Two pitched 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 an attractive appearance for many years.
Basic parameters of a gable roof
Selection optimal size roofs are a complex process of finding a compromise between the desired appearance of a 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 stingrays gable 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 walls of different heights or an adjacent extension to the house 
Minimum angle slope recommended by builders, 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 of the load-bearing wall with the roof to the bottom of the roofing sheet. Despite its modest dimensions and small specific percentage of the 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 V 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 the rafter legs
There are 2 types of overhangs, differing in location and width:
- pediment - a small section of the 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
The optimal width of the cornice is in the range of 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 of the 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. You can determine their meaning by contacting a special construction organization carrying out similar research. For those who are not looking 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, evaluate aerodynamic coefficient, 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 the vertical plane, pressing the roofing material against the sheathing
Calculation of wind load on a gable roof
The calculated wind load is the product of two components: the standard value of the parameter (W) and the 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 a snow load of 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 of gable roofs: attic and non-attic. Their names speak for themselves. Thus, an attic (separate) roof is equipped with a non-residential attic, and a non-attic (combined) roof is equipped with a usable 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 the rules against fire safety. 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 types of 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 larger 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 into the 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 a ridge girder, the 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 a gable roof, the total roof area 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 construction budget.
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 from the 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 They construct a continuous sheathing, and for corrugated sheets or asbestos-cement slate, a sparse one.
Let's look at the calculation of roofing materials using metal tiles as an example. This is 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. A standard roll of waterproofing material has an area of 65 m 2 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. His optimal value is 1:100, i.e. for every 1 cm paper sheet accounts for 1 m of the 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.
One of the main elements of the structure is the roof. The viability of the house and the peace of its residents depend on its quality and correctly chosen form.
Any pitched roof consists of several basic elements. These include:
- Rafter system;
- Lathing;
- Roof.
A preliminary calculation when designing a house should help determine required amount materials for its construction. Based on this, a budget (estimate) of expenses is drawn up. It is impossible to calculate the cost of a roof without determining its shape and height.
Types of roofs
In modern construction, almost all roof shapes existing in architecture are common. Gable and four-slope (hip) species are also widespread.
Besides them there are also hip roofs, and domed, and broken (attic) and complex multi-slope.
Among the most widespread roofs, the most common are gable roofs, which are a simple structure consisting of two inclined slopes and two gables - vertical walls triangular shape.
Roofs gable construction usually mounted on, . The gable roof with an attic also looks original.
The rafter system of such roofs consists of paired parts located at an angle to the horizontal line. A plank or continuous sheathing ensures their stability.
The upper part of gable roofs, the junction of the rafter legs, is called the ridge. This is the most top part the entire building on which many owners of private houses install decorative.
To determine the roof area and calculate the number of boards for sheathing, roofing material and the length of the logs themselves, you need to learn how to calculate the height of the ridge.
You can quickly and accurately calculate a gable roof, including determining the height of the ridge, using an online calculator on the Internet.
Parameters affecting roof height
The roof is the upper part of the building, so it absorbs all the loads falling on it. IN winter period- this is the accumulation of snow on the roof, during the year - the influence of wind, which is greater, the larger the area of \u200b\u200bthe slopes and the steeper they are located relative to the horizontal.
When designing, you can slightly reduce the influence of weather factors. So, when using smooth roofing materials, such as corrugated sheets or metal tiles, you can significantly reduce the amount of snow that will accumulate. If sufficient, it will slide down without significantly increasing the load on the rafter system and sheathing.
To reduce wind loads, it is advisable to make roofs with a lower slope. But this is fraught with the formation of large snowdrifts, which, when the snow melts, can lead to the collapse of the roof. Therefore, it is necessary to find a “golden mean” between increasing and decreasing the angle of the roof. 
Determining the height of the ridge
The first method is mathematical
To calculate the height of the ridge of a gable roof, it is necessary to present its structure in cross section. It will be an isosceles triangle. Therefore, the height of the ridge will be the height of this triangle.
By constructing the height (perpendicular to the base of the triangle), we get two right triangles, in which one of the legs will determine the parameter we need. The second leg can be determined by dividing the total width of the house by 2.
To comply optimal conditions operation of the house in conditions large quantity precipitation and enough strong winds The slope angle of the roof slopes is taken in the range of 20o - 45o. The Pythagorean theorem and the Bradis table will help you calculate the height of the ridge of a gable roof based on the specified parameters.
According to the theorem known to everyone since school years, the length of one leg (the height of the ridge) will be determined as the product of the second leg (half the width of the house) by the tangent of the angle opposite to the desired leg (roof slope angle).
Let us give the value of the tangent of angles from 20° to 45° in increments of 5°.
For example, let’s calculate the height of the ridge for a standard wooden house 6x8 meters, located in middle lane our country, with a roof slope of 40°. In accordance with the above formula, the leg at our disposal will have a length of 3 meters (6:2=3).
The tangent of an angle of 40° is determined from the table. It is equal to 0.839. We multiply the numbers we know and get:
Thus, with the specified parameters, the height of the ridge from the house will be 2.517 meters.
Method two - graphical
Less accurately, without using mathematical formulas and tables, you can determine the height of the ridge by drawing a section of the roof on a small scale. To do this, draw an isosceles triangle and draw a median, which will also be the height.
The angle at the base of the triangle must be accurately drawn using a protractor. When correcting for the accuracy of mathematical tools, it is possible to obtain an approximate value of the desired quantities. 
Important! After completing the process of installing the ridge on the roof, it is necessary to cover ridge girder lightweight side tiles. This is required by the design of the ridge of a pitched roof.
In this way, the height of the ridge of a gable roof is calculated. When planning use attic space needs to be determined optimal parameters internal space for free movement of residents and guests of the house.
Watch a video about building a ridge for a gable roof and installing rafters:
The height of the roof affects the appearance of the house, the complexity of assembling the rafter frame and technical characteristics. Therefore, it is important to pay Special attention determine the size and only then purchase the material. In order to make calculations, it is not necessary to contact specialized organizations. In the article we will discuss how to correctly calculate the height of the roof, as well as what affects it.
What affects the height of the skate?
A ridge is a horizontal edge connecting the vertices of two roof slopes. Overestimating and underestimating the height negatively affects the operation of the roof and spoils the appearance of the building. Therefore, when making calculations, it is not enough to be guided only by your own taste. Before calculating the height of the ridge, it is important to pay attention to various technical conditions.
In this article, we will assume by default roofs with equal slopes in length and angle of inclination. This will make it easier to determine the height, although all the principles described apply to asymmetrical structures.
According to geometry, one of the slopes will be the hypotenuse, and the distance from the ridge to the base will be the leg.
- type of roofing;
Now let's go through each point in more detail.
Roof covering
For different materials there are own requirements for the steepness of the slope. The calculation of the height of the ridge of a gable roof will depend on this indicator. Eat general principles choice of material depending on the angle of the slope:
- For small piece elements the slope of the slope should be greater than for long ones sheet materials. This is due to the fact that when moisture accumulates in the joints, leaks may appear. Therefore, skates are for slate roof higher than ridges on a metal roof. The fact is that the length of the wave slate is only 1.75 m, and metal roofing material can occupy the entire length of the slope.
- Height ridge roof also affects the number of joints. As the angle decreases, the number of connections and overlaps should also decrease. Therefore, large-sheet and roll materials are considered the most reliable options.
- Heavy roofing elements are placed on steep slopes. Slate roofs and ceramic tiles have large mass, so they make a steep slope. So, they do not bend the rafter beams.
It is worth remembering that the steeper the slope, the more material will be needed to cover the roof. So, if we take the need for a slope angle of 7-10° as 100%, then an angle of 45° will require a 150% overrun, and an angle of 60° will require 200%.
The size of the slopes relative to the width of the house will change with the height of the ridge.
Attic space
There are two types of houses: with and without an attic. Each option has its own conditions for calculating the height of the ridge. If the attic space is residential, then 30-40 cm is added to the height of the tallest owner. But it is better to think about the guests by making the ceiling at a height of 2.4 meters. But it is important to remember that this is only the ceiling, not the height of the roof. Here you will need to add another half meter or more, depending on your preferences.
If the attic space is non-residential, then the height of the ridge is calculated under the influence of fire safety. One of the clauses obliges the owners to provide a through passage under the roof with a height of at least 1.6 meters and a width of 1.2 m. With complex rafter systems, these dimensions can be reduced by 0.4 m. This space will provide free air exchange and passage for repairs, inspection.
Roofless buildings are constructed in such a way that additional walls are erected above the ceiling of the previous floor. For example, in semi-attic buildings the height of the walls is increased by 1.4 meters. In such structures, the height of the roof is measured from the bottom edge of the Mauerlat. Such designs are suitable for climatic zones with strong winds. This makes it possible to reduce the slope of the slope.
Attic structures are popular in the construction of garages, warehouses and other small domestic buildings. They usually do not provide attic floor, thereby saving material and time.
Atmospheric phenomena
Climatic conditions directly affect the height of the ridge. Therefore, different cities have their own “golden” slope. Atmospheric phenomena include the following factors:
- Precipitation. The more snow it rains in your area, the more slope you need to make. The height of the roof increases accordingly. If this condition is neglected, then the likelihood of leaks increases.
- Wind. For areas with medium and low winds there is no difference in the height of the ridge. But like this, where strong, gusty winds often blow, the roof slope usually does not exceed 10°. This imposes certain restrictions on the materials used. Without taking into account the strength of the wind, you risk losing the entire roof structure.
- Amount of snow. There is a relationship between the steepness of the slope and the amount of snow. The more it falls in winter, the larger the angle you need to make. The reason is the increased load on the rafter system. It is recommended to give preference to slopes with a slope greater than 45°.
You can determine the characteristics of your region of residence by contacting the local weather service or reference literature. The regulatory documentation SNiP 23-01-99 or SP 20.13330.2011 contains weather maps and recommendations for construction.
Methods for calculating ridge height
Calculating the height of the roof largely depends on your preferences. There are two main ways:
- mathematical;
- graphic.
Let's look at the mathematical method of calculation. As already mentioned in the first subtitle, the default is a gable isosceles roof. We have the opportunity to calculate the required height if we know the slope angle and the distance between the slopes. Now you will need a Bradis table and a calculator. In the reference literature we find the value of the tangent of our angle, and then multiply it by half the length between the slopes. The result is the height of the ridge.
Let's consider the calculation for real example. Let's assume that our building has dimensions of 7x10 meters. At the same time, we are in an area with average winds, and we use metal tiles as roofing. We are not planning to equip the attic, but we will take the slope equal to 20° so that rainwater It drained without any problems.
It turns out that the length of the leg is 7/10 = 3.5 meters. According to the table, the tangent of 20° is 0.839. Now we multiply the resulting numbers: 3.5 * 0.839 = 2.94. This means that the height of the ridge of the gable roof, from the bottom of the mauerlat, is 2.94 meters.
The graphic method is suitable for those who have a sheet of paper, a pencil and a ruler with a protractor on hand. All you need is to draw a sectional view of the roof, keeping to scale. To do this, draw a horizontal line and mark the boundaries of the roof base on it. Determine the middle and draw a perpendicular. Using a protractor, draw a line on one side at the desired angle. The intersection point will show the height, you just need to measure it with a ruler.
The resulting result will be approximate; you also need to add 2/3 of the thickness of the rafter leg to it. Small deviations are acceptable and do not critically affect the operation of the roof. These errors result from the need to provide ventilation under the metal tiles and sheathing.
In order to mark the desired height in reality, it is enough to determine the middle of the building. Then nail a vertical block or pole at the desired height. After the calculation has been made, try to transfer it from paper to the real building as accurately as possible. Then the roof will last for many years and will not leak on the rainiest days.
- What is important to know for calculations and the dangers of errors
- Types and shapes of modern roofs
- Ridge run and slope angles
- Roof height calculations different forms
- Roof calculation using online resources
- What to consider when starting roof calculations
The final stage in the construction of any house (be it a spacious main dwelling or a small country house) is the arrangement of the roof. It is this that gives the exterior a presentable and complete appearance, but at the same time performs a very important function - it retains heat, creates a cozy, most comfortable and pleasant atmosphere inside. It is this element of any structure that, without exaggeration, is called one of the most important.
What does the height of the structure depend on and what is taken into account when performing pre-installation calculations
It is especially important to know how to calculate the roof height for a house, and to understand exactly how to do it correctly. That is why you need to spend some time studying this issue. Inaccuracies made in pre-installation calculations lead to serious problems, which are then too difficult to cope with. Often, to eliminate errors, you have to start roofing work all over again. For example, if the slopes are made with a small angle of inclination, then winter snowfalls will cause serious damage to such a structure (due to the accumulation of snow, there is a risk that the roof will break). It is logical to assume that you can simply make a high ridge and all problems will be solved, but this is not true either, because a roof that is too high is most vulnerable to gusts of wind.
Thus, when starting to calculate the roof and slope angles, as well as arranging the roof, it is necessary to remember that its height is significantly influenced by:
- general square footage of the structure;
- climatic conditions(as you may have guessed, in regions with snowy winters they are not recommended sloping roofs, optimal for warm continents);
- material for roofing, as well as lathing;
- selected form;
- height of the main building;
- personal preferences and tastes of the owner.
The design parameters are largely influenced by a number of other factors, for example, there is a direct dependence on the layer of insulation installed or the installation of snow guards. The dimensions of the ridge are related to the characteristics of the rafter system, but at the same time they can increase total area roofing and the amount of materials required for its arrangement.
Everything described above confirms the fact that the strength of the structure, the durability of its operation, the aesthetics and harmony of the external appearance of the building depend on the size of the roof.
What are the common types of modern roofing structures?
The type of roof has the most direct impact on the calculation and the formulas used for it, as well as on the amount and, therefore, on the consumption of material that needs to be purchased for roofing. Today the following structures are most often erected:
- single-pitched (it is preferable to use it for outbuildings);
- gable (most popular for residential buildings);
- hipped. Also an excellent choice for residential buildings. There are a variety of options here: spectacular hipped ones (their characteristic feature is the same size and shape of all slopes) or complex hip ones (their feature is the participation of two triangular hips and two slopes with a break (trapezoid shape));
- attic (consists of two slopes, but always with a break). This break allows you to increase the area of the attic.
Ridge and determination of rational slope angles
To calculate different roof shapes, the size of the ridge is used. This name refers to the upper, horizontally located edge of the structure, which was formed at the intersection of two roof slopes (inclined planes).
There is a ridge on all types of roofs, except hipped and domed ones. If the structure is simple, gable, then there is only one, but if it is complex, then there are two or more ridges. When constructing the roof, they rest on the ridge purlins rafter legs, and based on what roofing material is chosen for the final covering, the base of the ridge is also selected.
Knowing how to correctly calculate the height of the roof of a house is necessary for constructing a reliable and durable structure, as well as in order to predict preliminary construction costs and plan a budget. When calculating the rational angle of inclination, the material from which it is decided to lay the roof is taken into account: some roofing coverings can be laid at an angle of up to 90 degrees, while others can only be laid at an angle of 15 to 60 degrees.
When choosing with what slope of planes to choose a roof for your home, you need to take into account functionality, the general appearance of the resulting structure (after all, you want to get an aesthetic structure) and climatic conditions. As practice shows, for European countries ideal solution you can call the angle 35-40 degrees.
Examples of calculations that are easy to do yourself
Basically, if we're talking about O simple designs roof, then you will need very little to calculate the height of the roof: a calculator and several well-known principles from the basics of geometry, which are taught in the school curriculum.
The basic principle of calculation is taken from the rule that the length of one leg in a right triangle will be equal to the length of the other if multiplied by the tangent of the angle formed with the base.
- we measure the width of the building (let’s say we have a four-meter house);
- we take the angle equal to 35 degrees (as the recommended optimal option for European latitudes);
- We calculate the tangent, it is obtained for a given angle of 0.7002;
- 4 meters * 0.7002 = 2.8 meters.
If selected gable design, then in this case the height of the ridge is also very simple to calculate: the width of the house can be divided by “two” and then multiplied by the tangent of the angle formed by the slope of the slopes. For clarity, let us consider what is described above, how to calculate the height of a gable roof using the example of a house whose width will be 10 meters . So, for the calculations:
- we take the angle equal to 35 degrees;
- We calculate the tangent, it turns out to be 0.7002;
- 10 meters/2 * 0.7002 = 3.5 meters.
The most used today are hipped structures, and to calculate them you can use the same principle (formula) as for how to calculate the height of the ridge of a gable roof, but only the width of the house is divided not by two, but by four. Plus, doing calculations for hipped roof, it is important to take into account the length of the ridge run, as well as the rafter system.
The most complex calculations accompany the arrangement of the roof mansard type, characteristic feature which can be called the presence of two slopes with a break, which from the outside makes it general form as if “broken”. Arrangement sloping roof will increase the functional area of the attic. The calculation of a hip roof is based on the example already discussed above of calculating the height of a gable roof, but do not forget that the roof has not one angle of inclination, but several. Before moving on to settlement operations, you need to decide on them. Practice shows that it is best to choose the following angle values:
- for the lower one - over 40 degrees;
- for the rest - less than 40 degrees, but definitely more than 15.
To simplify calculations, but at the same time quickly obtain the most accurate result, experts prefer to use the “golden section” method; for this purpose, the outline of the roof is inscribed in a circle in the drawing. By resorting to this successful rule, you can easily solve the problem of how to correctly calculate the height of the roof, and most importantly, avoid inaccuracies in the calculation, which in practice will lead to the fact that the overall appearance of the structure will be unaesthetic, inharmonious and simply ugly.
Where to go for help: online resource and consultants
If the roof being erected complex shape, then it requires more voluminous, time-consuming calculations. For calculations, data on the cross-section of the rafters, the pitch between them, and the size of the spans are used truss structure. In addition, the dimensions of roof windows, chimneys, the presence of parapets and overhangs are taken into account; it will be necessary to analyze the possibility of supports and the endurance of the foundation.
Today, anyone who does not know how to calculate the height of a roof can do this by turning to assistants who can be found on the Internet. These could be specialists who are ready to provide you with such services online, or a special Internet resource called a “calculator”, in which case the site visitor enters the requested data and the system performs calculations based on them.
When choosing who to turn to for help, remember that a hip roof is an expensive structure, so it does not tolerate errors and inaccuracies. The correctness of the calculations made must be guaranteed. For beginners, calculating hip, hip and hipped roofs turn out to be quite complex, so it is better to entrust them to a design specialist with experience in this field. You can only do calculations on your own regarding single-pitch structures for outbuildings and garages, or simple gable structures built to cover a small country house.
The classic roof of a Russian hut is gable. The rafter system for it is quite simple, and this has ensured great popularity of this type of roof. Hip roof(four-slope), for example, is geometrically more complex. It is more difficult to calculate and build, so we will take on the calculation of a symmetrical roof with two slopes. Its calculation consists of determining the length of the rafters, which form pairs. Each of these pairs joins its neighbors roof trusses using lathing. The ends of the roof are triangular gables. The length of the rafters, as well as the height of the roof, will be determined by its angle. How to choose it correctly? This will be determined by the prevailing weather in the area.
Selecting the ridge height
Anyone who has been to the Baltic countries or Scandinavia has noticed that the roofs of village houses there are pointed. This is due to the high amount of precipitation, which, in turn, is explained by the predominance of a marine and temperate climate. Water immediately drains from such a roof, and snow does not linger at all. However, the proximity to forested hills reliably protects these settlements from strong winds, so the large windage of such roofs is not of great importance. In Arab houses, the roofs were flat, because the amount of precipitation in desert areas is minimal. But strong dry winds do occur in such areas. Where the winds rage in the middle zone, you can find houses with completely different roofs - almost flat or arched, because the absence of windage or good streamlining plays a big role. And if such houses used to be built intuitively, based on the experience of generations, today for different regions Russia has created sets of rules that describe wind and snow loads on the roof. In particular, this is SP20.13330.2011, developed on the basis of SNiP 2.01.07-85 * “Loads and impacts”. In the central region of the country, for example, it is recommended to choose the height of the ridge so that the angle of inclination of the slopes is approximately 30–45°. It is this angle that will make it possible to calculate both the height of the roof ridge and the length of the rafters.
Let's turn to school geometry. Our roof must be imagined in the form of a triangle, which in fact is each of its gables. Such a triangle will be obtuse. Let's divide it along the axis of symmetry into two right triangles. We received two legs, one of which (a) is known to us - this is half the width of the house. The second leg (b), which is not yet known, is the height of our roof.
b = a * tan α, where:
α is the roof angle taken from the set of rules. The tangent of this angle can be calculated using an engineering calculator or using mathematical tables. The resulting leg b is the height of the roof. Knowing both legs, we can calculate the value of the hypotenuse. This is the approximate length of the rafters. However, since the roof often extends beyond the walls of the house, overhanging them, the length of the rafters can be increased. Here everything depends on the architecture of a particular building. Knowing the length of the rafters and the length of the roof itself, which in this dimension can also protrude beyond the edges of the house, hanging like a canopy over the gables, we can already calculate its area, and therefore the amount of roofing material.
Calculation example
Let's say the house has a width of 6 m. Divide it in half and get 3 m. This is our leg a. The slope angle recommended for building a house in this area is 45°.b = 3 * tan 45° = 3 * 1But even without using this formula, you can guess that with an inclination angle of 45°, our right triangle will turn out to be equilateral. That is, even without tables and a calculator it will become clear that the height of the roof will be equal to 3 m, that is, half the width of the house.
No house can be imagined without a roof. This design is necessary, because it protects the entire building from exposure environment, and correct device roof makes it possible to build an attic or attic.
The roof is exposed to various atmospheric phenomena. If you choose the wrong angle of the slope, and, accordingly, the height, then there is a risk that gusty winds or heavy rainfall can damage the integrity of the structure. At best, it will be necessary to carry out minor repairs, at worst - to build the structure anew.
When designing the construction of any facility, not a single parameter should be neglected, including the value of the roof height. The following series of arguments will confirm the significance correct definition this parameter:
- Long service life and reliability. The most important characteristic, which interests every home owner. An optimally selected roof height will allow the structure to be resistant to the existing loads exerted by roofing materials and other structures, seasonal loads, such as the mass of snow.
- Aesthetics of appearance. When building a house, it is important to take care of its appearance. Incorrect parameters used in the design will not allow the house to look complete and aesthetically pleasing.
- Convenience. Due to the height of the roof, you can build an attic space in the house and adapt it for living or storage, which provides certain amenities and increases the living space of the house.
The highest point of the roof is called the ridge. In other words, this is the junction of the inclined planes of the roof, located in a horizontal plane.
If the height of the roof level is calculated incorrectly and is below or above the required value, then this promises not only an imbalance in the architecture, but also problems during the period of use. The height parameter must correspond to the technological processes.
Atmospheric loads
What does it depend on
A very important parameter that will have to be taken into account in calculations and on which the reliability of the structure depends is the angle of inclination.
There are a number of factors on which this parameter depends, as well as the value of the height of the structure.
Atmospheric phenomena
It is necessary to adapt to such a factor, because it is pointless to resist such phenomena.
From atmospheric factors that affect the roof are the following:
- Wind. The slope angle is selected depending on weather conditions, which are inherent in the zone in which the house is located. If gusty winds prevail in the region, then the angle is chosen to be no more than 10-20 degrees. In other cases, the wind does not affect the angle of the roof slope.
- Precipitation. Region that experiences heavy rainfall It is recommended to choose a slope angle greater than 45 degrees. This roof design allows precipitation to drain quickly.
- Snow mass. Similar to the previous factor, the choice of height depends on the abundance of grazing snowfall in winter. It is advisable to choose a slope angle of 45 degrees or more if snow falls frequently and in large quantities in the region.
All information about the characteristics of the above parameters can be found from SNiP 2301-99.
The need to create an attic
Non-residential buildings are usually built without an attic. and quite light, for example, garages and sheds. For a residential building, it is always necessary to provide an attic space. To use it or not is a personal matter for everyone.
The need to construct an attic space is a factor that affects the value of the roof height based on the comfort of movement around the future room. Namely, there is a need to move around the attic and use it as a residential or storage space.
If the premises are intended to be non-residential, then There are a number of rules for this design:
- fire safety requirements for the house are taken into account when calculating the height of the roof;
- the size of the room should not be an obstacle to maintenance;
- It is necessary to have a through passage, 1.6 m high and 1.2 m long.
Roof type
Exist special rules, based on which the roof height parameter is determined regarding the material for its coating:
- If in roofing material a lot of custom items, then the angle of inclination is selected as large as possible.
- If the roof is selected low, then joints in the roofing material should be kept to a minimum.
- For material large mass elected maximum angle in order to total weight the material was evenly distributed over the surface.
NOTE!
These parameters should be taken into account together to provide reliable and long term roof operation.
Roof height in relation to the width of the house
From this angle, the roof height is determined based 
Pythagorean theorem. For this cross section the structure is represented as an equilateral triangle.
The parameter required for calculations is roof angle. The height of the structure is leg of a right triangle.
The calculation is carried out as follows:
- Necessary determine tangent selected value for the slope angle.
- Knowing the width of the house, one side adjacent to the corner can be calculated by dividing the value by 2.
- Next, the existing values need to be substituted under well-known formula a = b * tg a.
- Using this principle, you can understand the dependence of the height of the ridge on the width of the house. The greater the width of the house, the greater the slope angle.
Ratio of house width to ridge height
Height of the ridge of a gable roof
How to calculate the height of the ridge of a gable roof and not make mistakes? Above is the easiest way to determine the height of the roof for its gable variety. A mathematical formula is used for this. But there is another method of calculation - graphical. Initially, a drawing is made on paper, after which the resulting values are measured.
The principle of this method is to transfer the actual parameters of the roof structure in an exact proportional relationship on a smaller scale.
Despite the fact that the method is considered not as accurate as the mathematical one, it is convenient for many and also allows you to find out the necessary results.
The algorithm of actions is as follows:
- An isosceles triangle is drawn and is drawn to the meridian - this will be the height of the ridge.
- It is necessary to draw a triangle starting from the previously selected angle of inclination depending on the individual parameters of the house and its location.
- In order to accurately draw the angle of the roof, you should use a protractor.
- After the triangle has been drawn, the resulting meridians are measured, i.e. ridge height.
This method is especially convenient for those who are going to equip the attic for a residential space. In this situation, it is possible to clearly identify and indicate all the necessary parameters.
Height of gable roof
Calculation of the height of a hipped roof
Despite the fact that the hipped roof type is much more complex in design, in the calculations you can use parameters and formulas based on the principle of calculating the height of the gable roof variety.
The hipped roof has two types:
- Tent. In this design, all roof slopes have same values length, area and identical in shape. This variety is used in regions with strong winds. It can withstand strong gusty winds and high loads.
- Hip. The slopes are represented by two triangles and trapezoids. This type requires significant costs for materials for its construction, however, it is perfect option for device attic floor . However, this design is not suitable for regions where there are strong gusty winds. In such conditions, the structure needs additional strengthening.
In any of the listed types of roofs for calculations it is necessary to find the figure of a right triangle in the design. This will allow you to determine the values you are looking for.
For a hipped roof, the following method is suitable for calculating the height of a gable roof:
- A right triangle can be found in the design.
- In the figure found, mark the hypotenuse, which will be the rafters, and the other side – the width of the house, divided by 2.
- Based on the tilt angle parameter (tg angle), the third side of the figure is calculated, which represents the height.
Hip roof height
Useful video
You can learn how to determine the height and angle of the roof from the video lesson:
Conclusion
Determining the height for your future home yourself is a simple, but responsible task. Considering that this is a fairly important parameter on which the reliability of the entire structure depends, it is better to entrust such work to specialists. Especially if there are doubts about determining the angle of inclination of the slope. Special programs for design will also help in this matter.
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