Roof Calculation How to calculate the slope of a roof?

if you're thinking about ramp up or reform and you don't know anything about construction?

Find out how to calculate the slope of a roof!

## Roof Calculation — How to calculate the slope of a roof?

Calculating the slope of a roof is one of the subjects that involve the course of professional practices or even calculations for the elaboration of architectural design at the faculty of architecture, or civil Engineering.

Before starting the design of a roof itself, a good designer you must first know how to correctly calculate the slope of a roof.

In this article we will initially discuss how to learn how to calculate the slope of a roof and in another we will learn how to calculate the consumption of tiles, that is, the number of tiles that will be used in the project from the roof.

Before we start calculating, we will enumerate some important basic definitions, as you must have prior knowledge:

### 1 — The type of tile:

Although initially some students think that the slope calculation is something very complex and difficult, the thing is quite simple.

We must first have prior knowledge of the type of tile to be applied in the project, regardless of the tile material (ceramic, concrete, polycarbonate and others).

This specificity is factor number 1 to start the slope calculation of a project of roof.

### 2 — The size of the tile:

The larger the tile, the smaller the slope, and vice versa.

Regardless of the size of the tile, the purpose of calculating the slope of a roof is to determine what the final height of the ridge will be.

### 3 — Unit of measurement:

You should always pay close attention to the units of measurement involved in the calculation, as the fact that the calculation involves different units, the designer may get confused and end up calculating form erroneous the final height of the ridge, compromising the execution of the project.

Adopt a single unit of measurement, or meter, or centimeter, for example.

### 4 — The slope of the tile:

Each type of tile has its own slope determined by its size.

Before starting the calculation, it is recommended that the designer check with the manufacturer for the recommended slope.

Roof slope is measured in percentage (%) and not in angle (º).

## Roof Calculation — How to calculate the slope of a roof?

Now for the calculations:

When we hear the roofer or designer to mention:

“The roof will have a slope of 10%”, what exactly does that mean?

It means that 10% is equivalent to 10/100, or even: 10 divided by 100.

Using the unit of measurement in centimeters (cm), we have:

10% = 10cm/100cm, that is, every 100cm (1 meter) horizontally, the roof advances 10cm vertically.

See the calculation in the figure below:

The same reasoning applies to all roofs with different tile slopes.

So let's go to the calculation of the slope of a roof, in practice.

#### Example:

Calculate the final height of the ridge of a 2 gable roof with the following dimensions:

- Overall width = 8.0 meters
- 30% Slope, (Slope reported by tile manufacturer)

#### How to calculate:

First, if the roof will be 8.0m wide with gables, the ridge will ALWAYS be in the middle of the roof, that is, at 4.0m.

So if the roof has a slope of 30% = 30/100 = 30cm high for every 1.0m of width, then for every 4.0m of width we have 120cm or 1.20m in height as shown in the following figure.

You can use a simple direct account using the Pythagorean formula.

If I know the distance from the roof, in the case of 4 meters, and the slope of the roof, in the case of 30%, where H is the height of the ridge, we will have:

H= 4 mx 30 % = 1.20 m

Ready!

Now you know how to calculate the slope of a roof correctly!

Oh! and if you want to know more about the subject, **click here on this link** to add more information about tile calculation.

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Anonymoussays:I have the following question: why can't we convert the percentage of fall into degrees?

A drop of 100% represents a 90º angle.

So a drop of 10% would represent 9th.

Thus, the tangent of 9º would have to be equal to the height of the roof by its length, in the example above it would be (30/100) = 0.3.

But the 9th tangent is 0.158384...

Why?

Eng. Fernando Siedschlagsays:Friend, you are making a huge mess with percentage and trigonometry. It's like comparing bananas to tractors. In the case of a roof with a slope of 30%, the angle formed between the hypotenuse (scissor gable) with the adjacent side (scissor brace) would be approximately 16.7°.

Karensays:I am a Mathematics teacher and I teach Differential and Integral Calculus in the Architecture and Urbanism course. From what I understand about roof slope calculation (which I didn't know), the percentage is the relationship between the height of the roof and its base. The angle of inclination is that between the tip of the roof and its base; it is not worth 90 degrees. 90 degrees is the angle between the height and the base. The example you gave of 100% slope means that the height and base have the same measurement (for example, 100m), in which case the angle is 45 degrees. And the tangent of 45 degrees is equal to 1 (result of the ratio between the base and the height). Hope this helps!

Italiansays:Your explanation is very good :)

Luciana Paixãosays:Thank Yoouu! ;)

João Paulo M. Arumaasays:Mr. Anonymous, actually 100% of inclination does not imply 90º, but that for every 100cm of projection length there will be a vertical of 100cm of height, that is, 45º. Ten degrees of incline corresponds to 18% of incline. Hugs!

Renato Costasays:To calculate the angle, you must calculate the arctangent (height/length), that is, the inverse tangent. For example:

For slope 10% ==> arctan(10/100) = arctan(0,1) = 5.71°

For inclination of 30% ==> arctan(30/100) = 16.67°

Do not use rule of three, as it applies to linear relationships.

Brunosays:It is very important to remember that it is not said to a bricklayer that the roof will be at 16.67º, as he cannot measure the angle when making the woodwork. He has as a tool the "meter", or the "measuring", so say: 1.20 m high at the ridge!!! (avoid being cursed in thought by your mason…)

Gilsonsays:True, it is much easier to calculate with percentage than with degrees.

Divyansays:Good, Bruno!

Carlossays:For 30% —> H = root of (30)² + (100)² = 104,403

sin-1 (30 / 104,406) = 16° 70′ approx.

For 10% —> H = root of (10)² + (100)² = 100.5 approx.

sin-1 910 / 100.5) = 5° 71′

Note: if the sketch above is at the smallest scale and we put a degree protractor on the computer screen, we will find the angulation of the calculation above in the sketch. (I've already done this to relieve my conscience).

Carlossays:MISTAKE:

The correct character is (, not 9 as I did in calculating sin-1 for 10%. Sorry.

Marchsays:if we're talking about a roof, the slope or fall of the roof, whether in degrees or percentage, is an inclined plane from the ridge to the eaves, otherwise it would be a wall, wouldn't it?

so the slope you mention of 100% Mr. Anonymous, equivalent to a 45 degree angle!!!

Ricardo Chaarsays:Good afternoon. The explanation on roof slope calculation was very useful, but exploring a little of your knowledge, I would like you to provide me with the explanation and calculation memory to find the measure of the upper chord of a roof.

Thanks.

wagnersays:Good morning, I am a builder, and I live in the north of Mato Grosso, all the coverage I do, following the example above, with 4.0 meters being the environment to be covered and the slope of the roof of 30%, I do the following calculation: 3(30% )x4(4.0m)=12 ie 120cm(1.20m) the highest point. In the case of a larger environment ex. 10.0 meters with 20% of inclination, it would be 10×20=200cm, that is, 2.00m. Is this way I learned to work correct, because it's very simple, or do I have to learn all this math left in the previous comments? Thanks.

Luciana Paixãosays:Did you compare the two forms of calculation and see the result they give? Check and then tell me.

Gabrielsays:I have the following doubt in a house with a slab eaves, should I measure the eaves to calculate? like the house is 8 meters wide with 50 cm eaves on the 4 sides the coverage is 4 waters so would it be correct to calculate 30/4.50 or 30/400?

Luciana Paixãosays:Hi Gabriel, the eaves do count when calculating the roof slope.

nelson buildersays:gabriel, it depends on how the eaves will be, if the eaves will be the same level as the wall or if they will continue with the same roof trim

Atalibasays:Wow, this is really simple, which arouses skeptics' questioning, the calculation is a percentage, today I'm a building technician, but before that I'm a Carpintriro and environment designer by vocation, even with the more exact approximation that the friend gave 16 and fraction, the right is how the moderator explained excellent explanation.