Calculation of the angle of inclination of the roof. The optimal angle of inclination of the gable roof. The choice of roofing depending on the slope of the roof

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Building any roof is not as easy as it seems. And if you want it to be reliable, durable and not afraid of various loads, then beforehand, even at the design stage, you need to make a lot of calculations. And they will include not only the amount of materials used for installation, but also the determination of the angles of inclination, area of the slopes, etc. How to calculate the angle of inclination of the roof correctly? It is on this value that the rest of the parameters of this structure will largely depend.

The design and construction of any roof is always a very important and responsible business. Especially when it comes to the roof of a residential building or a roof complex in shape. But even an ordinary single-slope one, installed on a nondescript shed or garage, in the same way needs preliminary calculations.

If you do not determine in advance the angle of inclination of the roof, do not find out what optimal height the ridge should have, then there is a great risk of building such a roof that will collapse after the first snowfall, or the entire finishing coating will be torn off from it even by a moderately strong wind.

Also, the angle of inclination of the roof will significantly affect the height of the ridge, the area and dimensions of the slopes. Depending on this, it will be possible to more accurately calculate the amount of materials required to create the rafter system and finish.

Prices for various types of roofing skates

Roofing ridge

Units

Remembering the geometry that everyone studied in school, it is safe to say that the angle of inclination of the roof is measured in degrees. However, in books on construction, as well as in various drawings, you can find another option - the angle is indicated as a percentage (here we mean the aspect ratio).

Generally, the slope of the slope is the angle that is formed by two intersecting planes- overlapping and directly with a roof slope. It can only be sharp, that is, lie in the range of 0-90 degrees.

On a note! Very steep slopes, the angle of inclination of which is more than 50 degrees, are extremely rare in their pure form. Usually they are used only for decorative design of roofs, they can be present in attics.

As for measuring the angles of the roof in degrees, everything is simple - everyone who has studied geometry at school has this knowledge. It is enough to sketch a roofing diagram on paper and use a protractor to determine the angle.

As for the percentage, then you need to know the height of the ridge and the width of the building. The first indicator is divided by the second, and the resulting value is multiplied by 100%. Thus, the percentage can be calculated.

On a note! At a percentage of 1, the usual tilt is 2.22%. That is, a slope with an angle of 45 normal degrees is 100%. And 1 percent is 27 arc minutes.

Values table - degrees, minutes, percent

What factors affect the angle of inclination?

The angle of inclination of any roof is influenced by a very large number of factors, ranging from the wishes of the future owner of the house and ending with the region where the house will be located. When calculating, it is important to take into account all the subtleties, even those that at first glance seem insignificant. At one point, they may play their part. Determine the appropriate angle of inclination of the roof, knowing:

the types of materials from which the roofing pie will be built, starting from the rafter system and ending with external decoration;
climate conditions in a given area (wind load, prevailing wind direction, amount of precipitation, etc.);
the shape of the future structure, its height, design;
the purpose of the structure, options for using the attic space.

In regions where there is a strong wind load, it is recommended to build a roof with one slope and a small angle of inclination. Then, in a strong wind, the roof has a better chance of resisting and not being torn off. If the region is characterized by a large amount of precipitation (snow or rain), then it is better to make the slope steeper - this will allow the precipitation to roll / drain from the roof and not create additional load. The optimal slope of a pitched roof in windy regions varies between 9-20 degrees, and where there is a lot of precipitation - up to 60 degrees. An angle of 45 degrees will make it possible not to take into account the snow load in general, but the wind pressure in this case on the roof will be 5 times more than on the roof with an inclination of only 11 degrees.

On a note! The more the parameters of the slope of the roof, the more materials will be required to create it. The cost increases by at least 20%.

Slope corners and roofing materials

Not only climatic conditions will have a significant impact on the shape and angle of the slopes. An important role is played by the materials used for construction, in particular - roofing.

Table. Optimum slope angles for roofs made of various materials.

On a note! The lower the slope of the roof, the smaller the step is used when creating the lathing.

Prices for metal tiles

Metal tile

The height of the ridge also depends on the angle of the slope.

When calculating any roof, a right-angled triangle is always taken as a reference point, where the legs are the height of the slope at the upper point, that is, in the ridge or the transition of the lower part of the entire rafter system to the upper one (in the case of attic roofs), as well as the projection of the length of a particular slope onto the horizontal, which is represented by the slabs. There is only one constant value here - this is the length of the roof between two walls, that is, the length of the span. The height of the ridge section will vary depending on the angle of inclination.

Knowledge of formulas from trigonometry will help to design the roof: tgA = H / L, sinA = H / S, H = LхtgA, S = H / sinA, where A is the slope angle, H is the height of the roof to the ridge area, L - ½ of the entire length span of the roof (with a gable roof) or the entire length (in the case of a pitched roof), S is the length of the slope itself. For example, if the exact value of the height of the ridge part is known, then the angle of inclination is determined using the first formula. You can find the angle using the table of tangents. If the calculation is based on the roof angle, then you can find the ridge height parameter using the third formula. The length of the rafters, having the value of the angle of inclination and the parameters of the legs, can be calculated using the fourth formula.

The content of the article

The roofs of private houses, as a rule, always have slopes - this roof structure is the easiest to operate and maintain. Water and snow leave these roofs better and faster, which guarantees excellent waterproofing. And the appearance of a private house is becoming more attractive.

In addition, an additional room appears in the attic, which can be used for living and arranging the attic or for numerous household needs.

Factors affecting the shape of the roof

To make the roof reliable and comfortable, it is necessary to correctly calculate the angle of the roof slope, which depends on many reasons. First of all, these are the climatic conditions of residence and the characteristics of the roofing material. Natural conditions affecting the size of the roof slope:

with an increase in the slope of the roof, the wind load on the roof structure increases. For example, if the angle of inclination is increased from 10 degrees to 45 degrees, then the load on the structure due to the wind will increase fivefold. If the angle is made small, less than 10 degrees, then there is a high probability that the coating sheets will break off due to the strong wind that falls under the joints;
precipitation in the form of rain and snow also affects the slope of the roof. With an increase in the slope, precipitation is better off the roof slopes. The greatest snow load in winter occurs on slopes with a roof slope of about 30 degrees. At an angle of 45 degrees, the snow will completely melt.

With a small slope of the roof slopes, as a result of strong gusts of wind, water can get under the joints of the coating.

In the question of what angle of the roof slope must be made, the type of roofing matters:

When using metal tiles as a roofing material, you need to take into account the considerable weight of this coating. Therefore, the angle of inclination of the roof should not be very large. This is especially important in areas where constant and strong winds prevail, as the mechanical load on the roof structure increases. For this surface, the minimum slope angle is approximately 22 degrees.... In this case, moisture will not accumulate, but will be effectively removed from the roof. In addition, the joints of the coating will be reliably protected.
Decking is currently the most popular roof covering for private houses. It is lightweight, easy to install and maintain. The minimum roof slope angle using this material is 12 degrees.
When using roll materials, they are also called soft roofing, the angle of inclination of the slopes depends on the number of coating layers. For a coating that consists of two layers, the minimum angle of inclination is up to 15 degrees. For three layers, this value should be between two and five degrees. If the roof is to be covered with a membrane, the slope must also be between two and five degrees.

From the above, we can conclude that the decision on the optimal angle of the roof slope depends on natural conditions, the type of roofing material and the capabilities of the owner of the house.

With a large slope, the consumption of materials for the construction of the roof increases.

In addition, the type and pitch of the lathing depends on the size of the slope of the roof slopes. The smaller the slope of the roof, the smaller the sheathing step should be... For minimum angles, it is approximately 35 to 45 centimeters.

with a roof slope of up to ten degrees, the roof covering can be done using chips of stone and gravel;
if the roof slope is more than ten degrees, then waterproofing using bituminous materials should be used. For roll materials, it is necessary to use an additional protective coating;
when using corrugated board and slate, it is recommended to seal joints and seams, the joints should be double.
If the amount of precipitation in the area where the residential building is located is large, then the angle of inclination is best done at 45 degrees. With a minimum amount of precipitation, the roof slope can be made at 30 degrees. With strong and frequent winds, the angle of inclination should be between 15 and 20 degrees. If the wind loads are small, then it is better to make a roof, the angle of inclination of which is from 35 to 40 degrees.

When calculating the angle of inclination of the roof, it is necessary to take into account that the higher the average annual temperature and less precipitation, the more shallow the roof can be built.

It should be borne in mind that the type and design of the drainage system of the whole house depends on the slope of the roof.

The choice of the angle of inclination of the roof, depending on various factors

When determining the slope of a roof, there is no perfect solution for all climatic requirements. Here it is important to find the best option, which determines the consumption of materials and the cost of funds.

The larger the roof area, the more expensive it is.

The recommended roof pitch is 20 to 45 degrees... When increasing it, it is necessary to take into account the creation of additional structures to strengthen the entire structure. And a decrease in the angle will lead to additional costs of materials to ensure normal waterproofing of the roof of the house.

Roof angle calculator used to calculate as roof slope, and missing data on the roof - projection, height, length and angle of inclination of the roof slope. Visually, where and what values can be seen on the calculator drawing, located under the calculation form.

To calculate the angle of inclination of the roof or data, it is enough to indicate only two known quantities, and the rest of the values (if any) can be used for verification.

Calculation of the angle of inclination of the roof

Known parameters Fill in the data that you know. To calculate the angle of inclination of the roof and the length of the slope, it is enough to indicate 2 data out of 4... Units of measurement: Metric system Imperial system
Projection Length (W): Height (H): Roof slope length (L): Tilt angle (α): Degrees Radians Calculate the angle and length of the roof

Calculation result Projection length (W): Height (H): Roof slope length (L): Slope angle (α): degrees Slope angle (α): radian Roof slope:% Roof slope:: 12
Calculation link:

In the picture: a - slope angle, S - roof slope length, H - roof height in the upper part, L - roof slope projection length

Accordingly, all quantities can be found:

a = arctan (H / L) or a = arcsin (H / S)
H = L * tg a
S = H / sin a

Calculation of slope angles of roofs by type

Calculation of the angle of inclination of a shed roof

A pitched roof is one of the most popular and, at the same time, one of the easiest to calculate. In fact, our calculator will calculate exactly this, since more complex roofs (for example, the angle of inclination of a gable roof) require breaking the roof elements into separate slopes and calculating each of them.

When calculating the slope of a pitched roof and calculating the length and angle of the roof slope, be sure to take overhangs into account! You can count them by asking the data not of the slope itself, but the height and projection of the roof together with the overhangs.

Materials and angles for pitched roofs

roofing material roof - 5-10 degrees
from corrugated board - from 8 to 20 degrees
from metal tiles - 20-30 degrees
slate - 20-35 degrees
for a seam roof, an inclination of 18-30 degrees is required

Calculation of the angle of inclination of a gable roof

Calculating a gable roof is already more difficult than calculating the angle of inclination of a gable roof. In the case of two slopes, it is necessary to calculate each of the slopes individually on our calculator, and to calculate the material it is better to use the roof calculator, because the location of the material and its dimensions can be walked around.

Calculation of the angle of inclination of the hip roof

In turn, the calculation of the hip roof is even more difficult than the calculation of the angle of the gable roof. You need to not only split and calculate the angle of each slope separately, but also take into account that the angles for the hip roof are different.

For a hip roof, it is also especially necessary to take into account the walking dimensions of the sheathing, therefore, when calculating your real roof, the angles of the hip roof will be slightly different!

Roof types depending on the angle of the roof slope

There are 4 main types of roofs, depending on the angle of inclination:

3-10 ° - flat
10-30 ° - gentle
30-45 ° - pitched
45-60 ° - high

In order for the roof of the building to fully perform all the functions assigned to it, it is necessary to take into account a number of parameters when creating it. One of the most important parameters of the roof is its slope, which ensures the removal of precipitation from its surface and affects the ability to withstand external loads. How to calculate the slope of the roof, and will be discussed in this article.

Determining the slope of the roof - what depends on

To carry out the correct calculation of the roof slope, several factors must be taken into account, among which the following stand out the most:

Wind loads... The slope of the slopes is very strongly influenced by the wind. In order for the roof to normally resist its effects, you need to choose the right angle. At too large angles, the load on them will be high, but an excessive decrease in the angle can also be dangerous - a flat roof can simply be disrupted by a strong gust of wind.
Snow and rain loads... With snow, everything is quite simple - increasing the angle of inclination makes it easier for it to come off the roof surface. When the roof is tilted more than 45 degrees, snow will hardly linger on it. At a low angle of inclination of the roof, a snow bag may appear, which increases the load on the roof. The situation is the same with rainfall - if the angle of inclination of the roof is too low, then water can flow into the joints or even stagnate on the roof surface.

Based on these factors, you can calculate the angle of inclination of the slopes. In addition, before calculating the angle of a gable roof, you should pay attention to the recommended indicators: for areas with strong winds, a slope of 15-20 degrees is suitable, and in other cases the optimal slope value is 35-40 degrees. Of course, you need to understand that the calculation of a gable roof is individual, and it is simply undesirable to choose average indicators.

Calculation methodology

When designing a roof, it is imperative to carry out a number of calculations, among which there must always be a calculation of the angle of inclination of the slopes. This parameter directly affects the roof structure: with an increase in the slope, the snow load decreases, but the effect of the wind increases, so the rafter system has to be additionally strengthened. For equipping slopes at a high angle, even more materials are required, which negatively affects the cost of construction.

Before you know the degree of inclination of the roof, you need to calculate the operating load on the roof, which requires two parameters:

The total weight of the roof structure;
Peak levels of snowfall in the region where construction is taking place.

The simplified calculation algorithm is reduced to the following actions:

First, you need to determine the weight of one square meter of the roofing cake;
The resulting value is multiplied by the total roof area;
The roof weight is multiplied by a factor of 1.1.

An example of calculating the slope of the roof in degrees

To understand how to calculate the roof angle, it is worth considering the calculation process with a specific example. For example, the following data will be taken: the lathing has a thickness of 2.5 cm, one square meter of the roof weighs 15 kg, insulation material 10 cm thick is used as a heat-insulating material, a square meter of which has a weight of 10 kg, and ondulin with a weight of 3 kg is used for covering per square meter.

The calculation of the roof slope is carried out in accordance with the method described above. Substitution of the available data leads to the following expression: (15 + 10 + 3) x1.1 = 30.8 kg / sq. M. The resulting value is quite acceptable - the average load on the roof of residential buildings is slightly less than 50 kg / sq. M. In addition, the formula contains a factor of 1.1, which slightly increases the actual weight of the roofing structure and allows you to subsequently replace the roofing with a heavier one.

How to find out the angle of inclination of the roof

There is a direct relationship between the slope of the roof slopes and the snow load. If the angle of inclination of the roof is less than 25 degrees, then the coefficient of snow load is 1, and at angles varying from 25 to 60 degrees, then this coefficient increases to 1.25. A roof with a large slope will not be subject to snow loads at all, so they are not taken into account in the calculations.

To determine the angle of inclination of the roof, you need to use the Bradis table and a simple technique: the height of the roof structure is divided by the length of the pediment, divided by two, after which it remains to find the table the angle that corresponds to the result obtained.

The height of the roof in the ridge is determined as follows:

The first step is to calculate the span width;
The resulting value is divided by 2;
To calculate the height of the skate, the result of the previous calculation is multiplied by a factor corresponding to a certain angle of inclination.

Using an example, the implementation of such a calculation method looks like this: with a building width of 8 meters and a 25-degree roof slope, the design coefficient is 0.47. As a result of substitution of values, an expression of the following form is obtained: 4x0.47 = 1.88 m. The resulting value is the height of the roof, corresponding to the available initial data.

The choice of roofing depending on the slope of the roof

There are a large assortment of roof materials on the market, so there will be no special problems with the choice of a suitable option. Roof coverings differ in characteristics and application possibilities, and all their parameters must be studied before measuring the roof angle - only in this case it will be possible to create a reliable and effective structure.

When choosing a material for a roof, it is worth starting from the following recommendations:

If the angle of inclination of the rafters is between 2.5 and 10 degrees, then stone chips or gravel coverings are best suited. In the first case, the top layer of the coating has a thickness of 3-5 mm, and in the second - 10-15 mm.
With an inclination of more than 10 degrees, coarse-grained or roll materials, supplemented with bituminous waterproofing, will be the best option.
For the arrangement of pitched roofs with an angle of inclination of no more than 20 degrees, corrugated board or sheet asbestos cement is usually used. All seams and joints between roofing materials must be sealed with a sealant.
If the angle of inclination of the roof is in the range of 20-60 degrees, then it is most often covered with metal sheets. In this case, the joints of materials must be sealed without fail.

Conclusion

Knowing how to find out the angle of inclination of the roof in degrees will greatly simplify the design process and allow you to create the most reliable structure that can well protect the building box from precipitation, wind and cold.