It has been suggested that this article or section be merged into Telephone number. (Discuss) Proposed since May 2012.

The examples and perspective in this article may not represent a worldwide view of the subject. Please improve this article and discuss the issue on the talk page. (August 2010)

A telephone numbering plan is a type of numbering scheme used in telecommunications to allocate telephone numbers to subscribers and to route telephone calls in a telephone network. A closed numbering plan, such as found in North America, imposes a fixed total length to numbers. An open numbering plan features variance in the length of telephone numbers.

A dial plan establishes the expected number and pattern of digits for a telephone number. This includes country codes, access codes, area codes and all combinations of digits dialed. For instance, the North American public switched telephone network (PSTN) uses a 10-digit dial plan that includes a 3-digit area code and a 7-digit telephone number. Most PBXs support variable-length dial plans that use 3 to 11 digits. Dial plans must comply with the telephone networks to which they connect.

History[link]

In early telephone systems, connections were made in the central office by telephone operators using patch cords to connect one party to another. If a person wanted to make a phone call, in some phone systems he or she would pick up a phone and wind a crank. In other systems the person would wind the crank first, then pick up the phone. The crank was a small generator that would light a lamp at the central office. An operator would see the light and insert their patch cord into a socket and assist the customer with the call connection. The operator would use patch cords to connect the caller to the person being called. If the party being called was in another exchange, the operator would use a patch cord to connect to another exchange where an operator elsewhere would finish the connection. As technology advanced, electro-mechanical switches were introduced and calls were made using rotary dials.

Initial use of area codes in the United States and Canada began in 1947 with large cities.^[1] By 1966, the system was implemented fully in both countries.^[2] Area codes were assigned based on the length of time a rotary dial phone took to dial the area code. Densely populated areas like New York City, Chicago, Los Angeles, and Detroit had huge incoming call volume and were assigned numbers (212, 312, 213, 313) that could be quickly dialed from a rotary dial phone. On a rotary dial phone low digits (1, 2, 3, 4) could dial quickly as the time the rotary dial took to return to the home position was minimal. High digit numbers (7, 8, 9, 0) on rotary dial phones took much longer to return to the home position and were usually used in less densely populated areas like rural Texas (915). This numbering strategy became unnecessary when touch-tone phones arrived, as the tone allowed instant entry of digits.

This unreferenced section requires citations to ensure verifiability.

The original set of North American area codes was unique. When the North American Numbering Plan was first developed, logic circuits consisted of relays and vacuum tubes, and simplicity was mandatory. The second digit of all area codes was 0 or 1, while the second digit of the exchange triplet was never 0 or 1, thus facilitating readily the recognition whether the dialing of a full 10-digit number was in progress or whether the user was dialing only a local number. In this coding scheme, a leading 1 indicating long distance, or out of the area code call, was not necessary. In some regions, local numbers were 7 digits (occasionally less), but a toll call within the area code required a preceding “1”. This told the subscriber that the call being placed was a toll call. Area Code 617 in eastern Massachusetts used this system in the early 1970s, while the Chicago area (Area Code 312) did not. In the Chicago Area, one could call the Boston area by dialing only 10 digits, while in Boston, to call Chicago, one would be required to use 11 digits (preceding the 10 digits with a “1”)

By the 1990s, the mechanical Central Office Switches were rapidly being replaced with ESS machines (Electronic Switching Systems), and the Area Code logic was no longer necessary. The need for more telephone numbers was increasing rapidly, and the NANPA (North American Numbering Plan Administration) was running out of “n0n” and “n1n” combinations. This Area Code scheme was abandoned, with the result that former Area Code only numbers could now be Exchanges, and former Exchange only numbers could now be Area Codes. This caused a logic dilemma: The Switch had no way of knowing whether to expect 10 digits or 7 digits. The solution was simple. If a preceding “1” was entered (by dial and Touch-Tone key pad), then 10 more digits were expected. If the first digit entered was NOT a “1” only 7 digits were expected and the call would remain within area code. For a short while, in some area codes, one could enter the full 11 digits for a call within their own neighborhood or just enter the last 7 digits, and the call would be routed and billed identically.

Currently, because of Area Code overlays, nearly all metropolitan and many rural telephone calls require the full 11 digit entry to complete a telephone call.

Structure[link]

Most telephone numbers belong to the E.164 numbering plan, though some PABXs (business telephone systems) have internal extensions.

The E.164 numbering plan for telephone numbers includes:

• Country calling codes
• Regional numbering plans, such as:
  • the European Telephony Numbering Space
  • the North American Numbering Plan
• Various national numbering plans, such as:
  • Telephone numbers in the United Kingdom

Apart from the use of numbering plans for telephone numbers, they are also used in routing of SS7 signalling messages as part of the Global Title. In public land mobile networks, the E.212 numbering plan is used for subscriber identities (e.g. stored in the GSM SIM) while E.214 is used for routing database queries across PSTN networks.

Country code[link]

Country code - necessary only when dialing to phones in other countries. In international usage, telephone numbers are prepended with the country code preceded by a "+", and with spaces in place of hyphens (e.g., "+XX YYY ZZZ ZZZZ"). This allows the reader to choose which Access Code (also known as International Dialing Digit) they need to dial from their location. However, it is often quoted together with the international access code which must precede it in the dial string, for example "011" in NANP countries (including Canada, Bermuda, and the United States): "011-XX-YYY-ZZZ-ZZZZ", or "00" in most European countries: "00-XX-YYY-ZZZ-ZZZZ". This can cause confusion as a different Access Code may be used where the reader is located. On GSM networks, "+" is an actual character that may be used internally as the international access code, rather than simply being a convention.

Area code[link]

Area codes are also known as Numbering Plan Areas (NPAs) and formerly known as STD codes in the UK. These are necessary (for the most part) only when dialed from outside the code area, from mobile phones, and (especially within North America) from within overlay plans. Area codes usually indicate geographical areas within one country that are covered by perhaps hundreds of telephone exchanges, although the correlation to geographical area is becoming obsolete.^[3]

The area code is usually preceded in the dial string by either the national access code ("0" for many countries, "1" in USA and Canada) or the international access code and country code. However, this is not always the case, especially when 10-digit dialing is used. For example, in Montreal, Quebec, where area codes 514 and 450 are currently in use, users dial 10-digit number (e.g. 514 555 1234), dialing a 1 before this results in a recording advising not to dial a 1 as it is a local call. For non-geographic numbers, as well as mobile telephones outside of the North American Numbering Plan area, the "area code" does not correlate to a particular geographic area.

Area codes are often quoted including the national access code, for example a number in London: 020 8765 4321. Users must then correctly interpret the "020" as the code for London. If they call from another number in London, they merely dial 8765 4321, or if dialing from another country, drop the "0" and dial: +44 20 8877 9908.

000 area codes are sometimes used in the United States by telemarketers and VoIP services. They are only used for outgoing calls, and cannot be dialed.

Area codes were introduced in the United States by the Bell System, in 1947. The first direct dial long distance call occurred in 1951.^[4]

Local number[link]

The local number (or subscriber number) must always be dialed in its entirety. The first few digits in the local number typically indicate smaller geographical areas or individual telephone exchanges. In mobile networks they may indicate a network provider in case the area code does not. Callers from a number with a given area/country code usually do not need to (but optionally may) include the particular area/country code in the number dialed, which enables shorter "dial strings" to be used. Devices that dial phone numbers automatically can include the full number with area and access codes, since there is no additional annoyance related to dialing extra digits.

Standards[link]

Although the International Telecommunication Union (ITU) has attempted to promote common standards among nation states, numbering plans take different formats in different parts of the world. For example, the ITU recommends that member states adopt 00 as their international access code. However, as these recommendations are not binding on member states, some have not, such as the United States, Canada, and other countries and territories participating in the North American Numbering Plan.

The international numbering plan establishes country codes, that is, area codes that denote nations or groups of nations. The E.164 standard regulates country codes at the international level and sets a maximum length limit on a full international phone number (15 digits). However, it is each country's responsibility to define the numbering within its own network. As a result, regional area codes may be:

• A fixed length, e.g., three digits in the United States and Canada; two digits in Brazil; one digit in Australia and New Zealand,
• A variable length, e.g., between 2 and 5 in Germany, Argentina, United Kingdom and in Austria; between 1 and 5 in Japan; 1 or 2 in Syria and Peru, or
• Incorporated into the subscriber's number, as is the case in many countries, such as Spain or Norway. This is known as a "closed" telephone numbering plan. In some cases a trunk code (usually 0) must still be dialed, as in Belgium, Italy, Switzerland, South Africa and some locations within the NANP. Hong Kong used to have 1-digit area codes. They were incorporated into the subscriber's numbers back into the 1990s. No trunk code is required.

Area code and call pricing[link]

In countries other than the United States and Canada, the area codes generally determine the cost of a call. Calls within an area code and often a small group of adjacent or overlapping area codes are normally charged at a lower rate than outside the area code. This is not necessarily the case in the United States or Canada where rates are determined by the distance between rate centers. In most United States and Canadian locations area codes cover a sufficiently large territory that different rates will apply within the same area code determined by the distance between rate centers. Each rate center also has a local calling plan which determines which other rate centers, regardless of distance, are a local call. The area code plus the first three digits following the area code (the NPA-NXX) defines the rate center for any given telephone number. Multiple NPA-NXX combinations, often in different area codes, comprise each rate center, and each rate center is assigned a geographic point known as the rate center's V&H coordinates. The tariff distance in miles between any two rate centers may be calculated using by this formula: Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt { \frac{(V1-V2)^2 + (H1-H2)^2} {10} } .

Calls between nearby rate centers in different area codes may be cheaper (or even free local calls) as compared to calls to more distant rate centers in the same area code. Rates are set in zones of 0-6 mi, 6-12 mi, and so on, with these bands determined on a state-by-state basis for intrastate calls (calls within the same state) and determined by federal regulation for interstate calls (calls which cross a state line). As a specific example, callers in the Falls Church, Virginia, rate center (officially named "Washington Zone 17, VA"--example numbers beginning with 703-534, V=5636, H=1600) may make untimed local calls to 31 other nearby rate centers in Virginia, Maryland, and the District of Columbia in area codes 703, 571, 202, 301, and 240, while calls to distant locations in 703 such as Manassas and Haymarket, VA are charged as long distance.

Calls within a state [regulated by that state's public utilities commission] are often higher than rates to call more distant locations in some other state [regulated by the Federal Communications Commission]. The partial deregulation and introduction of competition for long distance phone services has established other methods of determining call pricing that do not necessarily follow the traditional model. Each year, more customers switch to a fixed rate, "all-you-can-dial" plan covering the state, the United States, or all North America generally (as of May 2008 and exclusive of taxes) for approximately $30 per month. Competition with cable telephony and Voice over Internet Protocol services have helped drive the cost of service down for residential and business customers.

Special area codes are generally used for free, premium rate, mobile phone systems (in countries where the mobile phone system is caller pays) and other special rate numbers. There are however some exceptions, in some countries (like Egypt), calls are charged at the same rate regardless of area and in others (like the UK) an area code is occasionally treated as two parts with different rates.

Dialing plans[link]

Example[link]

In the U.S., some typical dial plans include:

• Internal extension numbers of a varying number of digits
• Local numbers of seven or ten digits
• Long distance numbers of eleven digits, consisting of a 1, then a three-digit area code, then a seven-digit number
• International numbers of any length starting with 011

Many corporate telephone systems use a dialing prefix, typically the digit 9, to obtain a line to the public switched telephone network.

Example[link]

In Australia, the following dialing plans can be found:

• Internal extension numbers of a varying number of digits, usually 3 or 4 digits
• Local numbers of eight digits
• Long distance numbers of eight digits, when source and destination share the same area code, or ten digits, consisting of a 0, then an area code, then eight-digit number
• International numbers of any length starting with 0011

In Australia, the digit 0 is used to obtain a line to the public switched telephone network.

Open dialing plans[link]

An open dialing plan is one in which there are different dialing arrangements for local and long distance telephone calls. This means that to call another number within the same city or area, callers need dial only the number, but for calls outside the area, an area code is required. In this situation it is customary to show the area code in parentheses, signifying that in some cases the area code is optional or is not required, as suggested by ITU-T Recommendation E.123. The area code is prefixed by a trunk code (usually "0"), which (apart from rare cases such as Italian land lines) is omitted when calling from outside the country.

To call a number in Sydney, Australia for example:

• xxxx xxxx (within Sydney and other locations within New South Wales - no area code required)
• (02) xxxx xxxx (outside New South Wales - the area code is required)
• +61 2 xxxx xxxx (outside Australia; notice the dropped 0)

Note that the "+" is not dialed, it signifies that first the international access code must be dialed, followed by the country code, in this case 61, followed by the number. When using a mobile telephone to place a call, all GSM phones and many models using other technologies do allow the + to be entered and this is internally converted to the correct access code, based on caller location, as the call is made.

New Zealand has a special case of an open dialing plan. While most nations require the area code to be dialed only if it is different, in New Zealand, one needs to dial the area code if the phone is outside the local calling area. For example, the town of Waikouaiti is in the Dunedin City Council jurisdiction, and has phone numbers (03) 465 7xxx. To call the city council in central Dunedin (03) 477 4000, residents must dial the number in full including the area code even though the area code is the same, as Waikouaiti and Dunedin lie in different local calling areas (Palmerston and Dunedin respectively)^[5]

In the United States, Canada, and other countries or territories using the North American Numbering Plan (NANP), the trunk code is '1', which is also (by coincidence) the country calling code. The same rule also applies in many parts of the NANP, including all areas of Canada that still have an open dialing plan. This is not universal, as there are locations within the United States that allow long distance calls within the same area code to be dialed as seven digits. In Canada, the trunk code (also known as the long distance access code) must also be dialed along with the area code for long distance calls even within the same area code. For example, to call a number in Regina:

• xxx xxxx (within Regina, Lumsden and other local areas)
• 1 (306) xxx xxxx (within the 306 area code, but not within the Regina local calling area (e.g., Saskatoon))
• 1 (306) xxx xxxx (anywhere within the NANP outside the 306 area code)
• +1 (306) xxx xxxx (outside NANP)

To call a number in San Francisco, California the dialing procedure will vary:

• xxx xxxx (local calls, no area code required)
• 1 (415) xxx xxxx (outside San Francisco, and within the U.S., Canada, and other countries in the NANP)^[6]
• +1 (415) xxx xxxx (outside the NANP - 1 is the country code for the U.S.)

However, in parts of North America, especially where a new area code overlays an older area code, dialing the area code, or 1 + the area code, is now required even for local calls, which means that the NANP is now closed in certain areas and open in others. Dialing from mobile phones is different in the U.S., as the trunk code is not necessary, although it is still necessary for calling all long distance numbers from a mobile phone in Canada. (Most mobile phones today can be programmed to automatically add a frequently-called area code as a prefix, allowing calls within the desired area to be dialed by the user as seven-digit numbers, though sent by the phone as 10-digit numbers.)

In some parts of the United States, especially northeastern states such as Pennsylvania served by Verizon Communications, the full 10-digit number must be dialed. If the call is not local, the call will not complete unless the dialed number is preceded by a 1. In this situation, where the area code is not optional, the area code is not enclosed in parentheses. Thus:

• 610 xxx xxxx (local calls, area code required; one of two completion options for mobile phones within the U.S.)
• 1 610 xxx xxxx (intra-area code charged calls; second of two completion options for mobile phones within the U.S.)
• +1 610 xxx xxxx (outside the NANP)

In California, because of the existence of both Overlay Area Codes (where you must dial an area code with every call regardless) and non-Overlay area codes (where you only have to dial an area code for calls outside your 'home' area code), "permissive home area code dialing" of 1 + the area code within the same area code, even if no area code is required, has been permitted since the mid-2000's. e.g.: if you are the 213 area code (a non-overlay area code), you can dial calls as 7 digits (XXX-XXXX) or 1-213 + 7 digits. The manner in which you dial the call does not affect the cost of the call. This "permissive home area code dialing" helps maintain uniformity and eliminates confusion given the different types of area code relief that has made California the nation’s most "area code" intensive State. Unfortunately, unlike other States with Overlay Area codes (Texas, Maryland, Florida and Pennsylvania to name just a few), the California Public Utilities Commission maintains two different dialing plans: Landlines must dial 1 + area code whenever an Area Code is part of the dialed digits while Cell Phone can omit the "1" and just dial 10 digits.

Many organizations have private branch exchange systems which permit dialing the access digit(s) for an outside line (usually 9 or 8), a "1" and finally the local area code and xxx xxxx in areas without overlays. This "feature" is unintentionally helpful for employees who reside in one area code and work in an area code with one, two, or three adjacent area codes. "1+" dialing to any area code by an employee can be done quickly, with all exceptions processed by the private branch exchange and passed onto the public switched telephone network.

Open and closed dialing plans should not be confused with open and closed numbering plans. A closed numbering plan, such as found in North America, features fixed length area codes and local numbers. An open numbering plan, as found in assorted countries that have not yet standardized, features variance in length of area code or local number, or both. Closed dialing plans are rare where numbering plans are open.

Closed dialing plans[link]

A closed dialing plan is one in which the subscriber's full number is used for all calls, even in the same area. This has traditionally been the case in small countries and territories where area codes have not been required. However, there has been a trend in many countries towards making all numbers a standard length, and incorporating the area code into the subscriber's number. This usually makes the use of a trunk code obsolete. For example, to call Oslo in Norway before 1992, one would dial:

• xxx xxx (within Oslo - no area code required)
• (02) xxx xxx (within Norway - outside Oslo)
• +47 2 xxx xxx (outside Norway)

After 1992, this changed to a closed eight-digit numbering plan, e.g.:

• 22xx xxxx (within Norway - including Oslo)
• +47 22xx xxxx (outside Norway)

Therefore in other countries, such as France, Belgium, Switzerland, South Africa and some parts of North America where the dialing plan is closed, the trunk code is retained for domestic calls, whether local or national, e.g.,

• Paris 01 xx xx xx xx (outside France +33 1 xxxx xxxx)
• Brussels 02 xxx xxxx (outside Belgium +32 2 xxx xxxx)
• Geneva 022 xxx xxxx (outside Switzerland +41 22 xxx xxxx)
• Cape Town 021 xxx xxxx (outside South Africa +27 21 xxx xxxx)
• New York 1 212 xxx xxxx (outside the North American Numbering Plan +1 212 xxx xxxx)

while some, like Italy, require the initial zero to be dialled, even for calls from outside the country, e.g.,

• Rome 06 xxxxxxxx (outside Italy +39 06 xxxxxxxx)

Further, there are locations with closed dialing plans in the NANP that require the full phone number including area code to be dialed for all calls, but the trunk code is required for only long distance calls, even in the same area code.

While the use of full national dialing is less user-friendly than using only a local number without the area code, the increased use of mobile phones, which can store numbers, means that this is of decreasing importance. It also makes easier to display numbers in the international format, as no trunk code is required—hence a number in Prague, Czech Republic, can now be displayed as:

• 2xx xxx xxx (inside Czech Republic)
• +420 2xx xxx xxx (outside Czech Republic)

as opposed to before September 21, 2002:^[7]

• 02 / xx xx xx xx (inside Czech Republic)
• +420 2 / xx xx xx xx (outside Czech Republic)

Some countries already switched, but trunk prefix re-added with the closed dialing plan, for example in Bangkok, Thailand before 1997:

• xxx-xxxx (inside Bangkok)
• 02-xxx-xxxx (inside Thailand)
• +66 2-xxx-xxxx (outside Thailand)

has been switched in 1997:

• 2-xxx-xxxx (inside Thailand)
• +66 2-xxx-xxxx (outside Thailand)

Trunk prefix has re-added in 2001

• 02-xxx-xxxx (inside Thailand)
• +66 2-xxx-xxxx (outside Thailand)

Satellite phone numbering plans[link]

Satellite phones are usually issued with numbers in a special country calling code. For example, Inmarsat satellite phones are issued with code +870, while Global Mobile Satellite System providers, such as Iridium, issue numbers in country code +881 ("Global Mobile Satellite System") or +882 ("International Networks"). Some satellite phones are issued with ordinary phone numbers, such as Globalstar satellite phones issued with NANP telephone numbers.

• Inmarsat:+870: SNAC (Single Network Access Code)
• ICO Global: +881 0, +881 1.
• Ellipso: +881 2, +881 3.
• Iridium: +881 6, +881 7.
• Globalstar: +881 8, +881 9.
• Emsat: +882 13.
• Thuraya: +882 16.
• ACeS: +882 20.

+ 88184

Special services[link]

Some country calling codes are issued for special services, or for international/inter regional zones.

• +388 5 – shared code for groups of nations
• +388 3 – European Telephony Numbering Space – Europe-wide services (discontinued)
• +800 – International Freephone (UIFN)
• +808 – reserved for Shared Cost Services
• +878 – Universal Personal Telecommunications services
• +881 – Global Mobile Satellite System
• +882 – International Networks
• +888 - international disaster relief operations
• +979 – International Premium Rate Service
• +991 – International Telecommunications Public Correspondence Service trial (ITPCS)
• +996 9 - Kyrgyzstan PG.R.S. Server
• +999 – reserved for future global service

Numbering plans by global regions[link]

• Telephone numbers in the Americas
• Telephone numbers in Oceania
• Telephone numbers in Europe
• Telephone numbers in Asia
• Telephone numbers in Africa

Dial plan syntax[link]

The following syntax used to identify a dial plan in a digit map is adapted from [RFC 2705]^[8].

To specify a

Enter the following

Result

Some dial plan examples using the above syntax look as follows:

For calls to

Users dial

Dial plan

Numbering plan indicator[link]

The numbering plan indicator (NPI) is a number which is defined in the ITU standard Q.713, paragraph 3.4.2.3.3, indicating the numbering plan of the attached telephone number. NPIs can be found in SCCP and SMS messages. As of 2004^[update], the following numbering plans and their respective numbering plan indicator values have been defined:

See also[link]

• List of North American Numbering Plan area codes for the U.S., Canada, Caribbean, and Pacific Ocean islands
• List of dialling codes in the United Kingdom
• Telephone numbers in Australia
• Carrier access code

External links[link]

• http://www.itu.int/dms_pub/itu-t/opb/sp/T-SP-LT.1-2011-PDF-E.pdf
• List of ITU-T Recommendation E.164 assigned country codes as of 1 Nov 2011
• http://www.itu.int/dms_pub/itu-t/opb/sp/T-SP-E.164C-2011-PDF-E.pdf of ITU-T Recommendation E.164 Dialling Procedures as of 15 DEC 2011]
• World Telephone Numbering Guide

References[link]

v t e Telecommunications (general) History Beacons Broadcasting Communications satellites Computer networks Drums Electrical telegraphs Fax Heliographs Hydraulic telegraphs Internet Mass media Mobile phones Optical telegraphy Photophones Radio Radiotelephones Telegraphy Telephones The Telephone Cases Television Undersea telegraph lines Videophones Pioneers Edwin Howard Armstrong John Logie Baird Alexander Graham Bell Tim Berners-Lee Jagadish Chandra Bose Vint Cerf Claude Chappe Lee De Forest Philo Farnsworth Reginald Fessenden Elisha Gray Guglielmo Marconi Alexander Stepanovich Popov Johann Philipp Reis Nikola Tesla Alfred Vail Charles Wheatstone Vladimir K. Zworykin Media Coaxial cable Free-space optical Optical fiber Radio waves Telephone lines Terrestrial microwave Networks ARPANET BITNET Ethernet FidoNet ISDN Internet Local area Mobile NGN Packet switched Public Switched Telephone Radio Television Telex Wide area World Wide Web Wireless Geographic v t e Telecommunications in Africa Sovereign states Algeria Angola Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Central African Republic Chad Comoros Democratic Republic of the Congo Republic of the Congo Côte d'Ivoire (Ivory Coast) Djibouti Egypt Equatorial Guinea Eritrea Ethiopia Gabon The Gambia Ghana Guinea Guinea-Bissau Kenya Lesotho Liberia Libya Madagascar Malawi Mali Mauritania Mauritius Morocco Mozambique Namibia Niger Nigeria Rwanda São Tomé and Príncipe Senegal Seychelles Sierra Leone Somalia South Africa South Sudan Sudan Swaziland Tanzania Togo Tunisia Uganda Zambia Zimbabwe States with limited recognition Azawad Sahrawi Arab Democratic Republic Somaliland Dependencies and other territories Canary Islands / Ceuta / Melilla / Plazas de soberanía (Spain) Madeira (Portugal) Mayotte / Réunion (France) Saint Helena / Ascension Island / Tristan da Cunha (United Kingdom) Western Sahara v t e Telecommunications in Asia Sovereign states Afghanistan Armenia Azerbaijan Bahrain Bangladesh Bhutan Brunei Burma (Myanmar) Cambodia People's Republic of China Cyprus East Timor (Timor-Leste) Egypt Georgia India Indonesia Iran Iraq Israel Japan Jordan Kazakhstan North Korea South Korea Kuwait Kyrgyzstan Laos Lebanon Malaysia Maldives Mongolia Nepal Oman Pakistan Philippines Qatar Russia Saudi Arabia Singapore Sri Lanka Syria Tajikistan Thailand Turkey Turkmenistan United Arab Emirates Uzbekistan Vietnam Yemen States with limited recognition Abkhazia Nagorno-Karabakh Northern Cyprus Palestine Republic of China (Taiwan) South Ossetia Dependencies and other territories British Indian Ocean Territory Christmas Island Cocos (Keeling) Islands Hong Kong Macau v t e Telecommunications in Europe Sovereign states Albania Andorra Armenia Austria Azerbaijan Belarus Belgium Bosnia and Herzegovina Bulgaria Croatia Cyprus Czech Republic Denmark Estonia Finland France Georgia Germany Greece Hungary Iceland Ireland Italy Kazakhstan Latvia Liechtenstein Lithuania Luxembourg Macedonia Malta Moldova Monaco Montenegro Netherlands Norway Poland Portugal Romania Russia San Marino Serbia Slovakia Slovenia Spain Sweden Switzerland Turkey Ukraine United Kingdom England Northern Ireland Scotland Wales States with limited recognition Abkhazia Kosovo Nagorno-Karabakh Northern Cyprus South Ossetia Transnistria Dependencies and other territories Åland Faroe Islands Gibraltar Guernsey Jersey Isle of Man Svalbard Other entities European Union v t e Telecommunications in North America Sovereign states Antigua and Barbuda Bahamas Barbados Belize Canada Costa Rica Cuba Dominica Dominican Republic El Salvador Grenada Guatemala Haiti Honduras Jamaica Mexico Nicaragua Panama Saint Kitts and Nevis Saint Lucia Saint Vincent and the Grenadines Trinidad and Tobago United States Dependencies and other territories Anguilla Aruba Bermuda Bonaire British Virgin Islands Cayman Islands Curaçao Greenland Guadeloupe Martinique Montserrat Navassa Island Puerto Rico Saint Barthélemy Saint Martin Saint Pierre and Miquelon Saba Sint Eustatius Sint Maarten Turks and Caicos Islands United States Virgin Islands v t e Telecommunications in Oceania Sovereign states Australia East Timor (Timor-Leste) Fiji Indonesia Kiribati Marshall Islands Federated States of Micronesia Nauru New Zealand Palau Papua New Guinea Samoa Solomon Islands Tonga Tuvalu Vanuatu Dependencies and other territories American Samoa Christmas Island Cocos (Keeling) Islands Cook Islands Easter Island French Polynesia Guam Hawaii New Caledonia Niue Norfolk Island Northern Mariana Islands Pitcairn Islands Tokelau Wallis and Futuna v t e Telecommunications in South America Sovereign states Argentina Bolivia Brazil Chile Colombia Ecuador Guyana Paraguay Peru Suriname Uruguay Venezuela Dependencies and other territories Aruba Bonaire Curaçao Falkland Islands French Guiana South Georgia and the South Sandwich Islands

The combined area of these three shapes is between 15 and 16 squares.

Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (m²), which is the area of a square whose sides are one metre long.^[1] A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.^[2] For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.^[3]

For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.

Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry.^[4] In analysis, the area of a subset of the plane is defined using Lebesgue measure,^[5] though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.

Formal definition[link]

An approach to defining what is meant by area is through axioms. For example, we may define area as a function a from a collection M of special kind of plane figures (termed measurable sets) to the set of real numbers which satisfies the following properties:

• For all S in M, a(S) ≥ 0.
• If S and T are in M then so are S ∪ T and S ∩ T, and also a(S∪T) = a(S) + a(T) − a(S∩T).
• If S and T are in M with S ⊆ T then T − S is in M and a(T−S) = a(T) − a(S).
• If a set S is in M and S is congruent to T then T is also in M and a(S) = a(T).
• Every rectangle R is in M. If the rectangle has length h and breadth k then a(R) = hk.
• Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. S ⊆ Q ⊆ T. If there is a unique number c such that a(S) ≤ c ≤ a(T) for all such step regions S and T, then a(Q) = c.

It can be proved that such an area function actually exists. (See, for example, Elementary Geometry from an Advanced Standpoint by Edwin Moise.)

Units[link]