Roof rise or pitch or slope measurement on the roof surface (C) Daniel FriedmanFraming Square Instructions
Layouts, Measurements & Cuts Using a Framing Square & Its Tables
Roof rise, run, rafter cuts, braces, or stair stringer layout using a framing square

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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.

A carpenter's framing square includes some 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.

Definitions of Parts of the Framing Square

Parts of a framing square (C) Daniel Friedman

[Click to enlarge any image]

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.

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.

Definition of the Parts of a Framing Square: blade, tongue, heel, front, back

The parts and faces of the framing square labelled in the framing square photograph above, and are referred to as follows:

  1. The framing square blade or body: this is the wider and longer arm of the "L", normally 2" in width and 24" long.
  2. The framing square tongue: this is the shorter and more narrow arm of the "L", normally 1 1/2 " in width and 16" long.
  3. The framing square heel: is the point where the two arms of the framing square meet. In our framing square photo above the framing square heel is indicated by the yellow arrow. Below we take a closer look at the heel face and the back of the heel of the framing square.
  1. The framing square face or front is the side of the square you will see if you look at the square while holding its longer arm, the tongue, horizontally with the shorter arm, the tongue to your right and pointing down.

    When held in this position, the wider longer blade or body arm is pointing to my left and shows me a table of common rafter lengths per foot of tun, hip or valley rafter lengths per foot run. Below our photo shows the front or face view of a framing square.

    On the face of the framing square blade you'll find rafter framing tables.

Framing square face showing blade at top and tongue at right (C) Daniel Friedman

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.

Framing square heel face (C) Daniel Friedman

  1. The framing square back is the side of the framing square that you will see if you look at the square while holding its longer arm, the tongue horizontally with the shorter arm, the tongue, to your left and pointing down, as Fala is demonstrating in the framing square back photo below.

    When held in this position the wider longer blade or body arm is pointing to my right, showing at least three different tables

Photo of the back side of a framing square, tongue on left (C) Daniel Friedman

List of the Various Tables Found on a Framing Square

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.

Tables Found on the Front of a Framing Square Blade

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.

Table Found on the Front of a Framing Square Tongue

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.

Tables Found on the Back of a Framing Square Blade

Tables Found on the Back of a Framing Square Tongue

Details of Use of Each Table on the Face of a Framing Square

Rafter Length Tables on the Front of the Framing Square Blade

Roof rise or pitch or slope measurement on the roof surface (C) Daniel Friedman

[Click to enlarge any image]

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.

Framing square body table of rafter lengths per foot of run (C) Daniel Friedman

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. Below the number 18 we see a column of numbers.

Each number gives the length of a rafter type for a particular roof slope rise expressed as inches of rise per foot of run. In the photo above, under the inch number 18 (read as 18" of rise per foot of horizontal run) we see 21.63.

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.

Let's look at a 6/12 roof for some rafter lengths

Rafter tables on a framing square (C) Daniel Friedman

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.

Finally let's look at a common rafter length for a very low slope roof

Standard rafter length table on a framing square (C) Daniel Friedman

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 12" of run will be 12.37" long if the roof rise is 3" in 12.

Octagon Scale on the Front of the Framing Square Tongue - multiples of 5 on the octagon scale

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 from which we excerpt and paraphrase below. See REFERENCES for the full citation.

The octagon scale on a framing square is numberd in multiples of 5 (C) Daniel Friedman

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.

How to use the 5-unit Octagon Scale on a Framing Square (C) Daniel Friedman

[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.

  1. The dividers are then used to lay out their spread distance on each side of the rectangle to give the cut points or marking points of an octagon as follow:
  2. Place one point of the dividers on the end of the center line at the edge of the rectangle.
  3. The other point of the dividers will mark the first octagon cut line.
  4. Repeat this process for each of the other ends of the center lines of the rectangle to mark all of the other cut points of the octagon on the end of your timber or stock.
  5. Repeat this entire process, steps 1-4 above, on the other end of the square stock
  6. Draw lines along the sides of your square stock connecting the corresponding octagon cut marks that you made on the stock ends.

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.

Details About Tables on the Back of a Framing Square

The Number of Joists, Studs, Rafters N Run Ft-In Table on a Framing Square Blade Back

[Text in process]

Number of joists, studs, or rafters N run (C) Daniel Friedman

Convert Inches to Decimal Fractions of a Foot

This framing square table converts inch measurements into decimal fractions of a foot.

Table converting inches to decimal fractions of a foot (C) Daniel Friedman

For example:

Change of Inches of Rise per Foot into Degrees of Slope on a Framing Square Blade Back

This table provided on the back of the framing square blade helps you convert inches of rise to slope expressed in degrees.

Framing square table converts inches of rise to degrees of slope (C) Daniel Friedman

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

Convert Inch Fractions (32nds, 16ths, 8ths, 4ths) to Decimal Fractions

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.

Table of inch fractions converted to decimal fractions on a framing square (C) Daniel Friedman


Table of Wood Screw Pilot Hole Sizes on the Framing Square Blade Back

Table of wood screw sizes pilot holes (C) Daniel Friedman

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"

The Brace Triangle Table on a Framing Square Tongue-Back - The Diagonal Scale

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.

Brace length table on the back of a framing square tongue (C) Daniel Friedman

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.

Decimal Fraction to Inches Conversion Table

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.

Decmial to fraction of inch converstion table on a framing square body back (C) Daniel Friedman

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.

Special Case in the Brace Table on a Framing Square: the 3-4-5 or 6-8-10 rule for Finding a Right Angle

Below is a photograph of the back of the framing square heel.

Face of the heel of a framing square (C) Daniel Friedman

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

Warning About the Different Inch-Divisions on the Framing Square

Framing triangle with stair gauges attached (C) Daniel Friedman

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:

Inch divisions on the front heel of a framing square (C) Daniel Friedman

Framing square color and metal - do they matter?

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.

Framing square (steel), and speed square (aluminum) (C) Daniel Friedman

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.

Framing square number legibility improvement tip:

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.

Using the Framing Square to Build Stairs

Theoretical stair design (C) Daniel Friedman

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.

How to Obtain Roof Pitch or Slope by Using the Rafter Tables on a Framing Square

Roof rafter tables on a framing square (C) Daniel Friedman

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.

How to find rafter length on the framing square

Historic building, Herefordshire, U.K. (C) Daniel Friedman

How would we use our framing square to measure or to calculate the slope and rafter lengths of this historic Herefordshire U.K. home?

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.

How to use the framing square to get roof slope

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:

a2 = b2 +c2

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.

Roof rafter tables on a framing square (C) Daniel Friedman

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.

Reader Question: What does the number 27 have to do with a framing square?

2016/04/23 Jim said:

What dose the number 27 have to do with a framing square



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.


Continue reading at ROOF MEASURE by FOLDING RULE or select a topic from closely-related articles below, or see our complete INDEX to RELATED ARTICLES below.



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