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How to use a folding rule to measure angles, roof slope, pitch, area and other dimensions: here we show how to use a carpenter's folding ruler to obtain the slope and other dimensions of a roof. Simple observations made from the ground can give a good approximation of the roof slope. In turn number along with a table we provide, or with a simple calculator, it is easy to figure any measurement of a roof: rise, slope, area, pitch etc.
Although you do not need to understand Tangents, we include an explanation and examples of how to use the tangent TAN and inverse tangent to TAN-1 find roof slope in degrees, roof rise, run, etc.
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.
How to Measure Roof Slope From the Ground Using a Folding Carpenter's Rule
As you've see from out other roof measurement examples beginning at ROOF MEASUREMENTS, knowing the roof slope is really handy as something we can measure up close but also from a distance, obtaining a number that plugs into simple formulas for roof area too.
What if the roof is inaccessible from outdoors, and there is no access to the building interior (i.e. its attic) so we cannot make direct roof slope measurements, but we still need to know its slope?
You need a simple folding carpenter's rule. It helps to have a steady hand and to read the instructions on exactly where to read the inches on the bottom scale in the folding rule triangle that we show at left.
Use a Folding Rule to Get Roof Angle or Slope: Method 1 - align the folding ruler segments to match the roof slope at the building gable end
You need: a folding carpenter's rule and a second ruler, tape measure, or carpenter's rule. To be fancy and more precise you can also use a carpenter's 4 ft. level as we will describe.
Stand about 30 feet away from the gable end of the building where you can see the triangle formed by the front and rear roof slope edges.
Match the folding ruler first two segments to the roof slopes: Open the ruler to form three segments as shown in our photograph above. The beginning segment (held on on your left) and the second segment (held on your right) are held up and adjusted to exactly match the slope of the roof. The 3rd and 4th segments of the folding ruler are held horizontal or parallel to the ground. (Or parallel to your 4 ft. level if you like.)
Hold this assembly level and check that the angle formed by ruler segments1 and 2 match the roof slopes.
I place the roof inside the triangle formed by my folding ruler.
Set the folding ruler bottom segments horizontal: bring up the horizontal segments of the folding carpenter's rule to a horizontal position - level with the building. In fact, in my photo (above left) you can see a mistake - the left end of the first folding ruler segment projects a bit below the horizontal bottom of my triangle - excuse me but taking the photo while holding this stuff was a bit tricky.
You get the idea. In a perfect world the bottom corner of the first ruler segment should be in the center of the horizontal segment, not at the top, not at the bottom. We explain this detail below at FOLDING RULE CALIBRATION. But it's not critical because we read the horizontal ruler scale along the top edge of the horizontal portion.
Read the number of inches on top edge of the bottom segment of the folding ruler where ruler segment 1 bottom corner crosses the lower horizontal segment. This number will be along the inches scale somewhere between 15 1/2" (which would be a single slope on the right and a 90 degree slope on the left) and 24" (which would be a dead-flat roof).
The reasons we use the top edge of the bottom segment for our folding ruler roof-slope readings are two:
That is how we measured and calibrated our Folding Ruler to Roof Slope Table below.
We are aligning the actual building roof slopes with the inside of our folding ruler triangle. To be consistent we make our horizontal length measurement also inside the triangle formed by our folding ruler.
One can make an equally accurate folding ruler scale using inch-marks where the bottom-most corner of the left-hand sloping ruler segment touches the scale, but I find that that location is hard to keep consistent as the roof angles vary.
To convert the inches read along the folding rule, find the approximate roof slope in the folding ruler conversion table
at FOLDING RULER to SLOPE DATA TABLE - found just below. There we provide the necessary table converting folding ruler inch-scale to roof slope below.
In the table you will see data for two basic roof shapes: a single slope or shed type roof, and a double slope or conventional gable type roof.
When reading a folding ruler triangle opened to match two roof slopes (left and right seen from the building gable-end) and for anything but a vertical left slope or a dead flat roof, we are going to read a number typically somewhere between the 20-inch ruler mark and the 24-inch ruler mark. You will see that data in the Gable Roof column second from left in our table.
If we are reading a folding ruler triangle for a shed roof, that is a single slope, the other folding ruler segment will be set to vertical or 90 degrees and will cross the horizontal segment giving an inches-measurement. You will see that data in the Shed Roof or left-most column of our table.
To obtain roof area we can use slope or tangent number to obtain the actual dimension of the sloping roof edge - the roof width. That is, if we know the angle and the length of a single side of a right triangle we can calculate the lengths of the other two sides and thus we can obtain the total roof area too.
See ROOF SLOPE CALCULATIONS
Table of Conversion Numbers: Folding Ruler Scale Translates to Roof Slope
Watch out: roof slope obtained by this method is approximate, not precise.
Horizontal Scale 90 deg Reading in Inches1 Shed Roof
Horizontal Scale Left Slope Reading in Inches12 Gable Roof
Rise / Run
Roof Pitch in Degrees
Rise / Run
68 in 12
44.8 in 12
32.9 in 12
25.7 in 12
24 in 12
17 5/8" 3
20.7 in 12
18 in 12
17.3 in 12
16 in 12
14.3 in 12
14 in 12
13 in 12
19 3/4" 4
12 in 12
11 in 12
10.1 in 12
10 in 12
9 in 12
21 1/8 "
8 in 12
7 in 12
6 in 12
5 in 12
4.36 in 12
21 7/8" 5
4 in 12
22 1/4" 5
3 in 12
2.12 in 12
2 in 12
1.5 in 12
1 in 12
0 in 12 = a flat roof (exact)
1. These horizontal ruler scale numbers were actually measured using a protractor. For example,
19 7/8" on the scale was calibrated at 45 deg. using the procedure explained at FOLDING RULER CALIBRATION. All of these triangles are right triangles.
2. For a two-slope gable roof one cannot just double the single slope shed roof horizontal distance because as soon as we un-bend the vertical ruler segment used for the 90 deg. line for a shed roof we see that the lengths of the sloping roof segments change continuously as we change the angle.
That's the effect of a center-hinged folding rule and the use of either the outer or inner edge of the ruler to sight (in the field) or measure (with a protractor) roof slopes or angles. We would have to use a clear folding rule that sports a line running through the center of the rule's width as our alignment. For this reason, carefully setting the left and right gable roof angles with a protractor and noting the horizontal ruler scale cross-point along its top edge seems the best approach.
3. Since two of our roof angles are 60 deg. we know that all 3 angles are 60 deg and this is an equilateral triangle because triangle sides a + b + c = 180 deg.
4. Since two of our roof angles are 45 deg. we know that the third angle, the two slopes meeting at the ridge, or the apex of the triangle, will be at 90 deg. Because triangle sides a + b + c = 180 deg.
6. This approach works using a folding rule until the roof slopes get very low. Then it is impossible to read the scale on the inner edge of the ruler-formed-triangle.
7. Tangent = Rise / Run also allows us to obtain roof slopes in degrees, and vice versa.
The Tan value for a 55 deg slope roof = Tan ( 55) = 1.43
The inches of run for 12-inch rise for a 55 deg slope roof is calculated as 1.43 = 12 / run or Run = 12 * 1.43 = 17.3"
The inverse Tan-1 function can convert a Tan value back into degrees of roof slope.
Tan-1 (1.43) = 55 deg. and wonderfully, Tan-1 (1.00) = 45 deg.
Since Tan is a simple ratio of unit Rise / unit Run, we note that we can quickly convert a roof slope in degrees into the number of inches of rise per 12" of run as follows, using a 55 deg. slope as example:
Tan (55) = 1.43
Since 1.43 = rise / run we can use simple algebra to write:
1.43 x 12" run = 17.16" of rise per 12" of run
Calculations & Formulas for finding Rise, Run, % Slope of a Roof or other sloping surface
For a complete guide to calculating any roof data you need from whatever numbers or data you have, please see ROOF CALCULATIONS SUMMARY. There we explain how we obtain the total roof area, number of squares of roofing materials to order, roof pitch or slope, and other helpful data.
Below are a couple of details that I include to warn about messing with folding rulers.
Rise in inches = Tan x Unit-Run" = Unit Rise" for any slope expressed in degrees, use the Tangent value to calculate rise for a 12-inch run:
Watch out: for cases such as our folding ruler triangles, you are not working with a fixed horizontal unit run of 12-inches, nor an exact 6-inch roof slope length (hypotenuse of the triangle).
You will observe that the actual length of a folding ruler segment bent to follow a roof slope will lengthen as the slope is steeper and shorten as the slope is less steep. This is because the hinge point of the ruler segment is fixed and the edge of the sloping ruler segment moves closer to or further from the top of the horizontal ruler segment as you fold the ruler.
Slope in degrees = Tan * (Rise / Run)
Grade%: %Grade = Rise / Run x 100 but be sure Rise & Run are expressed in same units)
Methods of Folding Rule Inch-Scale Calibration to Read Roof Slopes & Angles
At FOLDING RULER ROOF SLOPE CALIBRATION we describe some fun approaches can be sued to calibrate the folding rule inch-readings that give roof slope in the procedure described above.
We can set the slope of folding ruler segments using a protractor and note where the folding ruler crosses the horizontal ruler scale: easy but you have to work with care, or we can calculate the number of inches of horizontal run for various triangles all of whom have a 6-inch hypotenuse but whose angle and thus horizontal run length change, using trigonometry.
Use a Folding Rule to Get Roof Angle or Slope: Method 2 - the 3-inch rule
Following the same procedure as used above, align the folding ruler so that its first two segments exactly match the roof front and rear slopes. But the calculation approach is a bit different and really neat.
The original 3-inch rule discussed by the South Dakota School of Mines and Technology  was documented as applying to acute angles (angles of 90 degrees and less) with some suggestions on how that approach might be used for obtuse angles such as found on most building roofs.
Here we elaborate that procedure to apply to building roofs that will normally be much less steep - properly, obtuse angles. We start by explaining the acute angle measurement and then explain how to make obtuse angle measurements using the folding ruler.
Acute angle measurement using a folding ruler
Using a folding carpenter's rule calibrated in inches, set the first and second segments of the rule to match the roof slopes while standing at the gable end of the building and sighting across the folding rule, holding it in alignment with the roof edges.
Without changing the angle to which the ruler segments are bent, use a second straight ruler or tape (or with help from an assistant) to measure the distance between a point that is exactly 3 inches down from the apex of the triangle, measuring along the inside edge of the ruler - mark or note this point on both the left and right ruler segments.
For consistency I align the inside of the folding rule to the roof edges and make all measurements along the inside edge of the folding carpenter's rule segments.
Now using a ruler or tape measure, measure the horizontal distance between those two 3-inch marks.
Multiply that distance by 20.
This approach works for angles up to 90 degrees. The number will be the approximate slope of the roof expressed in degrees as you will read in the table just below.
Obtuse angle measurement using a folding ruler
To measure an obtuse angle (which is normally the case for roof angles) let ruler segment 1 follow the roof slope, set segment 2 at 90 degrees to ruler segments 3-4, hold segments 3-4 level, and re-check that segment 1 still follows the roof slope. The obtuse angle is then split in two, we use the same 3-inch rule and table as before, and add the two angles together to get the obtuse angle in degrees.
As the original author explained:
This method can be easily applied to approximate an obtuse angle
as well. For example, one can approximate the corresponding supplementary angle and subtract this result from 180
can measure the angle's excess past 90
using the end of the ruler as
a convenient right angle, or if your ruler happens to be damaged from
years of use (or disuse!), divide the angle into two acute angles and add
their approximations. - South Dakota School of Mines and Technology 
This procedure was originated by Tor Bertinm a student at the South Dakota School of Mines and Technology, SDSM&T and is nicely documented by an author who modestly omitted his name, but posted a helpful and detailed analysis of this approach at the web link given below. [Click to enlarge the table or any other image at InspectApedia.com]
"How to Measure Angles with a Ruler", South Dakota School of Mines and Technology, Website: http://www.mcs.sdsmt.edu, http://www.mcs.sdsmt.edu/tkowalsk/portfolio/downloads/pub_HowToMeasureAngles.pdf retrieved 10/26/2013, copy on file.
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Books & Articles on Building & Environmental Inspection, Testing, Diagnosis, & Repair
 "How to Measure Angles with a Ruler", South Dakota School of Mines and Technology, Website: http://www.mcs.sdsmt.edu, http://www.mcs.sdsmt.edu/tkowalsk/portfolio/downloads/pub_HowToMeasureAngles.pdf retrieved 10/26/2013, copy on file.
"Choosing Roofing," Jefferson Kolle, January 1995, No. 92, Fine Homebuilding, Taunton Press, 63 S. Main St., PO Box 5506, Newton CT 06470 - 800-888-8286 - see http://www.taunton.com/FineHomebuilding/ for the magazine's website and for subscription information.
Owens Corning Corporation, One Owens Corning Parkway
Toledo, Ohio 43659
Telephone: (419) 248-8000
Fax: (419) 248-5337
http://www.owenscorning.com Owens Corning is credited as the inventor of fiberglass when Owens Illinois [O-I] researcher Dale Kleist and his colleague John Thomas stumbled onto and then realized the significance of producing glass fibers in 1932. O-I formed a joint venture with the Corning Glass Works in 1935, leading to the formation of Owens Corning Corporation in 1938. More on Owens Corning's history is at
Focus, Toledo, Ohio, Owens-Corning Fiberglas Corporation, October 1988.
"A History of Innovation," http://www.owenscorning.com, 1997.
Stewart, Thomas A., "Owens-Corning: Back from the Dead," Fortune, May 26, 1997.
International Directory of Company Histories, Vol. 20. St. James Press, 1998.
"Two-Year Wisconsin Thermal Loads for Roof Assemblies and Wood, Wood–Plastic Composite, and Fiberglass Shingles [on file as Roof_Thermal_Loads.pdf] - ",
Jerrold E. Winandy
Cherilyn A. Hatfield, US Department of Agriculture, US Forest Products Laboratory, Research Note FPL-RN-0301
ARMA - Asphalt Roofing Manufacturer's Association - http://www.asphaltroofing.org/
750 National Press Building, 529 14th Street, NW, Washington, DC 20045, Tel: 202 / 207-0917
ASTM - ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA, 19428-2959 USA The ASTM standards listed below can be purchased in fulltext directly from http://www.astm.org/
NRCA - National Roofing Contractors Association - http://www.nrca.net/, 10255 W. Higgins Road, Suite 600,
Rosemont, IL 60018-5607, Tel: (847) 299-9070 Fax: (847) 299-1183
UL - Underwriters Laboratories - http://www.ul.com/
2600 N.W. Lake Rd.
Camas, WA 98607-8542
Tel: 1.877.854.3577 / Fax: 1.360.817.6278
copy on file as /roof/Roofing_Historic_NPS .pdf Roofing for Historic buildings", Sarah M. Sweetser, Preservation Brief 4, Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS .pdf From Asbestos to Zinc, Roofing for Historic buildings, Metals", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS_3 .pdf From Asbestos to Zinc, Roofing for Historic buildings, Metals-part II, Coated Ferrous Metals: Iron, Lead, Zinc, Tin, Terne, Galvanized, Enameled Roofs", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS_4 .pdf From Asbestos to Zinc, Roofing for Historic buildings, Metals-part III, Slate", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS_5 .pdf From Asbestos to Zinc, Roofing for Historic buildings, Metals-part IV, Wood", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS_5 .pdf From Asbestos to Zinc, Gutters", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
copy on file as /roof/Asbestos-to-Zinc_Metal_Roofing_NPS_2 .pdf From Asbestos to Zinc, Roofing for Historic buildings, Metals- Roofing Today", Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source:
/exterior/NPS_Preserv_Brief_16_Subs_Mtls.pdf The Use of Substitute Materials on Historic Building Exteriors ",
Sharon C. Park, AIA, Preservation Brief 16, Technical Preservation Services, National Park Service, U.S. Department of the Interior, web search 9./29.10, original source: http://www.nps.gov/history/hps/tps/briefs/brief16.htm
Books & Articles on Building & Environmental Inspection, Testing, Diagnosis, & Repair
The Home Reference Book - the Encyclopedia of Homes, Carson Dunlop & Associates, Toronto, Ontario, 25th Ed., 2012, is a bound volume of more than 450 illustrated pages that assist home inspectors and home owners in the inspection and detection of problems on buildings. The text is intended as a reference guide to help building owners operate and maintain their home effectively. Field inspection worksheets are included at the back of the volume. Special Offer: For a 10% discount on any number of copies of the Home Reference Book purchased as a single order. Enter INSPECTAHRB in the order payment page "Promo/Redemption" space. InspectAPedia.com editor Daniel Friedman is a contributing author.
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Green Roof Plants: A Resource and Planting Guide, Edmund C. Snodgrass, Lucie L. Snodgrass, Timber Press, Incorporated, 2006, ISBN-10: 0881927872, ISBN-13: 978-0881927870. The text covers moisture needs, heat tolerance, hardiness, bloom color, foliage characteristics, and height of 350 species and cultivars.
Green Roof Construction and Maintenance, Kelley Luckett, McGraw-Hill Professional, 2009, ISBN-10: 007160880X, ISBN-13: 978-0071608800, quoting: Key questions to ask at each stage of the green building process Tested tips and techniques for successful structural design
Construction methods for new and existing buildings
Information on insulation, drainage, detailing, irrigation, and plant selection
Details on optimal soil formulation
Illustrations featuring various stages of construction
Best practices for green roof maintenance
A survey of environmental benefits, including evapo-transpiration, storm-water management, habitat restoration, and improvement of air quality
Tips on the LEED design and certification process
Considerations for assessing return on investment
Color photographs of successfully installed green roofs
Useful checklists, tables, and charts
Roofing The Right Way, Steven Bolt, McGraw-Hill Professional; 3rd Ed (1996), ISBN-10: 0070066507, ISBN-13: 978-0070066502
Slate Roofs, National Slate Association, 1926, reprinted 1977
by Vermont Structural Slate Co., Inc., Fair Haven, VT 05743, 802-265-4933/34. (We recommend this book if you can find it. It
has gone in and out of print on occasion.)
Roof Tiling & Slating, a Practical Guide, Kevin Taylor, Crowood Press (2008), ISBN 978-1847970237, If you have never fixed a roof tile or slate before but have wondered how to go about repairing or replacing them, then this is the book for you. Many of the technical books about roof tiling and slating are rather vague and conveniently ignore some of the trickier problems and how they can be resolved. In Roof Tiling and Slating, the author rejects this cautious approach. Kevin Taylor uses both his extensive knowledge of the trade and his ability to explain the subject in easily understandable terms, to demonstrate how to carry out the work safely to a high standard, using tried and tested methods.
This clay roof tile guide considers the various types of tiles, slates, and roofing materials on the market as well as their uses, how to estimate the required quantities, and where to buy them. It also discusses how to check and assess a roof and how to identify and rectify problems; describes how to efficiently "set out" roofs from small, simple jobs to larger and more complicated projects, thus making the work quicker, simpler, and neater; examines the correct and the incorrect ways of installing background materials such as underlay, battens, and valley liners; explains how to install interlocking tiles, plain tiles, and artificial and natural slates; covers both modern and traditional methods and skills, including cutting materials by hand without the assistance of power tools; and provides invaluable guidance on repairs and maintenance issues, and highlights common mistakes and how they can be avoided.
The author, Kevin Taylor, works for the National Federation of Roofing Contractors as a technical manager presenting technical advice and providing education and training for young roofers.
The Slate Roof Bible, Joseph Jenkins, www.jenkinsslate.com,
143 Forest Lane, PO Box 607, Grove City, PA 16127 - 866-641-7141 (We recommend this book).