Determination of the cross-sectional area of ​​a conductor by its diameter

When calculating any electrical networks, such a concept as the cross-sectional area of ​​the conductor is used. This property directly affects the safety and durability of the entire system, so it is important that the calculated cross-sectional area of ​​the electrical conductor matches the actual one. This article will discuss methods for measuring the diameter of a conductor and its cross-section, as well as other options for determining the characteristics of a wire.

Calculation of wire cross-section

Strictly speaking, the concept of “thickness” for a wire is used colloquially, and the more scientific terms are diameter and cross-sectional area. In practice, the thickness of the wire is always characterized by its cross-sectional area.

In practice, calculating the wire cross-section is very simple. Knowing the diameter (for example, by measuring it with a caliper), you can easily calculate the cross-sectional area using the formula

S = π (D/2)2 , where

• S – wire cross-sectional area, mm2
• π – 3,14
• D – diameter of the conductor of the wire, mm. It can be measured, for example, with a caliper.

The formula for the cross-sectional area of ​​a wire can be written in a more convenient form: S = 0.8 D² .

Amendment. Frankly, 0.8 is a rounded factor. A more accurate formula: π (1/2)2 = π / 4 = 0.785. Thanks to attentive readers

Let's consider only copper wire , since it is used in 90% of electrical wiring and electrical installations. The advantages of copper wires over aluminum wires are ease of installation, durability, and reduced thickness (at the same current).

But with an increase in diameter (sectional area), the high price of copper wire eats up all its advantages, so aluminum is mainly used where the current exceeds 50 Amperes. In this case, a cable with an aluminum core of 10 mm2 or thicker is used.

The cross-sectional area of ​​the wires is measured in square millimeters. The most common cross-sectional areas in practice (in household electrics): 0.75 (prohibited in fixed wiring), 1.5, 2.5, 4 mm2

There is another unit for measuring the cross-sectional area (thickness) of a wire, used mainly in the USA - the AWG system . On Samelektrika there is a table of wire cross-sections according to the AWG system and conversion from AWG to mm2.

Regarding the selection of wires, I usually use catalogs from online stores, here is an example of copper. They have the largest selection I've ever seen. It’s also good that everything is described in detail - composition, applications, etc.

I also recommend reading my article about choosing a wire cross-section for direct current; there are a lot of theoretical calculations and discussions about voltage drop, wire resistance for different cross-sections, and which cross-section to choose is optimal for different permissible voltage drops.

And another article - Voltage drop on long three-phase cable lines. a real example of an object is given, formulas and recommendations are given on how to reduce losses. Wire losses are directly proportional to current and length. And inversely proportional to resistance.

When choosing the cross-sectional area of ​​the wires, you should be guided by three basic principles.

1. The cross-sectional area of ​​the wire (in other words, its thickness) must be sufficient for the passage of electric current through it. Sufficient - this means that when the maximum possible current in this case passes, the heating of the wire will be acceptable (as a rule, no more than 60 0C)
2. The cross-section of the wire must be sufficient so that the voltage drop across it does not exceed the permissible value. This is especially true for long cable lines (tens and hundreds of meters) and high currents.
3. The thickness of the wire and its protective insulation must ensure its mechanical strength, and therefore reliability.

For example, to power a chandelier in the living room, light bulbs with a total power consumption of 100 W (current slightly more than 0.5 A) are used. It seems that wires with a cross-sectional area of ​​0.5 mm2 are quite enough? But what electrician in his right mind would install such a wire in a ceiling slab? In this case, 1.5 mm2 is usually used.

In fact, the choice of wire thickness depends on one parameter - the maximum operating temperature.
If this temperature is exceeded, the wire and the insulation on it will begin to melt and collapse. In other words, the maximum operating current for a wire with a certain cross-section is limited only by its maximum operating temperature. And the time that the wire can work in such conditions. Below is a well-known table of wire cross-sections for selecting the cross-sectional area of ​​copper wires depending on the current. The initial data is the cross-sectional area of ​​the conductor.

Calculation by formula

The main geometric indicator of a conductor is its cross-sectional area. The throughput of the electrical conductor, and, consequently, its performance characteristics, which affect safety and durability, depend on this size. As mentioned above, this parameter is easily determined after measuring the diameter of the conductor. To do this, use the formula to determine the area of ​​a circle:

Ready-made tables are a great way to quickly determine the cross-sectional area of ​​a wire, but to be one hundred percent sure of the obtained value, it is better to check and calculate it yourself.

Maximum current for different thickness of copper wires

Table 1

(Data from table 1.3.4 PUE)

The ratings of wires used in household electrics are highlighted. “One two-core” is a cable with two wires, one of them is Phase, the other is Zero. That is, this is a single-phase load supply. “Single Three-Wire” is for three-phase power supply.

This table shows at what currents and under what conditions a wire of a given cross-section can be operated.

A burning example from practice - if the socket says “Max.16A”, then you can lay a wire with a cross-section of 1.5 mm2 for this one socket . But be sure to protect the outlet with a circuit breaker for a current of no more than 13A, or better yet, 10A. On this topic, you can read my article About replacing and choosing a circuit breaker.

In the table, a single-core wire means that no more wires pass nearby (at a distance of less than 5 wire diameters). Two-core wire - two wires side by side, usually in one common insulation. This is a more severe thermal regime, so the maximum current is less. And the more wires in a cable or bundle, the less the maximum current for each conductor must be due to possible mutual heating.

I find this table not very convenient for practice. After all, most often the initial parameter is the power of the electricity consumer, and not the current, and based on this you need to choose a wire.

How to find the current knowing the power? You need to divide the power P (W) by the voltage (V), and we get the current (A):

I = P/U

How to find power knowing current? You need to multiply current (A) by voltage (V), we get power (W):

P = IU

These formulas are for the case of active load (consumers in residential premises, such as light bulbs and irons). For reactive loads, a factor of 0.7 to 0.9 is usually used (in industry where large transformers and electric motors operate).

I offer you a second table, in which the initial parameters are current consumption and power , and the required values ​​are the wire cross-section and the tripping current of the protective circuit breaker.

Section according to GOST or TU

A large assortment of electrical products helps to quickly solve problems associated with electrical installation work. The quality of these products plays a very important role and all products must comply with GOST requirements.

As a result, the market is oversaturated with low-quality and cheap goods that need to be double-checked before purchasing.

If the cables available in retail outlets of a suitable price do not correspond to the declared characteristics, the only thing that can be done is to purchase a wire with a reserve cross-section. The power reserve will never negatively affect the quality of electrical wiring. It would also be useful to pay attention to products from manufacturers who value their name - although they are more expensive, they are a guarantee of quality, and wiring replacement is not done so often that you can save on it.

Selecting the thickness of the wire and circuit breaker based on power consumption and current

Below is a table for selecting the wire cross-section based on known power or current. And in the right column is the choice of the circuit breaker that is installed in this wire.

table 2

Critical cases are highlighted in red, in which it is better to play it safe and not skimp on the wire by choosing a wire thicker than indicated in the table. And the current of the machine is less.

Looking at the plate, you can easily select the wire cross-section by current , or the wire cross-section by power .

And also - select a circuit breaker for a given load.

This table shows the data for the following case.

• Single phase, voltage 220 V
• Ambient temperature +30 0С
• Laying in the air or in a box (in a closed space)
• Three-core wire, in general insulation (cable)
• The most common TN-S system is used with a separate ground wire
• The consumer reaching maximum power is an extreme but possible case. In this case, the maximum current can operate for a long time without negative consequences.

If the ambient temperature is 20 0C higher, or there are several cables in the bundle, then it is recommended to select a larger cross-section (the next one in the series). This is especially true in cases where the operating current value is close to the maximum.

In general, in case of any controversial and doubtful issues, for example

• possible future increase in load
• high inrush currents
• large temperature changes (electrical wire in the sun)
• fire hazardous premises

you need to either increase the thickness of the wires, or approach the choice in more detail - refer to formulas and reference books. But, as a rule, tabular reference data is quite suitable for practice.

The thickness of the wire can be determined not only from reference data. There is an empirical (experienced) rule:

Segment cable cross-section

What is the difference between a cable and a wire?

Cable products with a cross-section of up to 10 mm2 are almost always produced in a round shape. Such conductors are quite sufficient to meet the domestic needs of houses and apartments. However, with a larger cross-section of the cable, the input cores from the external electrical network can be made in segment (sector) form, and it will be quite difficult to determine the cross-section of the wire by diameter.

Aluminum cable with sector conductors

In such cases, it is necessary to resort to a table where the size (height, width) of the cable takes the corresponding value of the cross-sectional area. Initially, it is necessary to measure the height and width of the required segment with a ruler, after which the required parameter can be calculated by correlating the obtained data.

Table for calculating the area of ​​an electric cable core sector

Rule for choosing wire cross-sectional area for maximum current

You can select the required cross-sectional area of ​​the copper wire based on the maximum current using this simple rule:

The required wire cross-sectional area is equal to the maximum current divided by 10.

This rule is given without reserve, back to back, so the result must be rounded up to the nearest standard size. For example, the current is 32 Amps. You need a wire with a cross section of 32/10 = 3.2 mm2. We choose the closest one (naturally, in the larger direction) - 4 mm2. As you can see, this rule fits well into the tabular data.

Important note. This rule works well for currents up to 40 Amps . If the currents are greater (this is already outside the boundaries of an ordinary apartment or house, such currents are at the input) - you need to choose a wire with an even larger margin - divide not by 10, but by 8 (up to 80 A)

The same rule can be stated for finding the maximum current through a copper wire with a known area:

The maximum current is equal to the cross-sectional area multiplied by 10.

And in conclusion - again about the good old aluminum wire.

Aluminum conducts current less well than copper. This is enough to know, but here are some numbers. For aluminum (the same cross-section as the copper wire) at currents up to 32 A, the maximum current will be only 20% less than for copper. At currents up to 80 A, aluminum conducts current 30% worse.

For aluminum the rule of thumb would be:

The maximum current of an aluminum wire is equal to the cross-sectional area multiplied by 6.

I believe that the knowledge given in this article is quite enough to choose a wire based on the ratios “price/thickness”, “thickness/operating temperature” and “thickness/maximum current and power”.

That’s basically all I wanted to tell you about the cross-sectional area of ​​the wires . If something is not clear or you have something to add, ask and write in the comments. If you are interested in what I will publish next on the SamElectric blog, subscribe to receive new articles.

Determination of the conductor cross-section at the input

You can check the nominal values ​​in the Energosbyt company or in the documentation for the product. For example, the input rating of the machine is 25 A, the power consumption is 5 kW, the network is single-phase, 220 V.

The cross-section is selected so that the permissible current of the cores over a long period is greater than the rating of the machine. For example, a three-core copper conductor VVGng, laid in an open manner, was installed in a house. The optimal cross-section is 4 mm2, so you will need VVGng 3x4 material.

After this, the indicator of the conditional shutdown current for a machine with a nominal value of 25 A is calculated: 1.45x25 = 36.25 A. For a cable with a cross-sectional area of ​​4 mm2, the parameters of the continuous permissible current are 35 A, conditional - 36.25 A. In this case, it is better to take the input copper conductor with a cross-section of 6 mm2 and a permissible maximum current of 42 A.

Table of dependence of the current of the circuit breaker (fuse) on the cross-section

(Addition to article, June 2014)

And here is how the Germans treat the maximum current depending on the cross-sectional area of ​​the wire. In the right column is a recommendation for choosing an automatic (protective) switch.

Table 3

Table for selecting a circuit breaker for different wire cross-sections

As you can see, the Germans are playing it safe and are providing for a larger reserve compared to us.

Although, perhaps this is because the table was taken from instructions from “strategic” industrial equipment.

Regarding the selection of wires, I usually use catalogs from online stores, here is an example of copper. They have the largest selection I've ever seen. It’s also good that everything is described in detail - composition, applications, etc.

A good Soviet book on the topic of the article:
• Karpov F. F. How to choose the cross-section of wires and cables, 1973 / Brochure from the Electrician's Library. Provides instructions and calculations necessary for selecting cross-sections of wires and cables up to 1000 V. Useful for those who are interested in primary sources., zip, 1.57 MB, downloaded: 4453 times./

What does cross section mean?

Before revealing the basic concept, you need to decipher the meaning of the term and understand how a wire differs from a cable. A wire is a conductor that is used to connect several sections of an electrical circuit. May have one or many current-conducting conductor elements. They, in turn, can be bare, insulated, single-core or multi-core.

Conductor cut area

The former are used in overhead electrical transmission lines. The latter are used in electrical devices, panels or cabinets. In everyday life, they are located inside electrical wiring.

For your information! Insulated and single-core conductors are used everywhere, and stranded conductors are used where bends with a small radius are needed.

What is a cross section

A cross section is a figure that is formed from a conductive section by a directional plane. The area obtained from a perpendicular cut of any type of wire is indicated in square millimeters. This is an important parameter for calculating the electrical network.

Tables for selecting a suitable conductor

A convenient and practical option for selecting the desired wire (cable) is to use special tables that indicate the diameters and cross-sections relative to the power and/or currents carried.

Having such a table at hand is an easy and simple way to quickly determine the conductor for the required electrical installation. Determining the required values ​​using a classic table is one of the most convenient ways to select the required conductor during installation work. Considering that traditional conductors for electrical installations are products with copper or aluminum conductors, there are tables for both types of metals.

Also, tabular data often presents values ​​for voltages of 220 volts and 380 volts. Plus, the installation conditions are taken into account - closed or open wiring. In fact, it turns out that one sheet of paper or a picture loaded into a smartphone contains voluminous technical information that allows you to do without the above-mentioned mathematical (linear) calculations.

Moreover, many manufacturers of cable products, in order to make it easier for the buyer to choose the right conductor, for example, for installing sockets, offer a table in which all the necessary values ​​are entered. All that remains is to determine what load is planned for a specific electrical point and how the installation will be performed, and based on this information, select the correct wire with copper or aluminum conductors.

What is the cross section measured in?

After determining the diameter using the indicated methods, the cross-sectional area can be determined using a formula or a special table. It is measured in square millimeters. This unit of measurement is derived according to the Unified International System of Measurements.

You may be interested in this The danger of step tension

Unit of measurement

At the same time, the cut of the vein was always round.

Methods for measuring conductor diameter

When selecting an electrical cable or wire to check the cross-section of the core, it is necessary to measure its diameter. There are several ways to do this. You can use measuring instruments such as calipers or micrometers. They measure the size of the exposed part of the conductor.

The device is simply attached to the core, clamped between the jaws, and the result is displayed on the scale. For private use, the measurements are quite accurate, with a small error. Especially if the devices are electronic.

For the second method, you only need a ruler and some kind of even rod. But in this case, you still have to do calculations, albeit very simple ones. More on this method later.

Ruler+rod

If there are no measuring instruments on the farm, you can get by with a regular ruler and any rod of the same diameter. This method has a high error, but if you try it will be quite accurate. Take a piece of wire about 10-20 cm long and remove the insulation.

We wind the bare copper or aluminum wire onto a rod of the same diameter (any screwdriver, pencil, pen, etc. will do). We lay the coils carefully, close to one another. The number of turns is 5-10-15. We count the number of full turns, take a ruler and measure the distance that the wound wire occupies on the rod. Then divide this distance by the number of turns. As a result, we obtain the diameter of the conductor.

For example, we wound 10 turns (it’s easier to count), they took up 3.8 cm (or 38 mm) on the rod. Next, we divide the distance by the number of turns, 38/10 = 3.8 mm, we get that the diameter of the wound wire is 3.8 mm.

As you can see, there is an error here. Firstly, you can lay the wire loosely. Secondly, it is not enough to take accurate measurements. But if you do everything carefully, the discrepancies with the actual sizes will not be so large.

Application of measuring instruments

To determine the diameter of the cores of wires and cables, various measuring instruments are widely used, showing the most accurate results. Basically, the use of micrometers and calipers is practiced for these purposes. Despite their high efficiency, a significant drawback of these devices is their high cost, which is of great importance if the tool is planned to be used only 1-2 times.

As a rule, professional electricians who are constantly engaged in electrical installation work use special devices. With the right approach, it becomes possible to measure the diameter of wire cores even on working lines.

Which cable to choose for apartment wiring

Despite the cheapness of aluminum conductors, it is better to avoid using them. The reason is the low reliability of the contacts through which currents will pass. The second reason is the mismatch of the wire cross-section with the power of modern household appliances. Copper cable is reliable and has a long service life.

In apartments and houses it is allowed to use wire marked:

• PUNP is a flat conductor with copper conductors in a PVC sheath. Designed for a nominal voltage of 250 V at a frequency of 50 Hz.
• VVG/VVGng – flat cables made of copper with double PVC coating. They are used inside and outside buildings and are not subject to fire. They come with 2, 3 and 4 cores.
• NYM - copper wire for internal single line. It has an insulating PVC sheath and outer covering, conductors with and without grounding.

When choosing the number of cores, you will need to take into account the conductivity per unit cross-section. In this case, it is better to make the apartment network from a single-core wire, the thickness of which is greater. Multicore elements can be bent many times and electrical appliances can be connected to them. Only a cable with thin cores will be of high quality.

The correct cross-section of conductors, taking into account the power of the equipment and the type of network are important factors when organizing an electrical line. The cable diameter can be calculated independently in several ways. Based on these readings, it is easy to determine the cross-section of the cores using formulas or using a table.

Parallel connection of electrical wiring wires

There are hopeless situations when you urgently need to lay wiring, but there is no wire of the required cross-section available. In this case, if there is a wire with a smaller cross-section than necessary, then the wiring can be made from two or more wires, connecting them in parallel. The main thing is that the sum of the sections of each of them is not less than the calculated one.

For example, there are three wires with a cross section of 2, 3 and 5 mm2, but according to calculations, 10 mm2 is needed. Connect them all in parallel and the wiring will handle up to 50 amps. Yes, you yourself have repeatedly seen the parallel connection of a large number of thin conductors to transmit large currents.

For example, welding uses a current of up to 150 A and in order for the welder to control the electrode, a flexible wire is needed. It is made from hundreds of thin copper wires connected in parallel. In a car, the battery is also connected to the on-board network using the same flexible stranded wire, since when starting the engine, the starter consumes a current of up to 100 A from the battery.

And when installing and removing the battery, it is necessary to move the wires to the side, that is, the wire must be flexible enough. The method of increasing the cross-section of an electrical wire by connecting several wires of different diameters in parallel can be used only as a last resort. When laying home electrical wiring, it is permissible to connect in parallel only wires of the same cross-section taken from the same reel.

Author: Sergey Vladimirovich, electrical engineer. More about the author.

How and with what to measure the diameter of a wire (wire)

To measure the diameter of the wire, a caliper or micrometer of any type (mechanical or electronic) is suitable. It’s easier to work with electronic ones, but not everyone has them. You need to measure the core itself without insulation, so first move it aside or remove a small piece. This can be done if the seller allows it. If not, buy a small piece to test and take measurements on it.

On a conductor stripped of insulation, measure the diameter, after which you can determine the actual cross-section of the wire from the found dimensions. Which measuring device is better in this case? If we talk about mechanical models, then a micrometer. Its measurement accuracy is higher. If we talk about electronic options, then for our purposes they both give quite reliable results.

If you don't have a caliper or micrometer, take a screwdriver and a ruler with you. You'll have to strip a fairly decent piece of conductor, so you'll hardly be able to do without buying a test sample this time. So, remove the insulation from a 5-10 cm piece of wire.

Wind the wire around the cylindrical part of the screwdriver. Lay the coils close to each other, without a gap. All turns must be complete, that is, the “tails” of the wire must stick out in one direction - up or down, for example.

The number of turns is not important - about 10. You can have more or less, it’s just easier to divide by 10. Count the turns, then apply the resulting winding to the ruler, aligning the beginning of the first turn with the zero mark (as in the photo). Measure the length of the section occupied by the wire, then divide it by the number of turns. You get the diameter of the wire. It's that simple.

For example, let's calculate the size of the wire shown in the photo above. The number of turns in this case is 11, they occupy 7.5 mm. Divide 7.5 by 11, we get 0.68 mm. This will be the diameter of this wire. Next, you can look for the cross section of this conductor.

Necessity and procedure for calculation

Electric current powers a wide variety of equipment with varying power levels. And the power range is very wide.

Each individual electrical device represents a load, depending on the magnitude of which a current supply of a certain strength is required.

By “default” or simple ignorance of the basics of electrical engineering, it is easy to connect conductors, ignoring all existing requirements for diameters and cross-sections. Another question is what can come out of this practice during operation.

The required amount of current for the required load can be passed through wires of different diameters (sections).

But when the cross-section of the conductor is insufficient to pass a given amount of current, the effect of increased resistance occurs. As a result, heating of the wire (cable) is noted.

If you ignore this phenomenon and continue to pass current, there is a real danger of heating up to the point of fire. This situation threatens a serious emergency. That is why increased attention must be paid to calculations and selection of current transmission circuits to the load.

The consequences of inaccurate calculations of electrical conductors by cross-section (diameter) can be accompanied by phenomena ranging from minor deformation of the insulating material to a real fire and a major fire

Correct calculation and proper selection of cables and wires also have a positive effect on the operation of equipment acting as a load.

So, in addition to the safety factor, calculating the cross-sections of the electrical cable by diameter or vice versa is a mandatory action from the point of view of ensuring the efficient operation of electrical machines.

Determining the diameter of the conductor core

Actually, this operation can be performed with a simple linear measurement. For accurate measurements, it is recommended to use a point tool, such as a caliper, or even better, a micrometer.

A relatively low accuracy result, but quite acceptable for many applications of wires, is obtained by measuring the diameter with a regular ruler.

Measuring and determining the diameter of the core using a point tool, which is a caliper. This method of linear measurement gives a result that is sufficiently accurate for subsequent calculation of the conductor cross-section

Of course, the measurement should be carried out in the state of a bare conductor, that is, the insulating coating is first removed.

By the way, the insulating coating of, for example, a copper wire is also considered to be a thin layer of sprayed varnish, which also needs to be removed when a very precise calculation is required.

There is a “household” method of measuring diameter, suitable in cases where point measuring instruments are not available. To use this method, you will need an electrician's screwdriver and a school ruler.

The conductor for measurement is first stripped of insulation, after which it is wound tightly turn to turn on the screwdriver rod. Usually ten turns are wound - a convenient number for mathematical calculations.

Linear diameter measurement is another widely used method for determining a conductor parameter for calculating power (throughput). It is used using a regular ruler and any base where it is permissible to wind a conductor (+)

Next, the coil wound on the screwdriver rod is measured with a ruler from the first to the last turn. The resulting value on the ruler must be divided by the number of turns (in this case, 6). The result of this simple calculation will be the diameter of the wire core.

Calculating the cross-section of an electrical wire

To determine the cross-sectional value of the conductor core, you will have to use a mathematical formulation.

Essentially, the cross-section of a conductor core is the cross-sectional area - that is, the area of ​​a circle. The diameter of which is determined by the method described above.

The cross-section of the core is actually the area of ​​a circle. Accordingly, the calculation of this segment of geometric mathematics can be performed using the traditional formula, provided that the diameter or radius is known

Based on the diameter value, it is easy to obtain the radius value by dividing the diameter in half.

Actually, you will need to add the constant “π” (3.14) to the obtained data, after which you can calculate the value of the cross section using one of the formulas:

S = π*R2 or S = π/4*D2 ,

Where:

• D —diameter;
• R —radius;
• S —cross section;
• π is a constant corresponding to 3.14.

These classical formulas are also used to determine the cross-section of stranded conductors. The calculation strategy remains virtually unchanged, with the exception of some details.

In particular, the cross-section of one core from a bundle is initially calculated, after which the resulting result is multiplied by the total number of cores.

It is possible to calculate the cross-section of a stranded conductor using the same mathematical method that is applied to a single wire, but the number of existing conductors is additionally taken into account as a multiplier

Why should cross-section determination be considered an important factor? An obvious point related directly to the Joule-Lenz law is because the cross-sectional parameter of the conductor determines the limit of the permissible current flowing through this conductor.

Determination of diameter by section

By mathematical calculation it is possible to determine the diameter of the conductor core when the cross-sectional parameter is known.

This, of course, is not the most practical option, given the availability of simpler ways to determine the diameter, but the use of this option is not excluded.

Measuring the diameter with high accuracy using a metalworking tool - a micrometer, gives almost the same result when calculations are carried out using the formula

To perform the calculation, you will need virtually the same numerical information that was used when calculating the cross section using a mathematical formula.

That is, the constant “π” and the value of the area of ​​the circle (section).

Applying these formula values ​​below gives the diameter value:

D = √4S/π,

Where:

• D —diameter;
• S —cross section;
• π is a constant corresponding to 3.14.

The use of this formula may be relevant when the section parameter is known and there are no suitable tools at hand to measure the diameter.

The cross-section parameter can be obtained, for example, from the documentation for the conductor or from the calculation table, which presents the most commonly used classic options.