Periodically, we need to know the area and volume of a room. This data may be needed when designing heating and ventilation, when purchasing building materials and in many other situations. It is also periodically required to know the area of the walls. All these data are calculated easily, but first you have to work with a tape measure - measure all the required dimensions. How to calculate the area of a room and walls, the volume of a room, and will be discussed further.
Room area in square meters
- Roulette. Better - with a retainer, but the usual one will do.
- Paper and pencil or pen.
- Calculator (or count in a column or in your head).
A simple set of tools can be found in every household. It is easier to take measurements with an assistant, but you can do it yourself.
First you need to measure the length of the walls. It is advisable to do this along the walls, but if they are all lined with heavy furniture, you can take measurements in the middle. Only in this case, make sure that the tape of the tape lies along the walls, and not obliquely - the measurement error will be less.
Rectangular room
If the room is of the correct shape, without protruding parts, it is easy to calculate the area of the room. Measure the length and width, write it down on a piece of paper. Write the numbers in meters, after the comma, put centimeters. For example, length 4.35 m (430 cm), width 3.25 m (325 cm).
We multiply the found numbers, 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 value, usually two digits are left after the decimal point, which means we round off. In total, the calculated area of the room is 14.14 square meters.
Irregular room
If you need to calculate the area of a room of irregular shape, it is divided into simple shapes - squares, rectangles, triangles. Then they measure all the required dimensions, make calculations according to the well-known formulas (there is in the table just below).
One of the examples is in the photo. Since both are rectangles, the area is calculated using the same formula: the length is multiplied by the width. The figure found must be subtracted or added to the size of the room - depending on the configuration.
Complex room area
- We consider the square without a ledge: 3.6 m * 8.5 m = 30.6 sq. m.
- We consider the dimensions of the protruding part: 3.25 m * 0.8 m = 2.6 sq. m.
- We add two values: 30.6 sq. m. + 2.6 sq. m. = 33.2 sq. m.
There are also rooms with sloping walls. In this case, we split it so that we get rectangles and a triangle (as in the picture below). As you can see, this case requires five sizes. It was possible to break it down in a different way by placing a vertical rather than a horizontal line. It does not matter. You just need a set of simple shapes, and the way you select them is arbitrary.
In this case, the order of calculations is as follows:
- We consider the large rectangular part: 6.4 m * 1.4 m = 8.96 sq. m. If we round up, we get 9, 0 sq. m.
- We calculate the small rectangle: 2.7 m * 1.9 m = 5.13 sq. m. Rounding up, we get 5.1 square meters. m.
- We consider the area of the triangle. Since it has a right angle, it 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, we get 1.2 square meters. m.
- Now we add everything to find the total area of the room: 9.0 + 5.1 + 1.2 = 15.3 sq. m.
The layout of the premises can be very diverse, but you understand the general principle: we divide into simple shapes, measure all the required dimensions, calculate the quadrature of each fragment, then add everything up.
Another important note: the area of the room, floor and ceiling are all the same size. Differences can be if there are some semi-columns that do not reach the ceiling. Then the quadrature of these elements is subtracted from the total quadrature. As a result, we get the floor area.
How to calculate the squaring of walls
Determination of the area of the walls is often required when purchasing finishing materials - wallpaper, plaster, etc. This calculation requires additional measurements. To the already existing width and length of the room, you will need:
- ceiling height;
- height and width of doorways;
- height and width of window openings.
All measurements are in meters, since it is customary to measure the squaring of walls in square meters.
Since the walls are rectangular, then the area is considered as for a rectangle: we multiply the length by the width. In the same way, we calculate the dimensions of windows and doorways, subtract their dimensions. For example, let's calculate the area of the walls shown in the diagram above.
- Wall with door:
- 2.5m * 5.6m = 14 sq. m. - the total area of the long wall
- how much does the doorway take: 2.1 m * 0.9 m = 1.89 sq.m.
- wall excluding doorway - 14 sq.m - 1.89 sq. m = 12.11 sq. m
- Wall with window:
- square of small walls: 2.5 m * 3.2 m = 8 sq.m.
- how much the window takes: 1.3 m * 1.42 m = 1.846 sq. m, we round up, we get 1.75 sq.m.
- wall without window opening: 8 sq. m - 1.75 sq.m = 6.25 sq.m.
Finding the total area of the walls is not difficult. Add up all four numbers: 14 sq. M + 12.11 sq. M. + 8 sqm + 6.25 sqm = 40.36 sq. m.
Room volume
Some calculations require the volume of the room. In this case, three quantities are multiplied: width, length and height of the room. This value is measured in cubic meters (cubic meters), also called cubature. For example, we use the data from the previous paragraph:
- length - 5.6 m;
- width - 3.2 m;
- height - 2.5 m.
If we multiply everything, we get: 5.6 m * 3.2 m * 2.5 m = 44.8 m 3. So, the volume of the room is 44.8 cubic meters.
Choose a tape measure or measuring tape. Choose a tape measure or measuring tape with graduations in centimeters (cm) or meters (m) on it. This device will make it easier to calculate the area in square meters, since they were designed in the same measurement system.
- If you find a tape measure in feet or inches, measure the area using the available units, and then skip to the step for how to convert other units to square meters.
Measure the length of the area you selected. Square meter is a unit of measure for the area or size of a two-dimensional object such as a floor or field. Measure the length of one side from one corner to the other and record the result.
- If the length is more than one meter, then count both meters and centimeters. For example, 2 meters 35 centimeters.
- If the object you are measuring is not a rectangle or square, then read the third section of this article - "Measuring the area of complex shapes".
If you cannot measure the length at one time, please do it in stages. Spread out the tape measure and mark where it ended (for example, 1 meter or 25 centimeters), then unfold it again and start from the marked area. Repeat until you have measured the entire length. Then add all measurements together.
Measure the width. Use the same tape measure to measure the width of the object. Begin measuring with the tape measure at a 90 ° angle to the length of the object you have already measured. That is, two lines of a square adjacent to each other. Also write the resulting numbers on paper.
- If the measured length is slightly less than one meter, then round towards the nearest centimeter when measuring. For example, if the width is slightly more than the 1 meter 8 centimeters mark, then simply write down "1 m. 8 cm." and don't count millimeters.
Convert centimeters to meters. Usually, measurements cannot be made exactly in meters. You will get indicators both in meters and in centimeters, for example "2 meters 35 centimeters". 1 centimeter = 0.01 meter, and therefore you can convert centimeters to meters by moving the comma 2 digits to the left. Here are some examples.
- 35cm = 0.35m, so 2m 35cm = 2m + 0.35m = 2.35m
- 8cm = 0.08m, so 1m 8cm = 1.08m
Multiply the length by the width. Once you convert all measurements to meters, multiply the length by the width and get the area of the object being measured. Use a calculator if necessary. For instance:
- 2.35m x 1.08m = 2.538 square meters (m 2).
Round up. If you get a lot of digits after the decimal point, for example, 2.538 square meters, then round, for example, to 2.54 square meters... It is likely that you did not measure to the nearest millimeter, so the last digits will still not be accurate. In most cases, we round to the nearest centimeter (0.01m). If you need more accurate measurements, read this material.
- Every time you multiply two numbers with the same units of measurement (for example, meters), the answer must be written in the same unit of measurement (m 2, or square meters).
Any surface in the room is subject to repair, be it walls or floors, so it is very important to know how to calculate the area of a room in whole or in parts.
But in an ordinary room, the floor always corresponds to the ceiling and is often calculated using the formula for a rectangle S = AB, where A and B If you are going to make repairs in a house that was not built by you or without your participation or control, make sure that the lengths of the opposite walls in each room are the same... A room sometimes looks like a perfect rectangle, but in fact, one wall may be several centimeters shorter than the other.
Using the above formula, you will get a fair amount of error. To avoid it, measure the correct rectangle, and for all deviations from it, count the square meters separately. Most likely, you will have to deal with triangles in which 2 sides converge at 90 degrees, so the formula will be the following S = AB / 2, where A and B- the length of the legs.
The biggest difficulty faced by those who started repairs on their own is irregularly shaped rooms. For example, it is difficult to perform calculations if, for example, an arched partition separates the living room from the corridor. Therefore, in this case, before calculating the square meters on which the room will be repaired, it is necessary to clearly define the border, as well as the bending radius of the wall.
Further, in order not to mess with the sines and cosines of the angles, we take the arc and the two radii that bound it as a sector of the circle and calculate its square meters: S = Lr / 2, where L- the length of the arc, and r- radius, the values of which are not difficult to find out by measurements. Now you need to determine the distance between the ends of the arched bend of the room. This will give us a chord of the calculated sector, together with the radii, it will form a triangle, the area of which is found by the formula S = b√ (4a 2 - b 2) / 4, where b- the base of the triangle (sector chord), a- its side (sector radius).
Subtract the quadrature of the triangle from the previously determined area of the sector and get the value for a complex section of the room that has the shape of a segment. To make it easier to determine the square meters for planning a complex configuration, it is enough to divide the room into simple shapes and calculate the area for each separately, and then add the results.
Consider the option when you need to make repairs in a room with 5 walls. If this is just a standard room, one of the corners of which is cut off, then everything is quite simple. First, we consider the area as if it were an even rectangle, that is, along the two longest adjacent sides, the formula S = AB. Then we draw from the ends of the fifth wall lines perpendicular to each other, converging at one point, and measure the resulting sides of a right-angled triangle. Next, we calculate by the formula S = AB / 2 and subtract the resulting value from the result of the first formula.
But it happens that the room has a "branch" leaving at an obtuse or acute angle to the main space. That is, the area includes not only 2 rectangles, but also a versatile triangle. Having determined its boundaries, we measure them, and then we use Heron's formula S = √ (p (p - a) (p - b) (p - c)), where p- semi-perimeter, which is calculated as follows p = (a + b + c) / 2, here and earlier a, b and c- the sides of the triangle. We sum up the result obtained with the solutions for two rectangles that make up the wrong layout of the room.
We calculate the area of the walls
Plasterboard cladding, plastering, painting, tiling - these and other types of work involve the repair of walls, which are an integral part of the room. Accordingly, for them, you also need to correctly calculate the area. All calculations are based on measurements of the perimeter of the room and its height. The results are substituted into the formula S = Ph, here h- height, and P(perimeter) is calculated as follows: P = 2 (A + B), where A and B- the lengths of adjacent walls that have a common angle.
Are you planning to buy or sell an apartment, furnish it, or are you just starting a renovation? In any such case, the price of the issue depends on the exact dimensions of each individual room. You can hire specialists to carry out the calculations, but this will entail additional costs. To avoid them, we suggest that you figure out how to calculate the area yourself.
How to calculate the area of a room - step by step instructions
When calculating the area, you need to know the length, width and height of the room.You can, of course, look into the technical documentation at home and see all the necessary characteristics in it. But, firstly, there are often errors, and secondly, sometimes it’s easier to calculate everything yourself than to find documents.
To carry out the calculations, we need certain tools, most of which can be easily found in every home. Namely:
- roulette;
- pencil;
- note paper;
- calculator (you can use the calculator posted on our website);
- sobriety of mind and clarity of thought.
Floor
It is better to take measurements at the base of the walls, and for this it is advisable to move or take out all the furniture. But, if such a procedure was not included in your plans, you can measure it in the center. The main thing is that the imaginary line along which the measurement will be made is located at an angle of 90 ° to the wall.
After the measurement data are obtained and verified, they must be multiplied by the formula, where S is the area in square meters, a and b are the length and width, respectively.
If there is a niche or some other adjacent to the main room, its area must be calculated using the same algorithm, and the results added to the area of the room. If there are various protrusions that occupy a part of it, they should also be measured and the result obtained is subtracted from the total.
It's simple with squares and rectangles. But how to count if it has an irregular shape? Here you will have to apply logical thinking, and recall a little the school course in algebra and geometry. But let's start in order.
Calculator
If the room is irregular
Try mentally or on paper to divide the room into simple elements (squares, rectangles, triangles). Next, you will need to calculate the size of each of them, and add the results.
- for a triangle -. Where a is the length of the base of the triangle, b is the height drawn from the top to the base;
- for a circle -. Where 3.14, r is the radius of the circle (to find out the radius - use a tape measure to find the longest distance between the walls and divide it by 2);
- for a semicircle - (the letter designations are the same as the previous paragraph).
As it turned out, in this case there is nothing complicated either. The main thing is to carefully check the measurement results so that an accidental error does not creep into the calculations, and they do not have to be repeated.
And further. If you want to make installation, do not forget to separately calculate the area occupied by the furniture and subtract it from the total value for the room.
We figured out the floor. But when preparing, for example, for re-gluing wallpaper, this will not help you much. You will need to find out the exact number of square meters that the walls occupy.
Walls
The area of each individual wall can be calculated in the same way as the square of the floor. Only now, instead of the width of the room, it will be necessary to measure its height. We multiply the length of the wall by the height and get the result we need in square meters.
And you can calculate for all walls at once. To do this, you need to know the perimeter of the space. Take a tape measure and measure the length of each wall, add the results - this will be the perimeter. It remains to measure the height of the room and use the following formula: where p is the perimeter and h is the height.
Now you need to deal with the window, door and other openings present in the room.
To get accurate numbers, builders recommend measuring the wall in three places (at the beginning, middle and end). After that, the data obtained should be summed up and divided by 3 and thus the arithmetic mean is calculated. This procedure helps to avoid errors, even if.
When measuring window and door ones, you should not calculate the correctness of their shape.
It is better to measure all four sides with your own hands, and not just two touching ones. This approach will protect you from the consequences of builders' negligence and unnecessary costs (for example, when replacing windows or doors).
Whatever the reason why you still decide to figure out how to independently calculate the area of the premises - remember that it is advisable to do any work with high quality. Therefore, try to carefully plan the entire process, prepare the necessary tools, and feel free to proceed with measurements and calculations. And we hope that our tips will make it easier for you to follow them.
Video: calculating the area of a room
If you are planning a renovation in the bathroom, and you have chosen ceramic tiles as finishing, then you need to know exactly how much material you need. Otherwise, you can get into an unpleasant situation when you have to urgently buy more tiles, but this one may no longer be on sale, or you simply overpay for extra material. To prevent this from happening, you need to calculate the exact number of tiles, but in order to make the calculation, you first need to know the area of the bathroom. Let's see how to do it.
When planning a renovation, it is important to accurately calculate the area of the surface to be coated.
Where to begin
The first step is to find out the size of the room. In order to measure and calculate the area of the bathroom, we need a minimum set of tools that are in every home:
- paper;
- pen or pencil;
- roulette;
- calculator.
Before proceeding with measurements, it is necessary to depict a sketch of the bathroom on paper, so that it is easier to write down the results and make a calculation. For maximum convenience, mark each wall in the picture (for example, a wall with a door, a sink, etc.) and do not forget about the floor as well.
For comfortable work, try to remove all unnecessary from the floor and walls to ensure free access to the entire perimeter of the room.
Detailed sketch example: flat pattern of walls showing plumbing and tile layouts
Measurements
So, let's start measuring. Using a tape measure, first of all, you need to measure the width and length of the room, then the height of the walls. You will also need to measure the width and height of the doorway and other objects that will not be tiled. For example, some people choose not to install tiles behind the bathtub or leave an unlined surface behind the cupboard. All received data are recorded on paper.
When taking measurements, it is imperative to take into account the possible unevenness of the room. Therefore, in order to avoid inaccuracies in the calculations, it is recommended to measure each side, checking the values at several points.
Please note: in some rooms the differences in the dimensions of the opposite walls can reach several centimeters, in this case it is recommended to take a larger value, this will allow the calculation with a small margin.
For accuracy of calculations, measurements should be carried out at several points.
Calculations
Suppose that the length of the room is 2.2 m, the width is 1.8 m, and the height of the walls is 2.8 m. By multiplying the length and width, we get the floor area in the bathroom:
2.2 x 1.8 = 3.96 m2
In a similar way, we determine the area of the doorway by multiplying its height by width:
2 x 0.6 = 1.2 m2
Then we calculate the area of all the walls. Initially, we calculate the perimeter of the room:
2.2 + 2.2 + 1.8 + 1.8 = 8 m
Then we multiply the perimeter of the room by the height of the walls:
8 x 2.8 = 22.4 m2
Then we subtract the area of the doorway from the resulting value:
22.4 - 1.2 = 21.2 m2
Thus, we managed to find the area of all the walls in the bathroom. To find the total area of the room, we sum up the areas of the floor and walls:
3.96 + 21.2 = 25.16 m2
Now, knowing the total area of the bathroom, you can easily calculate the required number of tiles. To do this, you need to divide the area of the room by the area of one tile, round the result to an integer and add 10%, this will help you avoid a lack of materials. Summing up, I would like to note that using these skills, anyone can easily take measurements of the room without outside help.