Roof slope definitions and illustrations (C) Carson Dunlop Associates Roof Measurements, Slope, Rise, Run, Area
How are roof rise, run, area or slope measured or estimated? Roof slope specifications by roofing type. How to use a framing square for rafter cuts.

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Roof 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.

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How to Measure Roof Slope or Angle or Rise & Run & Roof Area

Roof rise or pitch or slope measurement on the roof surface (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.

[Click to enlarge any image]

Here are examples of every method we can think of for measuring the pitch or slope of a roof from various positions on the roof, near the roof, and from ground level.

Article Series Contents

There are several neat tricks that allow you to just a carpenter's rule to get a close approximation of the roof slope or pitch. We describe all of them here. All of these examples work best for a simple gable end roof. Additional measures may be needed for hip roofs, mansards, and intersecting gables.

How to Measure Roof Slope from On the Roof

To use the direct roof slope measurement procedure shown just abofe, in addition to safe access to a roof that won't be damaged by touching or walking on it, you need: a tape measure and a carpenter's level. This procedure to measure roof slope can be performed on the roof or from a ladder at roof edge. [Click to enlarge the image].

How to Measure Roof Slope from Inside the Attic or Inside of a Cathedral Ceiling Structure

You need: a tape measure and a carpenter's level. The procedure is like the on-roof example above, but flipped upside down.

Measuring roof slope from inside the attic (C) Daniel Friedman

As with measuring roof slope on the roof, inside the attic allw e need is a simple carpenter's level and a tape measure. We use the level to measure out from the roof surface horizontally for a distance of 12".

Measuring roof slope from inside the building (C) Daniel Friedman

Then from that point on our level we measure the distance straight up to point of contact with the roof surface.

That distance in inches will be the inches of rise per foot of horizontal run for this (horrible leaky) roof.

Watch out: if you do not keep the level at right angles to the roof (parallel to the gable end wall of the building) your vertical measurement will be inaccurate. Hold your level with its side tightly against the side of a rafter to keep the level at right angles to the roof surface.

Or you can make this measurement inside the attic or even inside the building if a cathedral ceiling is installed (photo at left) by holding the level right against the gable end wall as we show at left.

For an outdoor version of this same approach see our example of MEASURING ROOF SLOPE OUTSIDE at the gable end of a building.

How to Measure Roof Slope Outdoors at the Gable End of a Building

You need: a tape measure and, if there is no horizontal siding installed, you will need a carpenter's level. [Click to enlarge the image]

How to measure roof slope at the building gable end (C) Daniel Friedman

From a ladder or other accessible area giving safe access to the sloping gable end trim or roof edges,

1. Measure out horizontally 12" (one foot) from the gable end sloping trim to a point along horizontal siding, or use your level to make a mark that is level, horizontally measured out 12" from the sloped gable trim or roof edge.

2. From the point you just marked, measure vertically straight up to the edge of the same sloping gable end trim or roof edge. This distance (green arrow in our photo) is the roof rise in inches per foot of run.

How to Measure Roof Slope & All Other Dimensions From the Ground - counting siding courses

All of the roof data: rise, run, and slope can be calculated from the ground if the building sports horizontal siding such as that shown in our photograph below.

Measuring the width of a siding course (C) Daniel Friedman

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.

Measuring the width of a siding course (C) Daniel Friedman

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)

Measure Roof Slope From the Ground Using a Folding Carpenter's Rule

Using a folding carpenters ruler to measure roof slope from the ground (C) Daniel Friedman

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.

Details of how to use a folding carpenter's rule to obtain roof slope, area, and other measurements along with a table that translates inches along the bottom scale of the folded rule into roof slopes are

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

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

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.

[Click to see an enlarged image]

Details of how we use the tables on a framing square to quickly figure out roof slope, rafter lengths, cuts etc. are

How to Obtain the Roof or Ceiling Slope, Rise & Run Using an Angle-Finder Level & the Tangent Function

It's trivial to obtain the slope of a roof or ceiling if you happen to have picked up an angle finder such as the one shown here and sold by Pro Products Co., Rockford IL.

We can simply place either of the Level + Angle Finder straight sides against a sloping surface and read the surface slope expressed in degrees right off of the tool's scale.

Angle finder level used indoors on a cathedral ceiling (C) Daniel Friedman

A weight inside the Angle Finder level moves the pointer to the proper position.

For more accurate angle or slope measurements, for example on a rough shingle surface outdoors, use a straight edge between the angle finder level and the roof surface to give a longer footprint for the sensor. If your framing square is steel (not aluminum), the angle finder level will clamp neatly right onto the framing square.

Angle finder level used indoors on a cathedral ceiling (C) Daniel Friedman

That's how I used the angle finder shown until someone ran over my steel framing square, forcing me to buy a new (aluminum model). The angle finder level still works but I have to hold it in place (leaving too scratches on my ceiling as I fumbled around for these photos).

You can see that the angle finder immediately gives the answer to the roof slope: 81 degrees. [Click to enlarge any image]

Now what? 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

Find Tan 9 deg using a handy dandy calclator, or table such as the one I give

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

How Various Roof Measurements are Calculated

Right triangle side lengths relationship  - InspectApedia

Details for calculating roof area are at ROOF AREA CALCULATIONS

RA = Roof Area = RW x RL 

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.

Calculating the slope of a frog's head (C) Daniel Friedman

Details for calculating the slope, pitch or grade of a roof or any other surface are

Or if you want to know more about the frog at left,

Slope is simply the relationship between increase in height and horizontal distance traveled. In my sketch above if we travel up my triangle along (a) from left to right, we will cross a horizontal distance (b) and we will ascend in height an amount (c).

Slope or pitch or grade has several means of expression: Rise/Run, Angle in degrees, Tangent, Pitch, or Percent Grade - all compared in our little table below.

Tangent = Rise / Run

E.g. Tan (45 deg) = 1.00 - that is, we will travel 12" up for 12" of run

Tan -1 is the inverse of a Tangent which will convert any rise/run ratio back to degrees.

E.g. Tan -1 (1.73) = 60 deg.
Put another way, a roof with a slope of about 27 in 12 has a Rise/Run of 27/12 = 1.73 (approximately)

So Tangent in its simple use here is just the ratio of increase in unit height for travel in unit run. "Units" can be inches, feet, meters, furlongs, or hammer handle lengths. A table of tangent values for common roof slopes is given at FOLDING RULER to SLOPE DATA TABLE. Below is a tiny summary that shows the range of these values.

Typical Range of Roof Slope Values

Horizontal Scale 90 deg Reading in Inches1
Shed Roof
Horizontal Scale Left Slope Reading in Inches1 2
Gable Roof
Range of Roof Slope
Rise / Run
Range of Roof Pitch in Degrees
Roof Pitch
Rise / Run
Shed roof shape (C) InspectApedia Gable Roof Shape (C) InspectApedia 24 in 12
(very steep)
3 in 12
(almost flat)
63.3 deg
14 deg
2 .00

A complete table of these values is given

A complete table of roof slopes expressed as rise / run, slope, and grade as well as roof walk-ability according to steepness is given

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

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

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
(a2 = b2 + c2)

Convert (c) to Inch Scale

(convert fraction to 16ths of an inch)

(c) x 2
(two roof slopes)
2 in 12  
12 3/16" 24 3/8"  
3 in 12  
12 3/8" 24 3/4"  
4 in 12  
12 5/8" 25 1/4"  
5 in 12  
13 " 26"  
6 in 12  
13 3/8" 26 3/4"  
7 in 12  
13 7/8" 27 3/4"  
8 in 12  
14 3/8" 28 3/4"  
9 in 12  
15" 30"  
10 in 12  
15 5/8" 31 1/4"  
11 in 12  
16 5/16" 32 5/8"  
12 in 12  
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.

A complete table of roof slopes expressed as rise / run, slope, and grade is given at ROOF SLOPE TABLE, TYPES, WALKABILITY

Building & Roof Measurement Articles


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