How do you calculate the area

How to calculate the square the room, the walls, ceiling and floor

From time to time we need to know the area and volume of the room. These data may be needed in the design of heating and ventilation, the procurement of materials and even in many other situations. Also need to know the wall surface periodically. All these data are easy to calculate, but first have to work with a tape measure - measuring all the required dimensions. To learn how to calculate the area of ​​a room and the walls, the amount of space and will be discussed further.

Often it needs to calculate the cubic capacity of the room, its volume

Room area in square meters

Calculate simple, you only need to remember a simple formula as well as to carry out measurements. It will need:

  • Roulette. Better - with lock, but the fit and normal.
  • Paper and pencil or pen.
  • Calculator (or read in a column, or in the mind).

A set of simple tools, there is in every household. Simply measurements carried out with an assistant, but it is possible to cope on their own.

First you need to measure the length of the walls. Doing this, it is desirable along the walls, but if they are made to heavy furniture, it is possible to measure and in the middle. Only in this case to follow the roulette tape lying along the walls, rather than obliquely - the measurement error will be less.

If the room is the correct form, with no protruding parts, calculate the area of ​​the room is simple. Measuring the length and width, recording on paper. Write numbers in meters, centimeters after the comma. For example, 4.35 m length (430 cm), width of 3.25 m (325 cm).

How to calculate the area of ​​a room

Point numbers multiply, we get the area of ​​the room in square meters. If we turn to our example, we get the following: 4.35 m * 3.25 m = 14.1375 sq. m. In this magnitude usually leave two digits after the decimal point, then rounded. Total calculated by squaring the room 14.14 square meters.

If you need to calculate the area of ​​a room of irregular shape, it is divided into simple shapes - squares, rectangles, triangles. Then measure all the necessary dimensions, calculations on known formulas (there is little in the table below).

Before you calculate the area of ​​a room, is also making changes. Only in this case, the numbers will not two, but four: Add more length and width of the protrusion. Dimensions of both pieces are considered separately.

One example - in the photo. So like that, and another - a rectangle, the area is considered to be on the same formula: multiply the length by the width. Figure should be found to take away or add to the size of the room - depending on the configuration.

The area of ​​the complex shape of the room

We show in this example how to calculate a projection area of ​​the room (shown pictured above):

  1. We believe without quadrature protrusion: 3.6 m * 8.5 m = 30.6 sq. m.
  2. We consider the size of the protruding portion: 3.25 m * 0.8 m = 2.6 sq. m.
  3. Add together two quantities: 30.6 sq. m. + 2.6 kb. m. = 33.2 sq. m.

Still there are rooms with sloping walls. In this case, we break it so as to obtain rectangles and triangles (as shown below). As you can see, in this case it is required to have five sizes. Break could be in another way, by placing a vertical rather than a horizontal line. It does not matter. Just requires a set of simple shapes, and the way to separate them is arbitrary.

How to calculate the irregular-shaped area of ​​the room

In this case, the order of evaluation is:

  1. We consider a large rectangular portion: 6.4 m * 1.4 m = 8.96 sq. m. If the round, we get 9, 0 sq.m.
  2. We calculate the small rectangle: 2.7 m * 1.9 m = 5.13 sq. m. Rounding it, we get 5.1 square meters. m.
  3. We consider the triangle area. Since it is a right angle, that is equal to half the area of ​​a rectangle with the same dimensions. (1.3 m * 1.9 m) / 2 = 1,235 sq. m. After rounding obtain 1.2 kb. m.
  4. Now all add up to find the total area of ​​the room: 9.0 + 5.1 + 1.2 = 15.3 sq. m.

Layout of the premises can be very varied, but the general principle you understood: divide by simple shapes, measure all the required dimensions, calculate the quadrature of each piece, then all add up.

The formula for calculating the area and perimeter of simple geometric shapes

One important note: area of ​​the room, the floor and ceiling - it's all the same size. Differences can be if there is some kind of semi-columns, not reaching to the ceiling. Then, out of the total of squaring squaring the subtracted these elements. The result is a floor area.

How to calculate the square the walls

Determination of the area of ​​the walls is often required in the purchase of finishing materials - wallpaper, plaster, etc. For this calculation, additional measurements are necessary. To the already existing width and length of the room will be needed:

  • ceiling height;
  • the height and width of doorways;
  • width and height of window openings.

All measurements - meters, as squaring the walls, too, usually measured in square meters.

The preferred size applied to the plan

Since the walls are rectangular, and the area is considered as a rectangle: multiply the length by the width. In the same way we calculate the size of windows and doorways, their dimensions subtract. For example, calculate the area of ​​the walls depicted in the diagram above.

  1. Wall with door:
    • 2.5 m * 5.6 m = 14 sq. m. - the total area of ​​the long wall
    • how long it takes the doorway: 2.1 m * 0.9 m = 1.89 sq.m.
    • Wall excluding doorway - 14 m - 1.89 sq. = 12.11 sq m. m
  2. Wall with window:
    1. squaring small wall: 2.5 m * 3.2 m = 8 sq.m.
    2. how long it takes the window: 1.3 m * 1.42 m = 1,846 sq. m, rounded obtain 1.75 sq.m.
    3. without the wall of the window opening 8 sq. m - 1.75 m = 6.25 sq.m.

Find the total area of ​​the walls is not difficult. Fold all four digits: 14 sqm + 12.11 sqm + 8 sqm + 6.25 sqm = 40.36 sq. m.

The formula for calculating the volume of the room

For some calculations required room volume. In this case, the three values ​​are multiplied by width, length and height of the room. This value is measured in cubic meters (cubic meters), also called the cubic capacity. For example, using data from the previous paragraph:

If all multiply, we obtain: 5.6 m * 3.2 m * 2.5 m = 44.8 m 3. Thus, the volume of the room 44.8 cube.

How to calculate the area of ​​the premises before repair?

Before you begin to repair, it is important to correctly calculate the amount of building materials. To do this, you must know the materials consumption rates per 1 sq. m., and treated surface area. Here you can learn how to calculate square meter.

Norms preliminary materials costs often indicate on the packaging, and if not specified, it is possible to find them in the directory. The area of ​​the house or apartment morzhno calculate self parking. It is usually measured in square meters. m. with two characters after the decimal point.

Be careful when measuring. Roulette or measuring tape is often on the other side of the tape are applied to the division in inches.

How to calculate the area of ​​the room?

By any calculation must be applied very simple formula mathematics and their designations. To obtain correct results, it is important to accurately determine the three basic sizes. Measurements were carried out up to see, using the rounding rules of mathematics.

  1. The length of the room is denoted by the letter A;
  2. Width - the letter B;
  3. The height of the ceilings - the letter S.

Pre-calculate the perimeter of the premises (P):

  • For room rectangle shapes P = (A + B) x 2;
  • For any other tetrahedron P = (A1 + A2 + B1 + B2).

where A1, A2 - two long opposite sides, B1, B2 - two short sides of the quadrangle.

The measurement area proper shape of the room

Cuboid - the ideal form of the room.

For repair purposes must be properly racesto read:

To calculate the area of ​​a rectangle offer the classic formula of the school textbook: S = A x B, Where

Wall area calculated by the formula S = P × C Where R - the perimeter of the room, FROM - ceiling height.

The apartments are often the opposite walls are slightly different in size. Ceiling height in different parts of the apartment can also be different. Then take computing mean values: (A1 + A2) / 2 = A sa, Where A1 and A2 opposite directions A sa - the arithmetic mean value.

Measurement area irregularly shaped spaces

The apartments are sometimes the room, other than a rectangular shape. In private homes, they are more common. If necessary, calculate the floor area of ​​a complex figure, divide it into rectangles, triangles and sectors. Calculating each of them add up.

  1. For a circular shape of the room Use formula range: S = πD² / 4, Where D - the diameter of a circle (room).
  2. Expecting an area of ​​a triangle use Heron's formula S = √ (P / 2 (P / 2 -A) x (R / 2 - V) x (R / 2 - C)), Where A, B, C - side of the triangle, R - its perimeter. The square root function is in each calculator.
  3. Terraces of private homes, often they take the form of a semicircle. Their area will consist of the sum of areas of a rectangle and a semicircle.
  4. The terrace design instead of the semi-circle is often used segment. Calculation of the segment area is quite complex. S segment =R 2/2 (πα / 180 -sinα), Where α - segment angle (between the points of the chord and the circle center), expressed in degrees.

It is necessary not only to measure the angle, but also to calculate its sine. Therefore, we offer an option through the calculation of the circle sector:

Room with an alcove or projections

It most commonly refers to an apartment kitchen. In old buildings housing in kitchens ventilation shafts are arranged forming both recess and protrusions.

  1. Floor or ceiling area is considered, in this case the same. If the room has a niche, then add it to the area of ​​the area of ​​a rectangle. If a projection - the take away.
  2. The area of ​​the walls does not change, if there is a projection. And if there is a niche, it will increase. Area wall with the niche is calculated by the previously given formula S = P × C, with one clarification: For perimeter must sum all the length and width of walls.

How do I know the general area of ​​door and window openings?

These openings usually have a rectangular shape, so calculated with the standard formula for rectangles. To obtain a surface area to be repaired, it is necessary from the calculated area obtained walls take sum of the areas of windows and doors.

For the arched openings, apply the formulas for calculating the area of ​​a rectangle, sector and summarizes the results.

Calculation of the area under the wallpapering

The cosmetic repair of the premises is always included painting ceilings and walls pasting wallpaper. It is important to correctly calculate the amount of wallpaper on the wall surface.

  1. Wallpapers of different parties differ from each other in tone color and depth of the relief. The need to re-buy a roll of wallpaper brings another party for a certain imbalance in the room.
  2. good quality wallpaper expensive. In order not to spend the extra money, it is important to within one roll to calculate the amount of materials.
  3. Examples of calculation area under the wallpaper to the standard rectangular space length of 5 m, a width of 4 m and exclude window width (1.4 m) and the door (1.5 m). The total perimeter of the premises will be (4 + 5) x 2 - (1.4 + 1.5) = 15.1 m.
  4. For rooms with a ceiling height of 2.6 m full area gluing strips of: 15.1 x 2.6 = 39.26 sq. m.
  5. With one roll of 10 m length obtain three full band: 10 / 2.6 = 3.85. This result is independent of the need for selection of drawing. Remains roll used for wallpapering over the doors and windows.
  6. Wallpapers are available in two standard sizes - 0.53 m and 1.06 m. There are wallpapers of 0.70 meters, but they are less common in our market. Wallpaper double-width (1.06 m) to quickly and easily glue on the smooth walls of large area.

If there are few indoor windows and doors, economical use wallpaper width 0,53 m. When working with them get less waste.

  • The area of ​​the three bands Wallpaper odinarhydrochloric width is: 2.6 x 0.53 x 3 = 4.13 sq. m. For pasting premises need to buy 39.26 / 4.13 = 10 rolls of wallpaper.
  • If there is a contract furniture in the room, for which no intention pasting, to save expensive number of rolls to be subtracted from the length of the perimeter wall, for example, 3 m obtain a result.: 15.1 - 12.1 = 3. In this case, the area will be 12.1 x 2.6 = 31.46 sq. m. Number of rolls 31.46 / 4.13 = 8 pieces.
  • When choosing wallpaper, length 15 m, the number of full bands from the roll will 15 / 2.6 = 5, which will make the area 0.53 x 5 = 2.65 sq. m. In our room needed 15.1 / 2.65 = 6 rolls.
  • In mathematics, there are many ways to calculate areas of figures of different configurations. In our recommendations, we are given the simplest ways to calculate the areas as simple shapes (rectangles) and more complex (segment). Arm yourself with tools and patience. You will succeed.

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    area figures

    The two figures are called equal if one of them you can apply to the other, that these figures coincide.

    Square shapes are equal. Their perimeters are also equal.

    To calculate the area of ​​the square is necessary to multiply its length by itself.

    SEKFM = EK · EK

    Formula area of ​​the square, knowing the determination of the degree can be written as follows:

    to calculate area of ​​a rectangle you need to multiply the length by the width.

    SABCD = AB · BC

    It is impossible to calculate the perimeter or area, if the length and width are expressed in different units of length.

    Be sure to check that both the length and the width were expressed in the same units, i.e. two in centimeters, meters, etc.

    The area of ​​the whole figure is the sum of squares of its parts.

    Objective: to find Horticultural land area.

    Since the figure in the picture is neither square nor rectangular, calculate its area is possible using the rule above.

    Divide the figure into two rectangles, whose areas we can easily be calculated by a known formula.

    SABCE = AB · BC

    To find the area of ​​the whole figure, add the area found the rectangles.

    S = 30 + 35 = 65 m 2

    Answer: S = 65 m 2 - Horticultural land area.

    The property is less than you might find useful in solving problems in the area.

    Diagonal of a rectangle divides the rectangle into two equal triangles.

    The area of ​​any of these triangles is half the area of ​​a rectangle.

    AC - diagonal rectangle ABCD. We find the area of ​​a triangle ABC and ACD

    First find the rectangle area formula.

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