How to calculate the slope of a roof in degrees. Roof pitch angle for various conditions and roofing materials
Professional builders know that the process of building a roof can sometimes be slowed down due to the fact that it is necessary to choose " the right material» and make an accurate calculation of the roof slope angle. These two issues are closely interrelated, because the choice of material for covering it depends on the angle of inclination of the roof.
We remind you that roofs can be single-, double- and four-sloped; it depends on how many slopes you choose for your roof, and the amount of slope of the slope angle will be determined.
What factors influence the calculation of roof slope
For example, the angle of inclination standard roof with one slope ranges from 9 to 60 degrees - it depends on the following factors:
- The material chosen for the roof;
- Climatic and atmospheric conditions;
- Purpose of the building.
If the roof has two or more slopes, then not only the region in which the building is located matters, but also why the attic is needed. For example, if you use the attic not as a living space, but as storage for old things, then there is no need to build it wide and high. But if you want the attic to become a full-fledged residential attic room, then you need to make a dense roof and know how to calculate the angle of the roof. In this case, the calculation of the roof slope angle depends on the following factors:
- The first is the design of the building and premises itself.
- The second is the choice of materials for the roof.
- The third is the climate conditions of the region.
We choose the material for the roof depending on its slope
In regions with strong winds, it is better to build a roof with a minimum slope - the material should not be subject to strong wind loads. The same is said about sunny areas, where there are the most hot days of the year - sunny regions have the least precipitation.
In those regions where there is a lot of precipitation (including rain, hail and snowfall), the roof slope should be large, up to 60 degrees, because only such a slope will reduce the load from snow, melt water And various kinds garbage.
So, let's figure out how to calculate the angle of the roof. We need to take into account all the factors that were described above, so the calculation of the roof slope is carried out in the range from 9 to 60 degrees. Interestingly, such a calculation usually leads to one optimal solution- 20 - 35 degrees.
With such a slope, any roofing material is used - profiled flooring, metal tiles, pieces of slate, etc.
All materials have a certain list of requirements that are presented to them during the construction of the structure.
If the roof is covered with metal tiles
It is known that metal tiles have considerable weight compared to other materials. This is why it is important to correctly calculate the slope of a roof with metal tiles, which should be optimally low.
Important to consider this requirement in a region with a lot of winds and hurricanes. Therefore, the inclination angle should be as low as possible. Because of of great importance angle of inclination, the roof may swell, which, in turn, will increase the pressure on load-bearing structure roofs. And increased pressure will prematurely destroy the roof.
On average, for roofs that will be covered with this material, the average optimal slope angle is 27 degrees. Consequently, your home will be protected from rainwater and snow infiltration.
The minimum angle of inclination of the roof is only 14 degrees. If soft tiles are used, then the angle of inclination can be 11 degrees, but the roof must be additionally slatted.
Corrugated roof
Corrugated sheeting is the most popular material for roofing - it is light in weight, durable, fastened and mounted quite easily.
Roof slope with corrugated sheets and loads.
If the roof is covered with various soft materials
Such materials include roofing felt, ondulin, polymer (membrane) roofing.
This one has roofing structure you need to make an angle of inclination from 6 to 15 degrees - the value varies depending on the number of layers of soft material.
For example, if the coating is two-layer, then the angle of inclination is taken to be equal to 15 degrees, but if it is three-layer, then the value can be reduced to 3-5 degrees.
But the membrane coating can be used on any roof, of any condition, in any conditions, here the angle of inclination can be reduced to 2-5 degrees.
From all of the above, we conclude that how to calculate the slope of the roof is decided by the owner of the building himself. However, we take into account a certain dependence: the roof must withstand not only temporary, but also permanent loads. “Temporary” includes rain, wind and the weight they exert on the roof covering; permanent load is the weight of the roof covering and material.
Slope for roofing made of soft materials
The amount of roof slope determines the type of sheathing and pitch. For a roof with a low slope, the sheathing pitch should be as short as possible. For a roof with a minimum value, the sheathing pitch is 35-45 cm.
Also, everyone is interested in one question - how much roofing material should be purchased.
The greater the angle of inclination of the roof you make, the more material you will need to use.
The greater the angle of inclination of the roof you make, the more material you will need to use.
If you adhere to all these requirements, you can make a roof that will last for decades! All the above requirements and factors help you understand how to calculate the roof slope. However, we remind you that the calculation is made individually for each house.
Finally, we'll give you a few useful tips that will help you choose roofing material:
So, if your roof slope is small, up to 10 degrees, then you can even cover the roof with stone chips or gravel (we calculate 5 mm for the roof and 15 mm for gravel).
If the angle of inclination of your roof is 10 degrees or more, then we use the basic bitumen waterproofing. When using rolled material, do not forget about the additional protective coating, which can be ordinary painting.
If you are planning to cover the roof with corrugated sheeting, you need to seal the butt seams. The joints must be double.
How to calculate the angle of a roof?
As a rule, to know how to calculate the slope of a roof, you need to know how high you will raise the ridge (and the height of the roof with the ridge depends directly on what the attic is intended for). So, if you are making a residential attic out of an attic, then we consider the following calculations valid.
We determine the width of the pediment - the roof end, for example, let it be 6 m. We divide the width in half: 6:2 = 3 m, and according to the standard, the height of the roof at the ridge is 1.8 meters.
tg A=a:b=3:1.8=1.67
We take the Bradis table and find an approximate value - if tg A = 1.67, then the angle of inclination will be approximately 58-59 degrees. We can take the maximum angle value as 60 degrees. This will be our desired roof slope angle.
The slope of any roof is given in accordance with the climatic conditions and the structure of the building. The abundance of precipitation makes the roof slope steeper and vice versa. In general, you need to remember that before calculating the angle of the roof, keep in mind that the slope of the roof can range from 10 to 60°. The steeper the roof, the more material you will spend.
The slope of the rafters or the height of the ridge is determined mathematically or by measurements.
It is known that roofs with a slope of 35-45 degrees are not made, since such a range will create all the conditions for snow accumulation in winter, and such roofs do not withstand winds well. It is impossible to make a monolithic roof, so the material is laid with joints. The joint is a place with an increased risk of corrosion, so they are given special attention Special attention during calculations. Also, during a hurricane, leaves and branches can get stuck in the cracks, which then swell and the roof deteriorates. Openings are created for rain and snow to penetrate, and the roof collapses.
When calculating the slope of the roof, remember not only about savings (cost of rafters, material, work), but also about performance. If the roof is installed according to all the rules, it will cost more, but your home will be warm and dry, which ultimately helps save significant amounts of money on repairs. This is where the correctly selected roof angle plays a role!
The roof is part of any home. It is very important for her to choose high-quality roofing material. Experts are of the opinion that when choosing it, one should take into account the angle of inclination of the roof, which serves to ensure that water does not linger on it. The slope of the roof is usually called the angle of its inclination to the horizon. It is usually expressed as a percentage or in degrees. Therefore, the higher its value, the steeper the roof will be. We will talk about methods for calculating this indicator further.
Depending on the angle of inclination, the following roof structures are distinguished:
It is worth saying that a flat roof is not completely horizontal. Otherwise, the water would not flow from it. Such a roof must have a slope of at least 30 degrees. Depending on the design features, there are three main types of roofs:
Arbitrary structures are those for which the load due to the influence of wind and precipitation is not calculated. Such roofs are usually erected only according to the wishes of the owner. They often house storage rooms or even living quarters. The average ones represent the best ratio of the roof slope angle, taking into account the influence of precipitation and wind. This type of roofing is best built in regions with high humidity. As for the low-slope roof, its design is made in such a way as to minimize the influence of wind force on it. In addition, this coating copes well with precipitation. Such roofs can be installed in almost any region. After all, they have minimum slope and fit almost every home design. A low-slope roof has several serious advantages, namely:
Although you may have to spend money on purchasing and installing additional funds protection from water, the undeniable advantages will pay for these costs. What does the slope of the roof depend on?
The angle of inclination is usually determined depending on the roof structure, the roofing material used, as well as the climate of the region where the house will be built. In order to know how roofing material is selected depending on the angle of inclination of the roof, you need to find out what affects this indicator. These factors include:
UnitsToday, roof slope is mostly measured in degrees or percentages. Correct angle can be selected with both systems. To find out the required value, you can take as a basis the results of measuring the roof itself, as well as a reduced model depicted on paper. The required degree must be laid down when installing the structure. Let's look at how to calculate the roof slope as a percentage. You need to take the height of the ridge, divide the resulting value by half the width of the house, then multiply everything by 100%. As a percentage, 100% corresponds to 45 degrees, and 1 degree equals 1.7%. If strong winds are possible in the region where the house is being built, then when making calculations it is recommended to keep the roof angle to a minimum. To measure and indicate the slope of the roof, there is a special tool called an inclinometer. How to calculate roof slopeUsing a schema
To make it easier, you can use a special diagram that allows you to select the roofing material depending on the level of its slope. The minimum angle corresponding to 0% and the maximum - 100% are indicated here. Percentage values are plotted on a vertical scale. In the center of the diagram there is a semicircular scale, in which there are calculations in degrees. In general, the higher the slope value, the more layers of material will need to be laid on it. By the way, the amount of material needed can be determined by the slope of the roof. Let's look at how calculating the roof slope affects the choice of material. According to the above diagram, if the slope is from 0 to 25%, then it can be used to cover the roof roll materials. With a slope of 0-10%, it is recommended to lay the flooring in three layers. If this value is 10-25%, then you can put one layer, for example, material with bedding. On roofs with a slope of no more than 28%, asbestos-cement corrugated sheets, such as slate, can be laid. If this figure is up to 29%, then it is recommended to use a steel coating. With a slope of 33% and above, tiles are often used as a roofing material. Calculation by formulaWhen the roof slope is determined and required material for covering, it is necessary to calculate the height of the ridge. To do this, you can use a simple mathematical method: you need to take the width of the span of the house and divide it by two. The result of the quotient must be multiplied by the relative value, which is calculated using a special Bradis table. It shows the values for each angle.
Now let's give an example of calculating the roof slope. If the width of the span is 8 meters and the angle of inclination of the roof is 25 degrees, then the height of the ridge is as follows: 8:2 = 4 4 * 0.47 = 1.88 meters. Counting in reverse side Using the same formula, you can determine the angle of inclination of the roof. This is unlikely to be needed during construction, but it may come in handy during renovations. Using an inclinometerThe magnitude of the slope can also be calculated using special tool, which is called an inclinometer. It is a strip with a frame attached to it. Between the slats there is an axis to which the pendulum is attached. There is a graduated scale inside the cutout. When the rod lies horizontally, it corresponds to zero on the scale.
Optimal roof slope for different materials
Important! It is worth understanding that all the values listed here are just recommendations. Therefore, everyone has the right to choose the angle of inclination of the roof to the horizon at their own discretion. Some builders forget about this very important detail, like planning a drain, but it is through it that water flows from the roof. If you do not take care of this in advance, then after the construction of the roof, difficulties may arise with water drainage. |
The gable roof has long become a classic of architecture. The list of its advantages includes ease of installation, low maintenance costs and practicality in terms of natural removal of rainwater and snow. To fully experience these benefits, you need to carefully think through the roof design and calculate the dimensions. This is the only way to make the structure durable and maintain its attractive appearance. appearance for many years.
Basic parameters of a gable roof
Selection optimal size roofs are difficult process finding a compromise between the desired appearance of the building and its safety requirements. In a properly designed roof, all proportions are close to ideal. Go to main parameters gable roof include the angle of inclination, the height of the ridge, the width of the roof and its overhangs.
The slope of the roof is the value that determines the position of the slope relative to the horizon line. The choice of this indicator is carried out at the design stage of the structure. Traditionally, both slopes are two pitched roof They are performed with the same angles of inclination, but there are also asymmetrical varieties.
The most common roofs have a slope of 20° to 45°
The unit of measurement for slope is degrees. For roofs, the accepted range is 1 0 -45 0. The higher the number, the more acute the structure, and vice versa, as the degree decreases, the roof becomes sloping.
Depending on the slope, there are several types of roofs:
- flat (less than 5°), the advantages of which are low consumption of materials and ease of maintenance, and the disadvantages are the mandatory presence of a good waterproofing system and measures to prevent snow accumulation;
- flat (up to 30°), allowing you to use everything as a roofing covering existing materials, but more expensive in cost than flat;
- steep (more than 30°), capable of self-cleaning, but not resistant to wind loads.
The tool for measuring the slope angle is an inclinometer. Modern models equipped with an electronic display and a bubble level. When the device is oriented horizontally, “0” is displayed on the scale.
Manufacturers offer to purchase inclinometers with laser sensors that allow measurements to be taken at a distance from the object
Photo gallery: roofs with different slope values
The load on a roof with a slope of 45° degrees is 5 times higher than on a roof with an angle of 11° 
Steep slopes, due to the large slope, drain precipitation well 
A multi-slope roof is erected if it is necessary to connect the walls different heights or an extension adjacent to the house 
The minimum slope angle recommended by builders is 14°
In a number regulatory documents, for example, SNiP II-26–76 “Roofs”, the slope is indicated as a percentage. There are no strict recommendations for a single parameter designation. But the value in percentage is very different from the option in degrees. So, 1 0 equals 1.7%, and 30 0 equals 57.7%. For error-free and quick conversion of one unit of measurement to another, special tables have been created.
Table: relationship between slope units
| Slope, 0 | Slope, % | Slope, 0 | Slope, % | Slope, 0 | Slope, % |
| 1 | 1,7 | 16 | 28,7 | 31 | 60,0 |
| 2 | 3,5 | 17 | 30,5 | 32 | 62,4 |
| 3 | 5,2 | 18 | 32,5 | 33 | 64,9 |
| 4 | 7,0 | 19 | 34,4 | 34 | 67,4 |
| 5 | 8,7 | 20 | 36,4 | 35 | 70,0 |
| 6 | 10,5 | 21 | 38,4 | 36 | 72,6 |
| 7 | 12,3 | 22 | 40,4 | 37 | 75,4 |
| 8 | 14,1 | 23 | 42,4 | 38 | 78,9 |
| 9 | 15,8 | 24 | 44,5 | 39 | 80,9 |
| 10 | 17,6 | 25 | 46,6 | 40 | 83,9 |
| 11 | 19,3 | 26 | 48,7 | 41 | 86,0 |
| 12 | 21,1 | 27 | 50,9 | 42 | 90,0 |
| 13 | 23,0 | 28 | 53,1 | 43 | 93,0 |
| 14 | 24,9 | 29 | 55,4 | 44 | 96,5 |
| 15 | 26,8 | 30 | 57,7 | 45 | 100 |
Ridge height
Another important roof parameter is the height of the ridge. The ridge is the top point of the rafter system, located at the intersection of the planes of the slopes. It serves as a support for the rafters, giving the roof the necessary rigidity and allowing the load to be evenly distributed over the entire structure. Structurally, it is a horizontal rib made of wooden beam. If you imagine a gable roof in the form of a triangle, then the height of the ridge is the distance from the base to the top of the figure.
According to the rules of geometry, the height of the ridge is equal to the length of the leg of the right triangle
Overall roof width and overhang width
The overall width of the roof is determined by the width of its box (the size of the rafter system) and the width of the eaves overhangs.
The overhang is the part of the roof protruding beyond the walls. The width of the overhang is the distance from the intersection load-bearing wall from the roof to the bottom of the roofing sheet. Despite the modest dimensions and small specific percentage in total area, the overhang plays a key role in the operation of the house. The cornice protects the external walls from precipitation, keeping their coating in its original form. He creates a shadow in local area in the summer heat and shelters people during snowfall. In addition, the overhang facilitates the drainage of rainwater from the roof.
The required size of the eaves overhang B is obtained by lengthening or building up rafter legs
There are 2 types of overhangs, differing in location and width:
- pediment - a small area in width roof slope, located on the pediment side;
- eaves - a wider overhang that is located along the roof.
To protect the lower surface, the overhang is sheathed edged board, siding or soffits
Photo gallery: roofs with different overhang widths
Optimal width the cornice is within 50–60 cm 
The edge of the roof ends at the top line of the gable or wall 
Houses built in Mediterranean style, have narrow overhangs and a small slope angle 
The wide cornice gives monumentality to the entire building
Factors influencing roof parameters
The first stage of roof construction is the development and preparation of a technical plan. It is necessary to take into account all the nuances that will affect the life of the roof. Design parameters are determined by considering a group of factors: climatic features region, the presence of an attic and the type of roofing material.
Depending on the area in which the building is located, it may be influenced by various natural forces and loads. These include wind pressure, snow pressure and water exposure. Their value can be determined by contacting a special construction organization that carries out such research. For those who are not looking for simple ways, there is an option to determine the parameters yourself.
Wind load
The wind creates significant pressure on the walls and roof of the building. The air flow, encountering an obstacle in its path, is divided, rushing in opposite directions: towards the foundation and the roof overhang. Excessive pressure on the overhang can cause the roof to fall off. To protect the building from destruction, the aerodynamic coefficient is estimated, depending on the angle of inclination of the slope.
The steeper the slope and the higher the ridge, the stronger the wind load per 1m2 of surface. In this case, the wind tends to overturn the roof. Hurricane winds have a different effect on flat roofs - the lifting force lifts and carries away the crown of the house. Therefore, for areas with low to moderate wind strength, roofs can be designed with any ridge height and pitch angle. And for places with strong gusts of wind, low-slope types from 15 to 25° are recommended.
In addition to the horizontal impact, the wind exerts pressure in vertical plane, pressing the roofing material against the sheathing
Calculation of wind load on a gable roof
The design wind load is the product of two components: normative value parameter (W) and coefficient (k), which takes into account the change in pressure depending on the height (z). The standard value is determined using a wind load map.
The country's territory is divided into 8 zones with different nominal wind load values
The height coefficient is calculated from the table below based on the corresponding type of terrain:
- A - coastal areas of water bodies (seas, lakes), deserts, steppes and tundra.
- B - urban area with obstacles and buildings 10–25 m high.
- C - urban area with buildings from 25 m in height.
Table: coefficient for calculating wind load
| Height z, m | Coefficient k for different types terrain | ||
| A | IN | WITH | |
| up to 5 | 0,75 | 0,50 | 0,40 |
| 10 | 1,00 | 0,65 | 0,40 |
| 20 | 1,25 | 0,85 | 0,55 |
| 40 | 1,50 | 1,10 | 0,80 |
| 60 | 1,70 | 1,30 | 1,00 |
| 80 | 1,80 | 1,45 | 1,15 |
| 100 | 2,00 | 1,60 | 1,25 |
| 150 | 2,25 | 1,90 | 1,55 |
| 200 | 2,45 | 2,10 | 1,80 |
| 250 | 2,65 | 2,30 | 2,00 |
| 300 | 2,75 | 2,50 | 2,20 |
| 350 | 2,75 | 2,75 | 2,35 |
| 480 | 2,75 | 2,75 | 2,75 |
Let's look at an example. It is necessary to determine the estimated wind load and draw a conclusion about the acceptable roof slope. Initial data: region - the city of Moscow with terrain type B, the height of the house is 20 m. We find Moscow on the map - zone 1 with a load of 32 kg/m 2. By combining the rows and columns of the table, we find that for a height of 20 m and type of terrain B, the required coefficient is 0.85. Multiplying the two numbers, we determine that the wind load will be 27.2 kg/m2. Since the obtained value is not large, it is possible to use a slope of 35–45°, otherwise you need to take a slope angle of 15–25°.
Snow load
Snow masses accumulating on the roof exert a certain pressure on the roof. The larger the snowdrifts, the greater the load. But not only the pressure of the snow is dangerous, but also its melting as the temperature rises. The average weight of newly fallen snow per 1 m 3 reaches 100 kg, and in its raw form this figure increases threefold. All this can cause deformation of the roof, failure of its tightness, and in some cases lead to the collapse of the structure.
The greater the slope angle, the easier it is for snow deposits to be removed from the roof. In areas with heavy snowfall, the maximum slope slope should be 60º. But the construction of a roof with a slope of 45º also contributes to the natural removal of snow.
Under the influence of heat coming from below, the snow melts, increasing the risk of leaks.
Calculation of snow load on a gable roof
The snow load value is obtained by multiplying the average load (S), characteristic of a certain type of terrain, and a correction factor (m). The average value of S is found from the snow load map of Russia.
The territory of Russia includes 8 snow regions
The correction factor m varies depending on the roof slope:
- at a roof angle of up to 25 0 m is equal to 1;
- the average value of m for the range 25 0 –60 0 is 0.7;
- for steeply sloped roofs with an angle of more than 60 0, the coefficient m is not included in the calculations.
Let's look at an example. It is necessary to determine the snow load for a house with a slope angle of 35 0, located in Moscow. From the map we find that the required city is located in zone 3 with snow load 180 kg/m2. The coefficient m is taken equal to 0.7. Therefore, the desired value of 127 kg/m2 will be obtained if we multiply these two parameters.
The total load, consisting of the weight of the entire roof, snow and wind loads, should not be more than 300 kg/m2. Otherwise, you should choose a lighter roofing material or change the slope angle.
Roof type: attic or non-attic
There are 2 types pitched roofs: attic and non-attic. Their names speak for themselves. Thus, the attic (separate) roof is equipped uninhabited attic, and a non-attic (combined) - an exploitable attic. If you plan to use the space under the roof to store items that are not used in everyday use, then there is no point in increasing the height of the roof ridge. Conversely, when planning a living room under the roof, the height of the ridge should be increased.
The height of any type of roof must be sufficient for interior repairs
For non-residential roofs, the height of the ridge is determined by fire safety rules. Building regulations state that the attic must contain a through passage 1.6 m high and 1.2 m long. For residential roofs, the height is set based on their convenience of living and trouble-free placement of furniture.
Type of roofing material
Until recently, the construction market offered only a few items roofing materials. It was traditional slate and galvanized steel sheet. Now the range has been significantly expanded with new products. When choosing a roofing material, several rules should be considered:
- When reducing the dimensions of piece roofing materials, the angle of inclination is increased. This is due to the large number of joints, which are potential leak points. Therefore, they try to make the precipitation disappear as quickly as possible.
- For roofs with a low ridge height, it is preferable to use rolled roofing materials or large-sheet sheets.
- The more the roofing material weighs, the steeper the roof slope should be.
The range of possible slopes is described in the manufacturer’s instructions for roof installation
| Material type | Minimum slope, 0 | Note |
| Metal tiles | 22 | Theoretically, installation on a roof with an angle of 11 0 –12 0 is possible, but for better sealing choose a higher slope |
| Corrugated sheet | 5 | When the angle of inclination changes upward, the overlap of one sheet onto another increases |
| Asbestos cement slate | 25 | If the slope is less than recommended, snow will accumulate on the roof, under the weight of which the roofing material will collapse |
| Soft roll roofing (roofing felt, ondulin) | 2 | The minimum slope angle depends on the number of layers: for one layer 2 0, and for three - 15 0 |
| Seam roofing | 7 | For roofs with a slight slope, it is recommended to purchase a double standing seam |
Cost of a gable roof
It is logical that as the slope of the slope increases, the roof area increases. This leads to increased consumption of lumber and roofing materials and components (nails, screws) for securing them. The cost of a roof with a 60° angle is 2 times more than the creation flat roof, and a slope of 45° will cost 1.5 times more.
The greater the total load on the roof, the larger the section of timber used for the rafter system. With a slight roof slope, the sheathing pitch is reduced to 35–40 cm or the frame is made solid.
Accurate calculation of roof dimensions will save the family budget
Video: rafter system and roof parameters
Calculation of roof parameters
To quickly calculate roof dimensions, you can use an online calculator. The initial data (dimensions of the building’s base, type of roofing material, lift height) are entered into the program fields, and the result is the required value of the rafter slope, roof area, weight and quantity of roofing material. A small minus is that the calculation steps are hidden from the user.
For greater understanding and clarity of the process, you can carry out independent calculations of the roof parameters. There is a mathematical and graphical method for calculating the roof. The first is based on trigonometric identities. A gable roof is represented in the form of an isosceles triangle, the dimensions of which are the parameters of the roof.
Using trigonometry formulas you can calculate roof parameters
Calculation of the slope angle of roof slopes
The initial data for determining the slope angle is the selected roof height and half of its width. As an example, consider a classic gable roof with symmetrical slopes. We have: ridge height 3 m, wall length 12 m.
Dimensions c and d are usually called roof pitch
Sequence of slope calculation:
- We divide the conditional roof into 2 right triangles, for which we draw a perpendicular from the top to the base of the figure.
- Consider one of the right triangles (left or right).
- Since the structure is symmetrical, the projections of slopes c and d will be the same. They are equal to half the length of the wall, i.e. 12/2 = 6 m.
- To calculate the slope angle of slope A, we calculate its tangent. From school course We remember that tangent is the ratio of the opposite side to the adjacent side. The opposite side is the height of the roof, and the adjacent side is half the length of the roof. We find that the tangent is 3/6 = 0.5.
- To determine what angle the resulting tangent has, we use the Bradis table. Having found the value 0.5 in it, we find that the slope angle is 26 0.
To convert tangents or sines of angles into degrees, you can use simplified tables.
Table: determining the slope of the slope through the tangent of the angle for the range 5–60 0
| Tilt angle roofs, 0 | Tangent angle A | Sinus angle A |
| 5 | 0,09 | 0,09 |
| 10 | 0,18 | 0,17 |
| 15 | 0,27 | 0,26 |
| 20 | 0,36 | 0,34 |
| 25 | 0,47 | 0,42 |
| 30 | 0,58 | 0,5 |
| 35 | 0,7 | 0,57 |
| 40 | 0,84 | 0,64 |
| 45 | 1,0 | 0,71 |
| 50 | 1,19 | 0,77 |
| 55 | 1,43 | 0,82 |
| 60 | 1,73 | 0,87 |
Calculation of the rise of a gable roof and the height of the ridge
The height of the roof is closely related to the steepness of the slope. It is determined in the way reverse method obtaining a slope. The calculation is based on the angle of inclination of the roof, which is suitable for the given area depending on the snow and wind load, and the type of roof.
The greater the slope, the more free space under the roof
Procedure for calculating roof lift:
- For convenience, we divide our “roof” into two equal parts, the axis of symmetry will be the height of the ridge.
- We determine the tangent of the selected roof slope angle, for which we use Bradis tables or an engineering calculator.
- Knowing the width of the house, we calculate the size of its half.
- We find the height of the slope using the formula H = (B/2)*tg(A), where H is the height of the roof, B is the width, A is the slope angle of the slope.
Let's use the given algorithm. For example, it is necessary to set the height of a gable roof of a house with a width of 8 m and an angle of inclination of 35 0. Using a calculator we find that tangent 35 0 is equal to 0.7. Half the width of the house is 4 m. Substituting the parameters in trigonometric formula, we find that H=4*0.7=2.8 m.
A well-calculated roof height gives the house a harmonious look
The above procedure relates to determining the rise of the roof, i.e. the distance from the bottom of the attic floor to the support point of the rafter legs. If the rafters protrude above the ridge beam, then the full height of the ridge is determined as the sum of the roof rise and 2/3 of the thickness of the rafter beam. Thus, the total length of the ridge for a roof with a rise of 2.8 m and a beam thickness of 0.15 m is equal to 2.9 m.
In places where ledges are cut for assembly with ridge run rafters are reduced by 1/3
Calculation of rafter length and roof width
To calculate the length of the rafters (the hypotenuse in a right triangle), you can go in two ways:
- Calculate the size using the Pythagorean theorem, which states: the sum of the squares of the legs is equal to the square of the hypotenuse.
- Use the trigonometric identity: the length of the hypotenuse in a right triangle is the ratio of the opposite leg (the height of the roof) to the sine of the angle (the slope of the roof).
Let's consider both cases. Let’s say we have a roof rise height of 2 m and a span width of 3 m. We substitute the values into the Pythagorean theorem and find that the desired value is equal to square root out of 13, which is 3.6 m.
Knowing the two legs of a triangle, you can easily calculate the hypotenuse or the length of the slope
The second way to solve the problem is to find the answer through trigonometric identities. We have a roof with a slope angle of 45 0 and a rise height of 2 m. Then the length of the rafters is calculated as the ratio of the number of rises of 2 m to the sine of the slope 45 0, which is equal to 2.83 m.
The width of the roof (Lbd in the figure) is the sum of the length of the rafters (Lc) and the length of the eaves overhang (Lкc). And the length of the roof (Lcd) is the sum of the length of the house wall (Ldd) and two gable overhangs (Lfs). For a house with a box width of 6 m and overhangs of 0.5 m, the roof width will be 6.5 m.
Building codes do not regulate the exact length of the slope; it can be selected in a wide range of sizes
Calculation of roof area
Knowing the length of the slope and the width of the roof, you can easily find its area by multiplying the indicated dimensions. For gable roof the total area of the roof is equal to the sum of the areas of both surfaces of the slopes. Let's dwell on specific example. Let the roof of the house have a width of 3 m and a length of 4 m. Then the area of one slope is 12 m 2, and the total area of the entire roof is 24 m 2.
Incorrect calculation of the roof area can lead to additional costs when purchasing roofing material
Calculation of materials for the roof
To determine the amount of roofing materials, you need to arm yourself with the roof area. All materials are overlapped, so when purchasing you should make a small margin of 5–10% of the nominal calculations. Correct calculation quantity of materials will significantly save the budget construction work.
General rules for calculating lumber:
- Dimensions and cross-section of the Mauerlat. The minimum possible cross-section of the timber is 100×100 mm. The length corresponds to the perimeter of the box, the margin for connections is set around 5%. The volume of the beam is obtained by multiplying the cross-sectional dimensions and length. And if you multiply the resulting value by the density of wood, you will find the mass of lumber.
- Size and number of rafters. The calculation is based on the total load on the roof (pressure roofing pie, snow and wind). Let's assume that the total load is 2400 kg/m2. The average load per 1 m of rafters is 100 kg. Taking this into account, the footage of the rafters will be equal to 2400/100 = 24 m. For a rafter length of 3 m, we get only 8 rafter legs or 4 pairs. The cross-section of the rafters is taken from 25x100 mm and above.
- Volume of material for sheathing. Depends on the type of roofing: for bitumen shingles construct a continuous sheathing, and for corrugated sheets or asbestos cement slate sparse.
Let's look at the calculation of roofing materials using metal tiles as an example. This sheet material, mounted on the roof in one or several rows.
Calculation sequence:
- Determining the number of sheets. The metal tile sheet has a total width of 1180 mm and a working width of 1100 mm. The latter is smaller than the real one and is not taken into account in the calculation, since it is used to cover joints. The number of sheets is determined as the ratio of the total width of the roof (including overhangs) to the useful width of the sheet. Moreover, the result of division is rounded up to the whole value. So, for a roof with a slope width of 8 m and a sheet of Monterrey metal tiles 1.1 m wide, the number of sheets is determined by the formula: 8/1.1 = 7.3 pcs, and taking into account rounding, 8 pcs. If the sheet is laid in several vertical rows, then the length of the slope is divided by the length of the roofing sheet, taking into account the overlap between the sheets of up to 15 cm. Considering that the roof is gable, the value is doubled, i.e. a total of 16 sheets will be required.
- Determination of the total area. To determine the total area of the roofing material, the number of sheets is multiplied by the total area (the product of the total width and length) of one sheet. In our case, 8 * (1.18 m * 5 m) = 47.2 m 2. For gable structures, the result is multiplied by two. We find that the entire roof area is 94.4 m2.
- Determining the amount of waterproofing. Standard roll waterproofing material has an area of 65m2 without overlap. The number of rolls is obtained by dividing the total roof area by the area of the film, i.e. 94.4 m2 /65 m2 = 1.45 or 2 full rolls.
- Determining the quantity of fasteners. There are 6–7 self-tapping screws per 1 m2 of roofing. Then, for our situation: 94.4 m 2 * 7 = 661 screws.
- Determining the number of extensions (skates, wind bars). The total footage of the planks is 2 m, and work zone- 1.9 m due to partial overlap. Dividing the length of the ramp by the working length of the planks, we obtain the required number of additions.
Video: calculating materials for a gable roof using an online calculator
A graphical method for determining roof parameters is to draw it on a reduced scale. For it you will need a piece of paper (plain or graph paper), a protractor, a ruler and a pencil. Procedure:
- The scale is selected. Its optimal value is 1:100, i.e. for every 1 cm of paper sheet there is 1 m of structure.
- A horizontal segment is drawn, the length of which corresponds to the base of the roof.
- The middle of the segment is located, from the point of which a perpendicular is drawn upward (a vertical line at an angle of 90 0).
- Using a protractor, the required roof angle is plotted from the boundary of the roof base and an inclined line is drawn.
- The intersection of the inclined line with the perpendicular gives the height of the roof.
Video: manual calculation of materials for a gable roof
The first thing people pay attention to is the visual appearance of the roof. Architects make sure that the roof is harmoniously combined with the facade of the building. But beauty alone is not enough. It is important to correctly calculate the parameters so that the design is durable and functional. Neglecting snow and wind loads or installing rafters at the wrong angle can cause roof destruction. And an incorrect determination of the roof area will lead to additional costs for the purchase of missing materials. Therefore, you should approach calculations responsibly, paying attention to all the nuances.
The angle of inclination of the roof depends on many indicators, but the most important of them is the design of the roofing covering and its material. Yes, y flat roofs the angle of inclination is small, but roofs made using truss structures, is a separate topic. Here it is especially important to correctly calculate the required angle of inclination, since the degree of removal of precipitation from the roof depends on this. Usually this indicator is expressed in degrees, percentage or ratio of legs. In our article we will learn how to determine the required roof slope angle.
The degree measure of roof slope shows us the angle formed by the roof in relation to the horizon. Roofs with a large angle of inclination are called steep, while those with a small angle are called flat.
Determining the angle of inclination in different measurement quantities
As you already understood, to determine the angle of the roof, you need to know exactly what kind of roofing will be used.
As a rule, the following materials can be used to cover pitched roofs:
- slate;
- flexible roll roofing materials
- metal tiles;
- roofing felt;
- natural tiles;
- corrugated sheets, etc.
If you imagine right triangle, then we can understand that its hypotenuse will in any case be larger than the legs, therefore optimal angle We will consider the slope of a particular roof to be the smallest permissible value. How to determine the angle of the roof? First of all, this indicator depends on the density of the roofing covering and the tightness of the entire roof structure as a whole. This is due to the fact that roofs with a large angle of inclination have a large windage area, so good tightness is required. And on roofs with a small slope angle, precipitation will be retained, thereby creating increased loads on the coating.
In the table below you can see a graph that helps determine the angle of the roof in percentage and the ratio of the legs. You can also associate these indicators with the degree definition of the angle measure. To understand how to use the graph, look at the 50% slope. It can be seen that the height of the ridge (H) fits twice into the leg at the base of the triangle (L/2), hence the ratio 1:2.
The most in a convenient way Calculation of the angle of inclination of the roof is a dimensionless indicator (the ratio of the legs). For example, the slope angle indicator in the form of a ratio of 1/3 indicates that to determine the height of the ridge, you need to find the midpoint of the span and set aside a third of its length.
Type of roof covering and roof angle
To give you an idea of the upper and lower permissible limits of the roof angle using a particular roofing covering, we have developed a special table. The study of various regulatory documents, as well as observations during construction work, allowed us to draw conclusions about the conditions for using various roofing materials.
However, it is worth remembering that the construction market is rapidly filling with new materials, and the performance qualities of existing ones roofing coverings may improve with development modern technologies. Therefore, over time, the strength of some materials may increase, and as a result, the angle of the roof may change.
Lower limit of roof angle
| Type of roofing | Weight 1 sq.m., kg | Dimensionless roof slope | Percentage measure of slope | Slope amount in degrees |
| Slate (medium profile/reinforced profile) | 11/13 | 1:10 / 1:5 | 10% / 20% | 6° / 11.5° |
| Pulp-bitumen sheets | 6 | 1:10 | 10% | 6° |
| Corrugated sheeting (single-seam) | 3-6,5 | 1:4 | 25% | 14° |
| Soft roll roofing | 9-15 | 1:10 | 10% | 6° |
| Corrugated sheeting (double-seam) | 3-6,5 | 1:5 | 20% | 11.5° |
| Metal tiles | 5 | 1:5 | 20% | 11.5° |
| Ceramic tiles | 50-60 | 1:5 | 20% | 11.5° |
| Cement tiles | 45-70 | 1:5 | 20% | 11.5° |
As for the maximum roof slope angle, for such lightweight roofing materials as cellulose-bitumen coatings, soft roof, metal tiles and corrugated sheets, it can be even more than 1:1. Maximum slope You can see all other roofing coverings in the table below.
Upper limit of roof angle
So that you can easily and quickly convert the degree measure of an angle into a percentage, you can use the proposed table.
| Degree | Percent |
| 1 | 1,8 |
| 2 | 3,4 |
| 3 | 5,2 |
| 4 | 7,0 |
| 5 | 8,8 |
| 6 | 10,5 |
| 7 | 12,3 |
| 8 | 14,1 |
| 9 | 15,8 |
| 10 | 17,6 |
| 11 | 19,4 |
| 12 | 21,2 |
| 13 | 23,0 |
| 14 | 24,9 |
| 15 | 26,8 |
| 16 | 28,7 |
| 17 | 30,5 |
| 18 | 32,5 |
| 19 | 34,4 |
| 20 | 36,4 |
| 21 | 38,4 |
| 22 | 40,4 |
| 23 | 42,4 |
| 24 | 44,5 |
| 25 | 46,6 |
| 26 | 48,7 |
| 27 | 50,9 |
| 28 | 53,1 |
| 29 | 55,4 |
| 30 | 57,7 |
| 31 | 60,0 |
| 32 | 62,4 |
| 33 | 64,9 |
| 34 | 67,4 |
| 35 | 70,0 |
| 36 | 72,6 |
| 37 | 75,4 |
| 38 | 78,9 |
| 39 | 80,9 |
| 40 | 83,9 |
| 41 | 86,0 |
| 42 | 90,0 |
| 43 | 93,0 |
| 44 | 96,5 |
| 45 | 100,0 |
Determining the height of the ridge
Knowing the angle of the roof, you can easily calculate the height of the ridge. To facilitate this calculation, you can use the table below, where each roof angle in degrees corresponds to a certain relative value, which will help calculate the height ridge beam. To do this, you need to multiply ½ the length of the roof span by the indicator from the rightmost column of the table.
| Roof inclination angle, degrees | Relative value |
| 5 | 0,8 |
| 10 | 0,17 |
| 15 | 0,26 |
| 20 | 0,36 |
| 25 | 0,47 |
| 30 | 0,59 |
| 35 | 0,79 |
| 40 | 0,86 |
| 45 | 1,0 |
| 50 | 1,22 |
| 55 | 1,45 |
| 60 | 1,78 |
For example, the span in your building is 16 meters, and the designed slope angle is 30 degrees. We find the height of the ridge as follows: 16:2x0.59=4.72. In this case, the number 0.59 is taken from the table, taking into account that the roof slope is 30 degrees.
Now you know how to correctly find the angle of the roof and what indicators this value depends on. We hope that our tables will help you easily navigate the roof slope values.