Formula for calculating a gable roof. Calculation of a gable roof: area, rafters, height



Specify required dimensions in millimeters

X- width of the house
Y- roof height
C- overhang size
B- roof length
Y2- extra height
X2- extra width


Reference

The program is designed to calculate roofing building materials: quantities sheet material(ondulin, nulin, slate or metal tiles), under roofing material(glassine, roofing felt), number of sheathing boards and rafters.
You can also calculate some useful dimensions roofs.

The program operates in two modes: simple mode gable roof and roofs with two side gables (side roofs), type 1 and type 2.

Attention! If you have a roof with one side gable, then for the calculation use first type 1, then type 2. And from the data obtained, calculate the amount of building materials: rafters, sheathing boards, roofing and sheet materials.
Otherwise there may be an error in the calculation. After all, the program takes into account the cutouts in the main roof for the roofs of the side gables.

In the calculation you will see several numbers: the size or volume of the building material of half the roof and in brackets - the full size or volume.
In counting additional roof- the full size and volume, and two numbers in parentheses: the size and volume of one and two additional roofs.

Attention! When calculating sheet roofing material, keep in mind that the program calculates by roof area.
For example, 2.8 rows times 7.7 sheets per row. During actual construction, 3 rows are laid.
To more accurately calculate the number of roofing sheets, you need to reduce the sheet height in the calculation until you get a whole number of rows.
Don't forget to set the amount of overlap more precisely.

When calculating the volume of material for the rafters of the main roof, in mode type 2, the program does not take into account the cutout for the side gable. This is due to some implementation difficulties in the program.
Maybe I'll solve this in the future.
However, the excess rafter material is unlikely to disappear, or make some adjustments to your calculations.
There will also be a separate program for more intelligent calculation of sheet roofing materials.

And don't forget what to buy Construction Materials it is necessary with some reserve for waste.

When constructing a roof, you cannot skimp on materials so that leaks do not occur in the future, but there should not be any excess left, therefore roof calculation must be as accurate as possible.

What does roof calculation depend on?

If the house is ready, just look at its roof to determine the scope of the measuring work. Simple truss structures will mean easy calculations, for example, it won’t be difficult to figure out how to correctly calculate a gable roof, not to mention a lean-to roof. However, it is very common and more complex options. In particular, pyramidal, broken mansard or half-hip hipped roofs will create certain difficulties for beginners. But even the multi-gable structure that crowns the building can be quickly and, most importantly, correctly calculated in terms of material costs, if you know all the necessary formulas.

Roofing Calculator

Specify all surfaces to be covered.
Sheet typeMetal profile Metal tiles

Necessary:
- - - -

Sheet
working size, not full size!		 x cm
Surfaces

Add everything rectangular roof sections

    L= m H= m
Surfaces

Add everything triangular roof sections

    L= m X= m
Surfaces

Add everything trapezoidal roof sections

    L= X= M= m

First of all, it should be remembered that no matter how many slopes the roof consists of, all surfaces are either already simple geometric shapes or can be divided into them. Further, the roofing calculator requires you to operate in the calculation process with such concepts as the real and effective coverage area. The first is the sheet’s own dimensions, and the second is taking into account the overlap of the row laid above. In other words, some of the material obviously needs to be subtracted, since it will overlap with other sheets. The percentage of losses depends on the slope of the slope and the characteristics of the coating (there is more waste from metal tiles than from roll material) .

Typical solution for calculating roof area

The option with one or two slopes is the simplest; to calculate the dimensions you only need to know the length of the house, rafter leg, as well as overhang (eaves and front). If we add and multiply everything correctly, we get the following formula: S = (L d + 2L fs)(L sn + L x), Where L d– length of the end wall of the house, L fs And L x– the length of the front and cornice overhangs, respectively, and L dn– rafter leg. In other words, the calculator for calculating the roof of a house can be used without climbing out onto it, but by taking all the measurements from the ground, the attic and a stepladder placed against the wall. But do not forget that in this way you get the area of ​​only one slope; to complete the picture, the result must be multiplied by 2.

More complex designs Usually they require measurements of the surface itself, that is, if there is no covering, then using the finished sheathing, and if you need to find out how to calculate the renewal of the roof, then using its old sheathing. Having found out the length and width of each roof plane, we draw its exact layout, and then divide it into the simplest geometric figures . For example, a half-hip consists of two trapezoids, two rectangles and four triangles. Regular broken line mansard roof on projection it will look like one large square or rectangle. The multi-pincer design will differ only in the large number of the above geometric shapes.

Formulas that tell you how to calculate the roof area can be found in school textbook, but for your convenience they will be given below. So, above we have already calculated a rectangle, but that formula was made up of many parameters, but in reality it looks like S = ab, Where a And b- adjacent sides of the figure. The trapezoid can be calculated as follows: S = h(a + b)/2, Where h- height. This option is the most convenient due to the fact that the sides, and, consequently, the angles between them and the base may be unequal. To determine the area of ​​a triangle we take the formula S = bh/2, Where b– the base, and h– the height lowered on it. If at least one angle is 90 degrees, you can use the formula S = ab/2, Where a And b– legs.

Instructions on how to calculate the roof of a house

Above we gave an example of calculation complex roof by drawing up its projection. You can take a simpler route and take a house plan, where the roof is shown schematically on a plane, then determine the area and multiply by the slope coefficient. For example, in order to find out how many rolls are needed soft covering, based on the fact that one roll is enough for 3 square meters, the formula is taken N = SK/3. Here S– area of ​​the created projection, K– slope coefficient, which can be found from the table:

If you are wondering how to calculate the height of the roof, this problem can be solved using the above indicators. For example, the width of the house is 10 meters, and the angle of the rafter leg is 35 degrees. We take half the width and multiply by the slope coefficient equal to 35 degrees, we get 5. 0.79 = 3.95. This is the desired height of the ridge. At the same time, if you know the angle of the slope, you definitely need to choose the right material relative to the steepness of the slope, which can also be done using data from the table, but this time it’s different:

For ondulin, the roofing calculator will be slightly different, since it is known that real area one sheet is 1.82 square meters, but decreases due to the top and side overlap of adjacent sheets to 1.62 m 2. It is precisely with the effective value that you will have to work, calculating the ratio between the area of ​​the roof and the material. In other words, the number of ondulin sheets is calculated by the formula N = S k /S l, Where S to– roof area, and S l– dimensions of the material.

How to calculate a metal roofing?

It is known that roofing metal is one of the most durable materials used for roof cladding. With proper care, such a coating will last up to 50 years or even more under moderate exposure to climatic factors. To calculate how much metal tiles will be needed, you need to find out its dimensions, and, having solved the problem of how to calculate the size of the roof, proceed to determining the number of sheets of material. However, both stages can be combined. To do this we use the formula N=(L ck /V l)(V ck /L l), Where Lck– slope length, V l– sheet width, In ck– width of the slope, and L l– length of the sheet.

When making any calculations, the length of the slope must be taken taking into account the cornice and minus the ridge overlay.

There are other tasks besides calculating the roof; for example, you need to determine other elements necessary for roof cladding. In particular, you will need valleys, ridges, elements of overhangs and cornices. Their number must be determined not in square, but in linear meters, taking into account overlaps, which are usually 10-15%. Also, do not forget about fastening elements, such as long self-tapping screws, which require at least 9 pieces per sheet of material. As for waterproofing, one roll is usually enough for 75 square meters of roof, taking into account overlaps this number will be reduced by approximately 15%. Thus, the roof area must be divided by 63.75 to find out how many rolls of waterproofing you will need.

Online calculators for calculating roofing and roofing are mandatory tools present in the arsenal of architects and professional construction companies. Although, in principle, such calculators are also useful for simple owners of suburban areas who have started building a house with their own hands (here you will also need to calculate the roof). And it’s not surprising, because the quality and accuracy of such calculations directly affect not only the durability of the entire roofing structure, but also on general form Houses. This section of the site contains best calculators for calculating the roof, which will help you in the most common cases when self-construction Houses! Here you will find useful tools for calculating the area of ​​a three-gable roof, the amount of slate, the area hip roof, rafter leg lengths, ridge heights and much more! All online calculators were created by experienced professionals, each tool is accompanied by detailed explanations and instructions for calculation.

What are the advantages of our online calculators? They differ from their numerous (and often paid) analogues in that they do not require downloading to local computer. Complex, carefully tested algorithms are used to carry out calculations, and the calculation results are displayed in a simple and accessible form. Another advantage is that you can add a page with an online calculator of interest to your browser bookmarks and use it at any time!

On a note! When making online calculations, we use building standards, GOSTs and SNiPs, which are adopted in the Russian Federation and the world. In addition, the world practice of modern construction is taken into account.

The roof of the house is load-bearing structure, which takes on the entire external load (weight roofing pie, its own weight, the weight of the snow cover, etc.) and transmits it to everything load-bearing walls at home or on internal supports.

In addition to its aesthetic and load-bearing functions, the roof is an enclosing structure, separating it from external environment attic room.

The basis of the roof of any house is the rafter system.

This is the frame to which the roof is attached.

All loads are taken by this skeleton.

The rafter system consists of:

  • rafter legs;
  • Mauerlat;
  • side purlins and ridge purlins;
  • struts, diagonal braces, braces.

When all these elements (except for the Mauerlat) are connected to each other, a roof truss is obtained.

The basis of such a truss is a triangle, which is the most rigid of the geometric shapes.

The main element of the roof frame is the rafters.

Calculation of rafters

Before you begin directly calculating the rafters, you should find out what loads will affect the roof of the house.

That is, on the rafter legs.

Loads acting on the roof frame are usually divided into constant and variable.

Constant loads are those loads that act constantly, regardless of the time of day, season, etc.

This is the weight of the entire roofing cake, the weight additional equipment, which can be installed on the roof (fencing, snow retainers, aerators, antennas, etc.).

Variable loads appear at certain times of the year.

For example, snow.

When snow falls on the roof, this is a very decent weight.

In any case, it should be taken into account.

It's the same with the wind.

It's not always there, but when the wind blows strong, there's quite a lot of wind force acting on the roof frame.

And an inexperienced person is unlikely to succeed.

It's worth a try though.

Just remember when calculating a large number of various factors affecting the roof.

At least the weight itself rafter system with all elements and fasteners.

Therefore, professionals use special tools to calculate rafters. computer programs and calculators.

How to find out the load on the rafter legs?

The collection of loads should begin with determining the weight of the roofing pie.

If you know what materials will be used and the area of ​​the slopes, then it’s easy to calculate everything.

It is customary to calculate how much 1 square meter of roofing weighs.

And then multiply by the number of squares.

Let's calculate the weight of a roofing pie as an example.

The roofing material is ondulin:

  1. Ondulin. A square meter of ondulin weighs 3 kg.
  2. Waterproofing. If polymer-bitumen insulation is used, then it weighs 5 kg/square meter.
  3. Insulation. Weight of one square basalt wool is 10 kg.
  4. Lathing. The boards are 2.5 cm thick. Weight square meter 15 kg.

We sum up all the weights: 3+5+10+15= 33 kg.

Then the value obtained as a result of the calculations should be multiplied by a factor of 1.1.

This is a correction factor.

It turns out 34.1 kg.

How much does 1 sq. meter of our roofing cake.

And if the total area of ​​our roof is 100 square meters, then it will weigh 341 kg.

Snow load calculation

There is a snow load map.

It shows the amount of snow cover in each region.

We calculate the snow load using the following formula: S = Sg x µ.

Sg is the mass of the snow cover.

µ—correction factor.

And this coefficient depends on the angle of inclination of the slopes of your roof.

The larger this angle, the lower the value of this coefficient.

At tilt angles greater than 60 degrees it is not used at all.

Since snow does not collect on the roof.

Calculating wind load

Just as the whole country is divided into regions according to the mass of snow, it is also divided according to the strength of the winds.

And there is also a special map on which the wind strength is indicated in each area.

To calculate wind loads, use the formula:

Wo - indicator taken from the map.

k is an adjustment factor depending on the type of terrain where the building is located and its height.

We calculate the cross-section of the rafter leg

The cross-section of the rafters depends on three factors:

  • on the length of the rafters;
  • on the distance between the railings;
  • from loads acting on the roof.

Knowing these parameters, it is easy to determine from the table.

How to calculate the length of the rafter legs of a pitched roof

Of all the types of roofs, the shed roof is the simplest.

There are no complex elements in it at all.

And it is installed on load-bearing walls that have different heights.

This kind of roofing is installed on garages, bathhouses, and utility rooms.

To calculate what the length of the rafters of a pitched roof will be, you need to determine the angle of inclination.

And the angle of inclination of the slope depends, first of all, on the type of roofing material that you want to use.

In the case when it is corrugated board, then optimal angle the inclination is 20 degrees.

But it is prohibited to make an angle less than 8 degrees!

Otherwise, in the cold season, the roof will not withstand the weight of the snow cover and will simply fail.

If you are laying metal tiles, then minimum angle the tilt increases to 25 degrees.

When using slate - 35 degrees.

If the roof is seam, then the angle of inclination can be different: 18 - 35 degrees.

After you have figured out the angle of the slope, you need to raise the back wall to such a height that you get the desired angle.

The most difficult thing in such calculations is to find the sine and tangent.

But for this they use the following sign:

Roof inclination angle, degrees Tangent tgA Sine sinA
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

For example, let's find the length of the rafters and the height of the facade wall for a house 5 meters long.

The tilt angle is 25 degrees.

To determine the height of the front wall, Lbc x tg 25 = 5 x 0.47 = 2.35 meters.

Accordingly, the length of the rafter leg is Lc = 2.35 x 0.42 = 5.6 meters.

And do not forget to add to the resulting length the length of the front and rear overhangs, which are necessary in order to provide the walls of the building with protection from slanting rain.

On average, the length of one overhang is 0.5 meters.

If required, this length can be longer.

But less than 0.5 meters is impossible.

This means that 1 meter should be added to the length of the rafter: Lc = 5.6 + 1 = 6.6 meters.

Calculation for a gable roof

The rafter system of a gable roof is much more complex than the rafter system of a shed roof.

There are more elements, and the principle of its operation is somewhat different.

To calculate the length of the rafter leg, we use the Pythagorean theorem.

If you look at the picture shown right triangle, then you can see that the hypotenuse b is our rafter.

And its length is equal to the length of the leg divided by the cosine of the specific angle of inclination of the slopes.

For example, if the width of the house is 8 meters, and the angle of inclination of the slopes is 35 degrees, then the rafter leg will have the length:

b= 8 / 2 / cos 35 = 8 / 2 / 0.819 = 4.88 meters.

Now all that remains is to add the length of the canopy, approximately 0.5 meters, to get the required length of the rafters.

It should be said that these are simplified options for rafter calculations.

In order to obtain the most accurate data, it is best to use special programs.

For example, free program"Arkon".

The built-in calculator, based on the parameters specified by you, will automatically calculate both the cross-section of the rafter leg and the length of the rafter.

Video about the rafter calculation program.

At the design stage gable roof there is a need to calculate the amount of roofing material. To do this, find the area of ​​the gable roof, taking into account gable and eaves overhangs, superstructures, ventilation, etc. To calculate the area, it becomes necessary to calculate a number of roof parameters. The main parameters include:

  • roof angle;
  • length by ridge run or eaves overhang (which is the same thing);
  • length of slopes;
  • height from ceiling to ridge.

Calculation of roof slope angle

The slope of the slopes is determined at the design stage and depends on the choice roofing, climatic conditions, type attic space(cold or attic), the design of the roof itself.

If the house will be built in places with strong wind loads, then they try to make the slope small in order to reduce the load on the roof. When building a house in regions with heavy rainfall, the slope is made significant (up to 60°) in order to reduce the load from snow, melt and rain water.

However, there is a need to find out the slope angle of the constructed roof. In this case, an inclinometer or simple trigonometric formulas are used.

But, more often than not, a novice builder does not have an inclinometer at hand, and geometry comes to the rescue. Let's take a gable roof and look at its section along the ridge. The resulting cross-section is pitched roof, the shape of which is a right triangle.


The first leg acts as half the width of the house. The second leg is the height from the ridge to the ceiling. Hypotenuse is the length of the slope. Knowing any two parameters, you can easily calculate the slope. Let us give an example for greater clarity and understanding.

The width of the house is 8 meters, the length of the rafter leg is 10 meters. Slope gable roof is found from the following expression:

where A is the roof slope angle;

c – half the width of the house;

b – length of the rafter leg.

In this example, half the width of the house will be c=8÷2=4 meters. Let's calculate the slope:

cos A=4÷10=0.4.

The resulting value is the radian measure of the angle. To convert radians to degrees, we use the Bradis table, which is widely available on the Internet. The desired slope will be 66°.

Determining the height of a gable roof

After determining the slope of the gable roof, it is necessary to calculate the height of the ridge. Knowing the height of the ridge, you can use trigonometric expressions to calculate the length of the slope, which is the length of the rafter leg.

Height can be calculated in two ways:

  • using a right triangle;
  • using a table of ratios of the angle of inclination to percentages.

The first method of calculating the height is using the values ​​of the angle of inclination and half the width of the house. Let's look at an example for clarity. The width of the house is 12 meters, the slope is 40°.

Half the width of the house will be:

The height of the ridge is determined trigonometric formula for right triangle:

a=c×tg A=6×tg 40°=6×0.84=5.05 m.

To find the tangent of 40°, the Bradis table was used, as in the example above.

In order not to look for a value in the Bradis table, you can use an engineering calculator that is installed on any operating system!

The second option for determining the height of the ridge is to use the table of ratios given below.


Here, each angle of inclination corresponds to a certain relative value, expressed as a percentage. The height is found by multiplying half the width of the span of the house by relative size. Let's look at an example for clarification. Let's take a house with a span width of 7 meters and a slope angle of 27°. The height of the ridge will be:

(7÷2)×0.509=3.5×0.509=1.78 m.

Determining the area of ​​a gable roof

When finding the area of ​​a gable roof, the following points must be taken into account::

  • The total area will be the sum of the areas of each of the slopes. Therefore, first find the area of ​​one slope and multiply by two;
  • Rarely, there are cases when the slopes in a gable roof may differ in one or more parameters (sizes). In this case, the area of ​​each slope is calculated separately. total area is found by summing the areas of individual slopes;
  • It is necessary to take into account that if the roof slope is an irregular rectangle (i.e. at least one of the angles of the quadrilateral is not equal to 90°), then the slope should be “broken” into more simple figures and find areas for them. When such a situation arises, the slope is divided into a rectangle and a right triangle;
  • When finding the area, chimney pipes, auditory and skylights, holes for ventilation;
  • Pediment and cornice overhangs, parapets, and firewall walls are taken into account.

Consider finding the area on simple example. The box of the house has dimensions of 7x9 m, the length of the rafter leg is 4 meters, the eaves overhang is 0.4 meters, and the gable overhang is 0.6 meters. The area of ​​one slope will be:

S=(L dd +2×L fs)×(L c +L x);

where Ldd is the length of the house (9 meters);

L fs – value of the length of the gable overhang (0.6 meters);

L c – length of the rafter leg, i.e. slope length (4 meters);

L ks – length of the eaves overhang (0.4 meters).

Let's find the required area of ​​the slope:

S=(9+2×0.6)×(4+0.4)=10.2×4.4=44.9 m2.

Square gable roof will be:

S=2×44.9=89.8 m2.

If you use a covering made of tiles or rolled material, the length of the slopes will decrease by 0.6-0.8 meters.

Roofing area

The area of ​​a gable roof is calculated in order to find out required amount material that will be placed on the roof. The steeper the roof slope, the more material will be required to cover it. It is recommended to purchase material with a reserve of 8-15%. This overspending is caused by the overlap with which the material is laid. To determine the missing material, you should use a table that takes into account the slope and determines the material reserve factor.


When calculating the area of ​​a gable roof, you must take all measurements correctly and use a roofing calculator on the Internet to check self-calculation. In addition, if the calculation is done correctly, you will not have to buy additional material.