on the outermost edge of the bracing member, will be 33" on the two short sides and 46" on the long side.
Below is a photograph of the back of the framing square heel.
Click to enlarge the framing square photo below and you will see
in the square's back inside corner the numbers 18 & 24 next to a large 30 (red arrow), referring to the 3-4-5 rule or as I learned it the more accurate 6-8-10 rule that give measurements of the three sides of a triangle you can use to make any pair of abutting framing members into a perfect 90 degree angle.
The 18-24-30 are simply the products of multiplying 3-4-5 by 6 to apply the rule to longer lengths.
Details of using this rule are at FRAMING TRIANGLES & CALCULATIONS
Why do we care about identifying the "face" or the "back" of the framing square? Because the two arms and four sides of them contain different tables of saw cut information that some texts will identify by their location on the framing square.
Watch out: you can get fouled up by different subdivisions of the inch markings on the face and back of a framing square. Remember to check the divisions as the 12ths and 10ths below can lead you to make a measuring or saw cut mistake.
Some texts say "always make your measurements using the outside edges of the framing square so that you won't get fouled-up. That advice does not work. For example, the front outside edges of the framing square measure 16ths or 8ths of an inch, depending on which blade you use, but the back outside edges of a framing square are marked in 12ths.
Our photo above shows the inch divisions on the backof a framing square:
Early framing squares were made of hardwood and carefully trued then braced into a right angle.
Modern carpenters have used steel squares and more recently aluminum framing squares for decades.
The traditional steel framing square was black while newer framing squares are often made of aluminum. Who cares what color or metal comprise your framing square? You might.
My first framing square was made of steel and was black in color with white numbers and lines. TIn the photo of my old hand tools (above), the red arrow points to this framing square while the green arrow points to an aluminum speed square whose added thickness forms a terriffifc saw guide. More about these hand tools is at DECK BUILDING & CARPENTRY TOOLS.
My old black steel framing square was easy to read in various llighting conditions, was very resistant to gouges from my rock knife when I used the square to make cuts in drywall or to make cuts in lumber as one might do to avoid chipping up wood when cross-cutting with a power saw.
This black square also got hot as hell when left flat in bright sunlight. And as the finish wore off of this tool, if I did not use it often enough it was prone to rust.
My current framing square, made by Empire Level, is made of light blue aluminum. The numbers and lines are of the same color and are quite a bit harder to read in some light conditions. This square is also easily gouged and scarred when in use. It is a bit lighter and a bit cooler in the hot sun. I miss my old square but truth is, I had allowed the old one to get a bit rusty.
As the numbers and line markings on your framing square are recessed, having been stamped into the metal of its body, you can improve the legibility of a monotonic framing square (for you carpenters that means it's all the same color), by painting the whole square surface with white latex paint.
Right after you've made a horrible white painted mess of the square's surface, wipe it off before the paint dries. You'll see that some white paint will remain in the recessed numbers and grooves of the tool. The manufacturer could have done this too, but then they'd have to charge you more for the tool.
Separately at DECK STAIR BUILDING DETAILS we explain in detail how a framing square is used to layout rise and run on the stair stringers when building stairs.
Measuring the roof slope, pitch, or rise and run is easy if you've got a tape measure and more accurate still if you've also got a level on hand.
But did you know that simple data already printed on your framing square can give key roof slope and rafter data?
[Click to enlarge any image]
A long-standing use of the framing square that is missed by many new carpenters is the rafter table imprinted right on the framing square itself. This data will tell us the required rafter length for a roof of a given pitch or slope.
The rafter table on a typical framing square gives rafter length for roof slopes with a rise anywhere between 2" to 18" per foot of run.
Find the unit rise (say inches per foot) of the roof on the top line in the framing square rafter table, e.g. a 6-inch rise per foot. Read this number along the inches scale at the top of the framing square.
Directly below the 6 (inch) mark on the framing square read the required rafter length (13.42) per foot of run for a 6-inch rise (6 in 12) roof.
To calculate the required rafter length multiply the total run length (half the building width plus the width that the roof is to overhang the house wall) by this number (13.42). For example if the building is 30 feet wide, half the building width is 15 feet. If we want a 2 foot roof overhang from the front of the building wall (ignoring the thickness of wall siding and trim), we add 15 + 2 = 17 feet of total run length.
17 ft. run x 13.42 inches (per foot for a 6 in 12 roof) = 228.14 inches of rafter length, or 19 feet.
Depending on your allowance for making the ridge board and fascia board plumb cuts, you can see that you should be able to cut these rafters out of a 20 ft. 2x piece of lumber.
We can reverse the usual use of a framing square (finding the rafter length) to figure out the roof dimensions (or slope). Basically, for any roof dimension or slope calculation, if we know some roof dimensions or slope we can calculate the unknown.
As we explain in detail at ROOF SLOPE CALCULATIONS, the basics of plane geometry tell us about the relationship of the lengths of sides of a right triangle:
a^{2} = b^{2} +c^{2}
the square of the length of the hypotenuse (a) equals the squares of the lengths of the opposite sides of a right triangle (b) and (c) - which is a mathematical way of saying that if we know any two roof slope measurement numbers we can compute the third.
Given the total rafter length (measure from ridge to lower roof edge) and rafter run (half the building width plus the roof overhang past the building wall) we can figure the roof rise.
If we know the roof run and rafter length, we find the roof slope by calculation or we use the framing square table (just below) and then easily find the roof rise.
For example, using the numbers from our roof framing square table example just above:
Measured rafter run RR = 17 ft. or 17 x 12 = 204 in.
Measured rafter length RL = 19 ft. or 19 x 12 = 228 in.
RR x (number on framing square) = RL
The trick here is understanding the number on the framing square is the unit-rise per foot of run.
204 x (number on framing square) = 228
(number on framing square) = 228/204 x 12in
228 / 204 x 12 = 13.412
13.412 is the unit rise in inches per foot of our example roof run. By "run" we mean the level or horizontal distance covered by the roof.
Now find the closest number to this on the framing square top row and read the inches just above. In our photo you'll see that 13. 42 is under the 6 on the inches scale. That's our roof slope in inches per foot, or 6 in 12!
Now if we still need to calculate the total roof rise, just multiply the unit rise (6) by the number of feet of run (17) and we've got the total rise in inches (6 x 17 = 102 in.) or (102 / 12) = 8.5 ft. (the total rise is 8 ft. 6 inches).
Of course if you go to ROOF MEASUREMENTS you'll see lots of other ways to figure the total roof rise, run, or slope.
2016/04/23 Jim said:
What dose the number 27 have to do with a framing square
Jim,
Somehow I smell a trick question from someone's homework or from a carpentry quiz. Arm-waving aside, I don't know. I've looked through our framing square articles, books, and on the framing square itself to look for something special about 27 and framing squares - to no avail.
While 27 feet is used as a rafter length in some texts to calculate run length, and while 27 appears ALMOST as a whole number in some framing square tables, that's about it.
Perhaps if you can give me some details about the origin of your question I can have better success.
At the end of this article at REFERENCES you'll find more texts and articles on using a framing square and written by other experts.
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