How to calculate the area of ​​a room

How to calculate the area of ​​a room

Someone probably seem ridiculous as "childish" question - "how to calculate the area of ​​a room." But let's accept the fact that, firstly, many of us were finishing school for a long time. Second, not everyone in everyday life are constantly faced with the need for geometrical calculations, and something that might have forgotten. And, thirdly, the room and the walls are not always and not everywhere have a rectangular shape with an area to calculate quickly and easily. So, sometimes you have to show ingenuity and apply more sophisticated methods of calculation.

How to calculate the area of ​​a room

How to calculate the area of ​​a room

And what do you need to be able to determine floor space, walls and ceiling of the room?

  • These data are necessary for the planning of repairs in the apartment - it is possible to calculate the amount of required construction materials.
  • If the work is done by hired masters, they often require payment per square meter. To avoid becoming a victim of fraud, be able to monitor the integrity of employees and does not pay too much, you must be able to correctly determine the amount of work done.
  • Numeracy construction schemes and to define the area may be necessary when viewing premises options presented for sale or lease. Incidentally, the amount of the payment of some public services also depends on the size of it is useful and common area.
  • Proper selection of lighting depends on the area - in this respect there are special illumination standards.
  • Knowing the area, it is easy to calculate, and the amount of space. And this - the main option in the selection of heating equipment, HVAC equipment, ventilation systems.

In short, this skill will never be over. And if the reader has come to this page, so it took him to learn or brush up on area calculation algorithms. Therefore, we begin to consider, according to the principle "from simple - to difficult".

Preparations for calculation

This phase, in fact, includes two main points. Is required to prepare the place of performance measurement work, the necessary tools and accessories, and in fact, to conduct measurements, transferring the results to the scheme or drawing.

  • Ideally, it is best to make all measurements in a fully liberated from furniture and other room items. When the repair is usually so happens. But if the measurement is carried out for purposes other then to make all of the room, of course, no one will undertake.

Measurements of the lengths of the sides of the room is usually carried out along the walls. Therefore, it is necessary to try to free these areas, so that you can fully, from wall to wall, stretch tape measure tape.

  • Check the squareness of the room the easiest way to perform soundings diagonals. Therefore, you may need the space in the center of the room. Or it must be possible to move objects that could be a hindrance for the measurements.

Surely follow ironic remarks - Is the author by giving such advice, never heard of the modern electronic laser roulette? Of course, these modern devices not only help to quickly and accurately measure linear and angular values ​​- many of them have built-in features make the necessary calculations.

Laser Tape Measure - it is convenient, but such tools have few

Laser tape Measure &# 8212; convenient, but such a tool is, in a few

However, let's "Down to earth" &# 8212; such a tool has so far not many. Professionals, so, without it is currently difficult. However, in a domestic environment, most people rely on traditional long measurement methods. Incidentally, for measuring laser tape measure space anyway still have to create - for the smooth passage of the beam.

Basic set - the usual measuring tape, notebook, pencil or marker

basic set &# 8212; normal roulette, notebook, pencil or marker

  • Now, we assume that the measurements are usually carried out with a tape measure. In addition to notepads, you may need:

&# 8212; longest line spacing for straight lines (for example, a rule can approach or longest building level);

Generally - will help to fight off the straight lines

rule &# 8212; It helps fight off the straight line

&# 8212; as large as possible (the more - the better) building square;

Construction triangles - regular and folding

Construction squares &# 8212; ordinary and folding

&# 8212; improvised compasses - it can be a piece of strong cord tied to any sharp pins, which will play the role of the center;

&# 8212; to measure the angle - or need a special tool, or carrying out calculations using trigonometric functions. However, in those methods to be offered, the measurement of the angle does not become a mandatory procedure - dispense linear values.

&# 8212; perhaps on the floor will have to carry out some supporting markup. In order not to dirty the floor with chalk or marker, you can use a thin masking tape.

Masking tape bright colors - good help when performing auxiliary markup

Masking tape of bright color &# 8212; good help when performing auxiliary markup

  • All measurements are best done twice - so it will be less likely to prevent any annoying error inadvertently.
  • roulette tape during the measurements should not sag in the measured area should be a straight line, in the stretch.
Attention! Do not confuse the scale!

Attention! Do not confuse the scale!

  • Focus on the scale! Do not confuse the metric system and "inch - foot", as many measuring tools applied both scales.
  • Work will be much easier if you sketch a rough plan in advance the room on paper. It is not necessary to plot it in this case, the super-accurate, to scale to meet the drawing standards.
Even such shemka & quot; by the hand & quot; It will be a good helper

Even such shemka &# 171; from the hand&# 187; It will be a good helper

Just become much easier just to transfer the measurement results on the paper, for further calculations.

When measuring distances will need to write them down in meters, rounded to the nearest centimeter, for example, 0.82 m or 5.38 m. Then all at once the results are obtained in the desired square meters.

  • Some calculation formula - rather cumbersome contain trigonometric functions and square root calculation, that is, "in a column" does not get counted. Well, if there is the ability to perform calculations to Excel - all clearly, plus the entire process can be saved in a file. If it not - then sets in motion calculator. Convenient to use that is built into the Windows- just remember to transfer it from "normal" to "engineering" through the "View" menu, or by simultaneously pressing the buttons «Alt + 2."
Translation calculator mode & quot; engineering & quot;

Translation calculator mode &# 171; Engineering&# 187;

Now on to the room configuration options.

Determine the floor area of ​​the room

Rectangle

1. Probably the most common configuration of the room, especially in urban high-rise buildings. And, accordingly, the most simple method of calculating the area.

Side of the rectangle can be designated as A and B. Thus, the area will be equal to:

S = A × B

Easier than you can imagine - the rectangle area

Easier than you can imagine &# 8212; area of ​​a rectangle

Opposite sides of a rectangle are equal to each other, in pairs, that is, in fact, can be measured only two values.

But we must not forget about checking - and whether it is a rectangle? It can be applied in every corner of the square building, but do not always give a clear picture. It will be easier to make a diagonal measurements and compare the results. If they are the same or the difference is quite small, it can be assumed that this is really a rectangle.

Determine the area of ​​the rectangular room

Determine the area of ​​the rectangular room

In the present example, the area of ​​the room is:

S = A × B = 5.82 × 3.77 = 21,94 m²

2. The room can have projections, recesses, passageways, etc. rectangular shape. Do not worry - you can break in the scheme a total area of ​​several rectangles. It is understood that after the area calculation on sites all values ​​are summed.

A little complicate the task - a room with a niche

Up a notch &# 8212; room with a niche

The diagram shows an example of extensive areas with the projecting portion. In the diagram, the red dotted line shows the separation into two rooms of rectangular section. It remains only to find the area of ​​each and summarize it:

Σs = S1 + S2 = 8.26 × 3.73 + 2.63 × 1.50 = 30.81 + 3.95 = 34.75 m²

3. Sometimes it happens that the protrusion on the contrary, to the room side and therefore "eats" part of the area.

Reverse example - the area of ​​the room is reduced due to the protrusion

counterexample &# 8212; area of ​​the room is reduced due to the protrusion

Then the calculations can go another way - to find the area of ​​the "stolen" space and subtract it from the area of ​​the large rectangle.

trapeze

This situation often happens in the corners of rooms.

A characteristic feature of the quadrangle called trapezoid - the two sides of it are parallel to each other, and the other two can be arranged at an arbitrary angle.

The area of ​​the trapezoid - is necessary to know three parameters

The area of ​​a trapezoid &# 8212; you need to know three parameters

In this case, to determine the area you need to know three parameters - the length of two parallel sides and the height of the trapezoid, ie the perpendicular distance between them.

S = ½ (A + B) × h

This formula is universal - from the sides of the angle does not change, and their importance to us to know necessarily. But height hbetter fathom in several places &# 8212; It is confident that the two sides really are parallel to each other.

Consider this example:

We expect a trapezoidal area of ​​the room

We expect a trapezoidal area of ​​the room

The typical trapezoidal room. We do measurements and use the formula:

S = ½ (A + B) × h = 0,5 × (6,27 + 7,00) × 2,73 = 15,83 m²

Sometimes a knowledge of the formula area of ​​a trapezoid and is useful for complex, polygonal shape of the room. For example, below is shown in the drawing pentagonal room. Its most conveniently divided into two portions - a rectangle and a trapezoid (conditional divided red line).

An example of the calculations in the pentagonal room

An example of the calculations in the pentagonal room

The area of ​​the rectangle:

S1 = 6.33 × 3.95 = 25 m²

One of the sides of the rectangle and a trapezoid base. A trapezoid height - the difference of the lengths of the opposite sides of the room:

h = 7.71 - 6.33 = 1.38 m

We find the area of ​​a trapezoid:

S2 = 0.5 × (3.95 + 2.55) × 1.38 = 4,49

Total area of ​​the whole premises is:

Σs = S1 + S2 = 25.0 + 5.71 = 29.49

Calculator to calculate the area of ​​rectangular or trapezoidal space

Calculator shown below allows the calculation area as a rectangular or trapezoidal rooms &# 8212; the only difference that the value of the lengths of the rectangular A1 and A2 It will be the same.

Numbering scheme for the parties calculator

Numbering scheme for the parties calculator

If necessary, you can immediately make amendments to the existing niches or projections.

triangles

So far, all the examples observed some "correct" &# 8212; premises or rectangular, or, at least, have parallel walls. And what if the complex shape of the room does not allow her to break such "correct" figure?

Nothing to do, will have to be split into triangles completely derivative form, and then in turn to calculate their area and to summarize.

area of ​​a triangle actually calculate simple - you need to multiply the length of its base is perpendicular to the base height, carried out from the opposite angle, and divide by two.

S = ½ × a × h

The formula is simple, but not always easy in practice

The formula is simple, but not always easy in practice

The problem is that just beat off the perpendicular height measurement conditions on the ground, at great distances, and even without special tools - not so simple. You can easily perform purely geometrical error which drags along incorrect result calculated area.

In this case it is better to use Heron's formula for triangles. She, however, somewhat cumbersome, but it allows you to pinpoint an area solely in terms of the lengths of sides of a triangle. It looks like this:

curved shape

It happens that in the room there are portions having rounded shapes. So, we need to consider options for how to approach the calculations in this case. In addition, such computing skills will be needed to calculate the area of ​​the wall, which has an arched door and window openings.

Too complex curved shape, the area of ​​which can be determined only integral calculus, will not be considered - these options are extremely rare, and no special tools have nothing to do here. But the figures, which are based on a circle, it is possible to calculate. Most often, in practice there are a semicircle, a quarter of a circle or a segment.

Circle and sector

Very easy to find the area of ​​a circle - only need to know the radius (R).

S = π × R²

area of ​​a circle - just need a radius

Area of ​​a circle &# 8212; only the radius

Now - some examples of determining the area of ​​a circle with the sectoral fragments (half and quarter):

The room with the semicircular portion

The room with the semicircular portion

Tedious to determine the area of ​​a semi-circular room (or arches on the wall). Fashionable shape divided into two - the rectangle (S1) and a semicircle (S2).

S1 = 5.00 × 2.00 = 10.00 m²

S2 = ½ × 3.14 × 2.50² = 9.8 m²

Σs = 10,00 + 9,8 = 19,8 m²

Another example is when an arc connects two perpendicular walls, thus forming a quarter circle.

Arc two perpendicular connected walls

Arc two perpendicular connected walls

This room can be divided into three parts: two rectangles (of the part marked with blue and yellow arrows), and a quarter of a circle with a radius of isolated green arrow.

The lower rectangle (blue):

S1 = 3.67 × (3.0 - 1.5) = 5.51 m²

The upper rectangle (yellow):

S2 = (3.67 - 1,5) × 1.5 = 3.25 m²

Quadrant:

S3 = ¼ × 3.14 × 1.5² = 1.76 m²

Total gross area:

Σs = 5.51 + 3.25 + 1.76 = 10.52 m²

Segment

And now - a task more complicated. Sometimes rounded arches or rooms do not take the form of sector and segment, that is part of the circle bounded by the arc and forms an arc chord (segment connecting two points on the circle).

There is a special formula to help you determine this area of ​​the figure is not based on its angle, and only the linear dimensions.

The starting value for determining the area of ​​a segment

The starting value for determining the area of ​​a segment

Baseline values ​​will serve range (R) And the length of the chord (C) Or height (H).

The formula through chord length:

S = R² × arcsin (C / 2R) - 0.25 × C × √ (4R² &# 8212; C²)

If a start of segment height, the first value can be determined L:

L = R &# 8212; H

A formula takes the following form:

S = R² × arccos (L / R) - L × √ (R² &# 8212; L²)

Investigated for example.

It is necessary to calculate the area of ​​the premises:

First of all, in this case it is necessary to find the center of the circle to determine its radius. This may be done experimentally, by moving homemade dividers (e.g., string) along the axial line until the point where the distance from the arc and to the edges to be detected and to its center become equal. This distance - and the radius.

Now easy to fathom and all other parameters. R = 2.91 m, H = 1.41 m, L = 1.5 m.

As a result, we get two shapes - rectangle segment.

EXAMPLE area calculation portion in the form of a segment

EXAMPLE area calculation portion in the form of a segment

The area of ​​the rectangle:

S1 = 5.00 × 2.00 = 10.00 m²

Find the segment area based on the radius and the chord length (in this case the length of the chord, it is obviously equal space width).

S2 = 2.91² × arcsin (5 / (2 × 2.91)) - 0.25 × 5.0 × √ (4 × 2.91² &# 8212; 5.0²) =

= 5.01

(In calculating the calculator sure to set the unit of angular measurement - When counting in radians. Excel radians installed by default)

Just for fun - the same area, but in the height of the segment:

S2 = 2.91² × arccos (1.5 / 2.91) - 1.5 × √ (2.91² &# 8212; 1.5²) = 4.99 m²

The resulting difference of 0.02 m² - a result of the rounding of fractional numbers long. It is clear that here it is possible to take an average value of 5.0 m²

Total, total floor area:

Σs = 10.00 + 5.00 = 15.00 m²

Determining the areas of the walls and ceiling

The floor in the room - not a single plane, the area where you need to know. Often, to calculate the number of necessary construction and finishing materials, to determine the scope of work necessary to find the area of ​​the walls and ceiling.

geometry laws are the same for all of two-dimensional shapes, so that nothing new of mathematics will be told no. There are only some of the nuances:

Walls

It would seem that what could be simpler: the wall area - is its length times the height. Therefore, the total surface area of ​​the walls in the room can be found on the perimeter of the room product of height.

Yes, it is true, but only for rooms in which the ceiling height of the walls of the same at any point. And, for example, in the attic room wall can be trapezoidal or triangular. Therefore, it is worth paying attention to. How to find the area of ​​a triangle or trapezoid - will not repeat.

Next - the total area of ​​the walls is necessary to subtract windows or doorways. Nothing complicated - measurements are made on the outer surface of boxes and frames, and make the appropriate calculations, depending on the geometrical figure.

From the square of the walls, if necessary, take up an area of ​​window and door openings

From the square of the walls, if necessary, take up an area of ​​window and door openings

By the way, if the area of ​​the walls is calculated in order to determine the number of standard rolls of wallpaper for repair, it is possible to offer our plate, which immediately tell this number based on the perimeter of the room and ceiling height:

The number of standard rolls of wallpaper 10.5 × 0.52 m (room perimeter includes all door and window openings).

Ceiling Height (m) The perimeter of the room (m)
910121314151617192021222325262728thirty
2,15 ÷ 2,30455667788991010eleven12121313
2,30 ÷ 2,4555667788991010eleveneleven12131314
2,45 ÷ 2,60556778991010eleven12121314141515
2,60 ÷ 2,75556778991010eleven12121314141515
2,75 ÷ 2,9066778991010eleven1212131414151516
2,90 ÷ 3,056678891010eleven121213141415161617
3,05 ÷ 3,20678891010eleven12131314151616171819

Ceiling

In the majority of cases with the ceiling all the problems should not arise. If it is horizontal, it is an exact projection of the floor area of ​​which has already been determined.

Attic, roof space may be an exception, since the plane of the ceiling there is an angle to the floor, and sometimes &# 8212; even polygonal line consisting of multiple surfaces intersecting each other.

Do not be afraid of complex surfaces - they are easily broken down into the usual plane figures

Do not be afraid of complex surfaces &# 8212; they are easily broken down into the usual plane figures

Nothing wrong. No need to delve into and trigonometry to calculate angles between the floor, walls and ceiling. Just have to "virtually" break such difficult surface for a few plane figures, fathom their linear values. But everything else we already know - the calculation formula will be the same.

Finally, in the conclusion of the article - a video telling how an assistant could be a laser rangefinder (Roulette).

Video: definition of area non-rectangular walls