Roof Area Calculations
Methods for calculating the area of a roof depending on what measurements you already know
ROOF AREA CALCULATIONS - CONTENTS: how to calculate or estimate roof area from whatever numbers are at hand: roof rise, slope, angle, width or length or roof angle can give us the roof area with just a tiny bit of arithmetic.
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Roof area calculation & measurement methods: here we describe various methods for measuring all roof data: roof slope or pitch, rise, run, area, and other features. We include on-roof measurements, roof measurements or estimates that can be made from ground level, and several neat tricks using a folding ruler to measure roof angle or slope. This article shows how simple measurements can give the roof area without having to walk on the roof surface.
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.
Roof rise (b): first we will obtain the total roof rise by counting siding courses. We measure siding width & then we count courses at the building gable end. If we start counting siding at a horizontal lilne even with the lower roof edge or eaves and count up to the ridge, we've got a close guess at the total roof rise.
The number of siding courses from the roof triangle base to the roof peak x siding course width = total roof rise = (b)
Roof length (c): Measure or step off building gable end width.
Roof width (a): This data allows us to calculate the roof triangle as we know two sides (b) and (c) of the three sides of a right triangle (the red lines in our photo at above left). Let (b) = the vertical rise in the roof and (c) = the roof length (building length + gable overhangs). The third side of the triangle, its hypotenuse or the sloping surface of the roof, or side is (a) which is calculated as follows:
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).
Given a^{2} we use our calculator to take the square root and bingo, we have the length of the sloping side of the roof.
Given that we now know all of the lengths of our triangle we can easily obtain roof slope too if we need it.
Now finally to get the roof area, we just need one more figure, the length of the roof along the building eaves or ridge. From the ground we measure or step off building length (L).
The roof area(RA) is calculated easily: we multiply the Roof Length (c) (which is the sum of building length plus the gable end overhangs of the roof) by the Roof Width of slope (a) that we just figured out above when we computed the hypotenuse of the roof triangle (that's why we needed the roof rise number).
RA = (a) x (c)
We can use the TAN or tangent feature of a calculator as a trivial way to convert degrees of slope (or grade if we're building a sidewalk or road) into units of run per unit of rise. The Tangent of any angle expressed in degrees is nothing more than a ratio:
Tangent = Rise / Run
Let's calculate rise per foot of run for this roof using the number from an angle level
I'll show that even if we screw up we can still come out ok finding the angle and then the rise and run of a roof using the angle finding level.
I read 81 deg. on my angle level. Now let's figure run for 12" of rise for an 81 degree slope - HOLD ON! something's crazy here. This is a low slope roof, how can it be sloping 81 degrees? Egad! that's nearly straight up! This is a good lesson in thinking for yourself - or performing a sanity check on calculations.
The answer is I was holding my angle level on the wrong scale. I could have made my photos over again holding the angle level the right way, but there's an easier trick:
81 degrees is just 9 degrees off of dead vertical (90 - 81 = 9). So really I could go just 9 degrees off of flat. As "flat" is 0 degrees of slope, flat+ 9 = 9. My roof actually slopes 9 degrees. Whew!
The Tan value for my 9 degree slope roof = Tan ( 9) = 0.1583
The inches of rise for 12-inches of run on a 9 deg low-slope roof is calculated as follows:
Tangent is defined as a ratio: Rise / Run so all we need is a little algebra (don't faint, it's easy):
0.1583 = Rise / Run
Set run to 12-inches because we're going to calculate the rise per foot of run.
0.1583 = 12 / Run
Use simple algebra:
0.1583 x Run = 12" of rise
Run = 12" / 0.1583
Run = 75.8"
That makes sense: we travel about 75 inches horizontally for every 12 inches of vertical rise on this low slope 9 degree roof.
Calculate Unit Rise for the Roof Rise
To calculate total rise if I knew the total run (say we had made an on-roof measurement) we take the following steps:
Total Rise = (Total Run in Feet) x (Rise per Foot)
The Tan value for my 9 degree slope roof = Tan ( 9) = 0.1583
0.1583 = Rise / Run
Using a little high school algebra we can re-write the equation as
0.1583 x Run = Rise
If I want to know the rise per foot of run I calculate
0.1583 x 12 = 1.89 " of rise per foot of run.
Calculate Total Rise for the Roof
I measured the total horizontal run - my building width is 20 ft. + a total of 2 ft. of overhang at the eaves.
0.1583 x 22 = 3.5 ft.
My roof increases in height 3.5 ft. from the eaves to the high end (this is a shed roof).
I can check this result against the rise per foot we got above.
(22 ft. x 1.89" rise per foot) / 12 = 3.5 ft. (thank goodness)
For the Tangential Enthusiast - Usnig Inverse Tangent Function Tan^{-1}
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
Summary of How Roof Measurements are Calculated
How to Measure or Estimate the Total Roof Area
If you have safe access to the roof surface you can quickly make the needed area measurements: just measure from the ridge to the lower edge or eaves, keeping your tape straight. With a decent 3/4" or 1" wide 30 ft. tape measure you can extend the tape out to catch the roof eaves without having to walk dangerously close to the roof edge. Also measure the roof edge or length.
RW = Roof Width = dimension from ridge to eaves. In my sketch I use (a) or the dimension of the sloping surface as RW. Remember to include in (a) the amount by which the roof extends out over the building walls - its eaves.
RL = Roof Length = dimension of the roof from one gable end of the building to the other. You don't see RL in my sketch at left. RL is simply the building width plus the amount of overhang at the two gable ends of the building.
RA = Roof Area = RW x RL
Well this is only true provided the roof surface is a rectangle. If you are working with hips and gables and you want to get precise area measurements you may find it easiest to divide the individual roof slopes up into sub-components: a rectangular part and a triangular part.
For a rectangle just multiply the width and length of its two sides to obtain area.
For a right triangle, its Area = 1/2 x ( c x b )
For a triangle such as the red example in our photo, just divide the triangle into two halves (green line) and you can still make these calculations with ease.
Remember to keep your dimensions all the same (inches or feet).
Roofers measure or estimate the total roof area in square feet that is then converted to roofing squares - the unit of ordering of roofing material. One roofing "square" covers 100 sq.ft. of roof area. Convert roof area in square feet to squares of roofing material by dividing by 100.
Roofing Squares = RA / 100
Watch out: do not walk on roofs that are fragile (you will damage the surface, make leaks, and make people mad.) Do not try to access a roof that is unsafe for any reason: height, slope, condition, wet, slippery, windy, etc. In those conditions you'll be better off making a few simple measurements from the ground level to figure the roof areas involved.
Estimating the Roof Area for Complex Roofs
Watch out: also that roof measurement is only trivial for simple shed or gable roofs whose slopes are a simple rectangle. For hipped roofs, mansards, and intersecting gables some simple triangles need to be measured if you want an accurate estimate of roof area.
Accurate Calculation of the Area of an Individual Roof Slope from Available Measurements
To be more accurate, and in cases where we need to get the roof area while working from the ground we can get the actual or accurate area of an individual roof slope as follows
Measure the building length (BL) and width (BW)
Get roof length: Measure or estimate the additional horizontal distance of roof overhang (eaves) at the building front (or rear) corresponding to the individual roof slope being calculated - Eaves Overhang Width (EOW)
Measure or estimate the additional horizontal distance of roof overhang at the both left and right gable ends for the roof slope being calculated - Gable End Overhang x 2 = (GEO)
Flat or Horizontal Projection of Roof Length = BL + GEO - this is also the true roof length = RL_{True}
Measure or estimate or calculate the roof rise - the height increase from the eaves to the ridge.
Get roof width: Use the roof rise to calculate the true roof width as follows:
From a right triangle a^{2} = b^{2} + c^{2} or hypotenuse
RW_{True2} = Rise^{2}+ RL_{True2 }
Example: RW_{True2} = (6ft. rise)^{2} + (30 ft roof length)^{2}
RW_{True2} = 36 + 900
RW_{True2} = 936
SQRt of RW_{True2} = 30.6 ft.
RW_{True}= 30.6 ft.
Calculate the Roof Area (RA_{True}) for the slope whose true dimensions were just calculated avove
RA_{True}= RL_{True} x RW_{True}
Example:
RA_{True}= 30 x 30.6
RA_{True}= 918 sq.ft. - I would roundup to 1000 sq.ft.
Add 10% for wastage, add additional if needed for ridge or hip cap shingles. (You will need additional material depending on the type of roof covering material being used. Allow for errors, wastage, damaged shingles, for the shingle starter course and for hip and ridge cap shingles. )
Calculate number of roofing squares of material: divide the roof area in square feet by 100 to obtain the needed number of roofing squares of roof covering material.
Example: 1000 sq.ft. + .10 (1000) = 1100 sq.ft.
1100 sq.ft. / 100 = 11 squares for this roof slope.
Add all of the roof slopes to obtain total roof area in square feet
How to Use Horizontal or "Flat" Roof Projections as Rough Estimates of Roof Area for Inaccessible Roofs
Another simplistic approach used by some estimators is to ignore complex roof structure, just measuring the building's footprint and the roof slope - an approach that gets you into the right "ballpark" but will very seriously under-estimage the roof area for steep slope roofs.
Frankly, as we illustrate beginning at ROOF MEASUREMENTS, there are some easy and accurate alternatives that can give a good estimate of roof area while making measurements only from the ground. But to understand how some people use a flat or horizontal projection of a roof to guess at roof area, here is the procedure.
BF: Measure the building footprint or BF
EO: Measure or estimate the increase in footprint size given by the roof eaves overhang. (Tip: look at the drip line under the roof eaves and measure the distance from the outer edge of the drip line to the building exterior wall. This is EF.
GO: Measure or estimage the increase in footprint size given by the gable end overhangs. This is GO.
RF: If the eaves overhang and gable end overhang are the same on both front and back and left and right building ends we just add these up to obtain Roof Footprint or RF.
RF = BF + (2 x EO) + (2 x GO)
RA: Obtain the approximate roof slope to convert Roof Footprint to Roof Area - RA using the ROOF SLOPE MULTIPLIER TABLE given below.
You can calculate the roof slope if you know just a few measurements. Details are at ROOF SLOPE CALCULATIONS
You can estimate the roof slope from the ground by any of several methods described at ROOF MEASUREMENTS
How to convert the building footprint or roof "footprint" (building footprint + roof overhangs) to roof area
To convert the rectangular footprint of the building roof to roof area we need to increase the footprint area to account for the greater area covered by the sloping roof. Using any of the roof slope estimating or measuring methods described above, just this simple roof slope multipication chart:
Roof Slope Multipliers: convert a "flat" or "projected horizontal" building footprint
to sloped roof coverage area
[Watch out: calculations have not been verified]
Roof Slope
or
Rise
or
Roof Length
Multiplier to convert a flat horizontal
footprint to roof area
Triangle side (a)
Hypotenuse or
Roof Length
Triangle side (b)
Vertical dimension
Triangle side (c)
Hypotenuse or
Roof Width
SQRT
(a^{2} = b^{2} + c^{2})
Convert (c) to Inch Scale
(convert fraction to 16ths of an inch)
(c) x 2
(two roof slopes)
2 in 12
1.102
12
2
12.16
12 3/16"
24 3/8"
3 in 12
1.134
12
3
12.36
12 3/8"
24 3/4"
4 in 12
1.159
12
4
12.65
12 5/8"
25 1/4"
5 in 12
1.191
12
5
13
13 "
26"
6 in 12
1.230
12
6
13.4
13 3/8"
26 3/4"
7 in 12
1.274
12
7
13.9
13 7/8"
27 3/4"
8 in 12
1.322
12
8
14.4
14 3/8"
28 3/4"
9 in 12
1.375
12
9
15
15"
30"
10 in 12
1.432
12
10
15.6
15 5/8"
31 1/4"
11 in 12
1.493
12
11
16.3
16 5/16"
32 5/8"
12 in 12
1.554
12
12
16.9
16 7/8"
33 3/4"
Notes: for fractional slopes, when estimating roof area use the next higher slope multiplier.
Roof Pitch = rise / run = Roof Slope = Tangent Function. Tangent calculations are illustrated at ROOF SLOPE CALCULATIONS
Roof slope or pitch can also be expressed in degrees or angular degrees, as we illustrate at ROOF SLOPE DEFINITIONS
The numbers in the table above can be calculated as follows: (and as illustrated below)
For a 12-inch unit-length roof we calculate the hypotenuse dimension to obtain the roof true width for each roof slope. In the table above the roof slope or rise (e.g. 6 in 12) gives us the vertical dimension of a right triangle. The horizontal dimension is fixed at 12 inches.
More Reading
Green link shows where you are in this article series.
Books & Articles on Building & Environmental Inspection, Testing, Diagnosis, & Repair
[1] "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
U.S.A.
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
Michael Grambsch
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
E-mail: cec.us@us.ul.com
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:
http://www.nps.gov/history/hps/tps/briefs/brief04.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/metals2.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/metals.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/slate.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/slate.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/gutters.htm
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:
http://www.nps.gov/history/hps/tps/roofingexhibit/roofingtoday.htm
/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
Our recommended books about building & mechanical systems design, inspection, problem diagnosis, and repair, and about indoor environment and IAQ testing, diagnosis, and cleanup are at the InspectAPedia Bookstore. Also see our Book Reviews - InspectAPedia.
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.
Or choose the The Home Reference eBook for PCs, Macs, Kindle, iPad, iPhone, or Android Smart Phones. Special Offer: For a 5% discount on any number of copies of the Home Reference eBook purchased as a single order. Enter INSPECTAEHRB in the order payment page "Promo/Redemption" space.
Architectural elements: the technological revolution: Galvanized iron roof plates and corrugated sheets; cast iron facades, columns, door and window caps, ... (American historical catalog collection), Diana S Waite, available used out of Amazon.
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
Problems in Roofing Design, B. Harrison McCampbell, Butterworth Heineman, 1991 ISBN 0-7506-9162-X (available used)
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).
Solar heating, radiative cooling and thermal movement: Their effects on built-up roofing (United States. National Bureau of Standards. Technical note), William C Cullen, Superintendent of Documents, U.S. Govt. Print. Off (1963), ASIN: B0007FTV2Q
"Weather-Resistive Barriers [copy on file as /interiors/Weather_Resistant_Barriers_DOE.pdf ] - ", how to select and install housewrap and other types of weather resistive barriers, U.S. DOE