# Roof Area CalculationsMethods for calculating the area of a roof depending on what measurements you already know       (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/platform.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

• 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.

## How to Calculate Roof Area

The attractive New Zealand slate roof shown here protects the beloved Catholic Church of St Werenfried in Waihi Village, at the edge of southern Lake Tekapo, in New Zealand (South Island).

Making one or two simple straightline measurements from the ground along with clever use of a folding rule or other methods discussed in this article series can give us accurate measurements of the church roof dimensions, slope, and area.

[Click to enlarge any image]

### Definition of Roof Dimensions

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:

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).

Given a2 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

### How to 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

Find Tan 9 deg using a handy dandy calclator, or table such as the one I give
at ROOF MEASURE by FOLDING RULE.

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 = RLTrue
• 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 a2 = b2 + c2 or hypotenuse
• RWTrue2 = Rise2 + RLTrue2
• Example: RWTrue2 = (6ft. rise)2 + (30 ft roof length)2
• RWTrue2 = 36 + 900
• RWTrue2 = 936
• SQRt of RWTrue2 = 30.6 ft.
• RWTrue= 30.6 ft.

• Calculate the Roof Area (RATrue) for the slope whose true dimensions were just calculated avove
• RATrue= RLTrue x RWTrue

• Example:
• RATrue= 30 x 30.6
• RATrue= 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.

RA = RF x Roof Slope Multiplier

#### All of the Ways to Get the Roof Slope

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
(a2 = b2 + c2)

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.

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