Latitude
Overview

In geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

, the latitude of a location on the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

is the angular distance
Angular distance
In mathematics and all natural sciences , the angular distance between two point objects, as observed from a location different from either of these objects, is the size of the angle between the two directions originating from...

of that location south or north of the Equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

. The latitude is an angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

, and is usually measured in degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s (marked with °). The equator has a latitude of 0°, the North pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...

has a latitude of 90° north (written 90° N or +90°), and the South pole
South Pole
The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is one of the two points where the Earth's axis of rotation intersects its surface. It is the southernmost point on the surface of the Earth and lies on the opposite side of the Earth from the North Pole...

has a latitude of 90° south (written 90° S or −90°). Together, latitude and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

can be used as a geographic coordinate system
Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...

to specify any location on the globe.

Curves of constant latitude on the Earth (running east-west) are referred to as
lines of latitude
Circle of latitude
A circle of latitude, on the Earth, is an imaginary east-west circle connecting all locations that share a given latitude...

, or parallels.
Encyclopedia
In geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

, the latitude of a location on the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

is the angular distance
Angular distance
In mathematics and all natural sciences , the angular distance between two point objects, as observed from a location different from either of these objects, is the size of the angle between the two directions originating from...

of that location south or north of the Equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

. The latitude is an angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

, and is usually measured in degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s (marked with °). The equator has a latitude of 0°, the North pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...

has a latitude of 90° north (written 90° N or +90°), and the South pole
South Pole
The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is one of the two points where the Earth's axis of rotation intersects its surface. It is the southernmost point on the surface of the Earth and lies on the opposite side of the Earth from the North Pole...

has a latitude of 90° south (written 90° S or −90°). Together, latitude and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

can be used as a geographic coordinate system
Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...

to specify any location on the globe.

Curves of constant latitude on the Earth (running east-west) are referred to as
lines of latitude
Circle of latitude
A circle of latitude, on the Earth, is an imaginary east-west circle connecting all locations that share a given latitude...

, or parallels. Each line of latitude is actually a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

on the Earth parallel to the equator, and for this reason lines of latitude are also known as circles of latitude. In spherical geometry
Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy....

, lines of latitude are examples of circles of a sphere, with the equator being a great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

.

Latitude (usually denoted by the Greek letter phi
Phi (letter)
Phi , pronounced or sometimes in English, and in modern Greek, is the 21st letter of the Greek alphabet. In modern Greek, it represents , a voiceless labiodental fricative. In Ancient Greek it represented , an aspirated voiceless bilabial plosive...

(φ)) is often measured in degrees, minutes and seconds. The Eiffel Tower
Eiffel Tower
The Eiffel Tower is a puddle iron lattice tower located on the Champ de Mars in Paris. Built in 1889, it has become both a global icon of France and one of the most recognizable structures in the world...

has a latitude of 48° 51′ 29″ N-- that is, 48 degrees plus 51 minutes plus 29 seconds. Or latitude may be measured entirely in degrees, e.g. 48.85806° N.

If the Earth were actually spherical, and homogenous, and not rotating, then latitude at a point would just be the angle between a vertical line at that point and the plane of the equator. Everywhere on Earth a vertical line would point to the center of the Earth. In reality the earth is rotating and is not spherical, so a vertical line — a line in the direction of apparent gravity — doesn't point to the center of the Earth (except at the poles and the equator). If the Earth were homogenous, then a vertical line would still point to some point on the Earth's axis, and latitude at a point would still be the angle between the vertical line there and the plane of the equator.

But the Earth is not homogenous, and has mountains-- which have gravity and so can shift the vertical line away from the Earth's axis. The vertical line still intersects the plane of the equator at some angle; that angle is astronomical latitude, the latitude you would calculate from star observations. The latitude shown on maps and GPS devices is the angle between a not-quite-vertical line through the point and the plane of the equator; the not-quite-vertical line is perpendicular to the surface of the spheroid chosen to approximate the Earth's sea-level surface, rather than perpendicular to the sea-level surface itself.

## Examples

Besides the equator, four other lines of latitude are commonly used to mark map
Map
A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes....

s of the Earth. Each of these lines plays an important role in the geometrical relationship between the Earth and the Sun:
• Arctic Circle
Arctic Circle
The Arctic Circle is one of the five major circles of latitude that mark maps of the Earth. For Epoch 2011, it is the parallel of latitude that runs north of the Equator....

: 66° 33′ 39″ N
• Tropic of Cancer
Tropic of Cancer
The Tropic of Cancer, also referred to as the Northern tropic, is the circle of latitude on the Earth that marks the most northerly position at which the Sun may appear directly overhead at its zenith...

: 23° 26′ 21″ N
• Equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

: 0° Latitude
• Tropic of Capricorn
Tropic of Capricorn
The Tropic of Capricorn, or Southern tropic, marks the most southerly latitude on the Earth at which the Sun can be directly overhead. This event occurs at the December solstice, when the southern hemisphere is tilted towards the Sun to its maximum extent.Tropic of Capricorn is one of the five...

: 23° 26′ 21″ S
• Antarctic Circle
Antarctic Circle
The Antarctic Circle is one of the five major circles of latitude that mark maps of the Earth. For 2011, it is the parallel of latitude that runs south of the Equator.-Description:...

: 66° 33′ 39" S

Only at latitudes in the tropics
Tropics
The tropics is a region of the Earth surrounding the Equator. It is limited in latitude by the Tropic of Cancer in the northern hemisphere at approximately  N and the Tropic of Capricorn in the southern hemisphere at  S; these latitudes correspond to the axial tilt of the Earth...

is it possible for the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

to be directly overhead (at the zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...

). Alternatively, only within the Arctic and Antarctic circles is it possible to have a polar night
Polar night
The polar night occurs when the night lasts for more than 24 hours. This occurs only inside the polar circles. The opposite phenomenon, the polar day, or midnight sun, occurs when the sun stays above the horizon for more than 24 hours.-Description:...

or midnight sun
Midnight sun
The midnight sun is a natural phenomenon occurring in summer months at latitudes north and nearby to the south of the Arctic Circle, and south and nearby to the north of the Antarctic Circle where the sun remains visible at the local midnight. Given fair weather, the sun is visible for a continuous...

.

The latitudes of the two tropics are determined by the axial tilt
Axial tilt
In astronomy, axial tilt is the angle between an object's rotational axis, and a line perpendicular to its orbital plane...

of the Earth with respect to the sun, which is approximately 23° 26′ 21″. The latitudes of the Arctic and Antarctic circles are the complements
Complementary angles
In geometry, complementary angles are angles whose measures sum to 90°. If the two complementary angles are adjacent their non-shared sides form a right angle....

to this angle.

### Table of latitudes

The following table lists the regions of the Earth (excluding oceans) at various latitudes:
Latitude Locations
90° N North pole
North Pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is, subject to the caveats explained below, defined as the point in the northern hemisphere where the Earth's axis of rotation meets its surface...

75° N
75th parallel north
The 75th parallel north is a circle of latitude that is 75 degrees north of the Earth's equatorial plane, in the Arctic. It crosses the Atlantic Ocean, Europe, Asia, the Arctic Ocean and North America....

Arctic ocean
Arctic Ocean
The Arctic Ocean, located in the Northern Hemisphere and mostly in the Arctic north polar region, is the smallest and shallowest of the world's five major oceanic divisions...

; northern Siberia
Siberia
Siberia is an extensive region constituting almost all of Northern Asia. Comprising the central and eastern portion of the Russian Federation, it was part of the Soviet Union from its beginning, as its predecessor states, the Tsardom of Russia and the Russian Empire, conquered it during the 16th...

, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

; Greenland
Greenland
Greenland is an autonomous country within the Kingdom of Denmark, located between the Arctic and Atlantic Oceans, east of the Canadian Arctic Archipelago. Though physiographically a part of the continent of North America, Greenland has been politically and culturally associated with Europe for...

60° N
60th parallel north
The 60th parallel north is a circle of latitude that is 60 degrees north of the Earth's equatorial plane. It crosses Europe, Asia, the Pacific Ocean, North America, and the Atlantic Ocean....

Shetland Islands
Shetland Islands
Shetland is a subarctic archipelago of Scotland that lies north and east of mainland Great Britain. The islands lie some to the northeast of Orkney and southeast of the Faroe Islands and form part of the division between the Atlantic Ocean to the west and the North Sea to the east. The total...

(United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

); Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...

(through Oslo
Oslo
Oslo is a municipality, as well as the capital and most populous city in Norway. As a municipality , it was established on 1 January 1838. Founded around 1048 by King Harald III of Norway, the city was largely destroyed by fire in 1624. The city was moved under the reign of Denmark–Norway's King...

); Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

; Finland
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...

; Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

Alaska is the largest state in the United States by area. It is situated in the northwest extremity of the North American continent, with Canada to the east, the Arctic Ocean to the north, and the Pacific Ocean to the west and south, with Russia further west across the Bering Strait...

; Yukon
Yukon
Yukon is the westernmost and smallest of Canada's three federal territories. It was named after the Yukon River. The word Yukon means "Great River" in Gwich’in....

to north tip of Newfoundland
Newfoundland and Labrador is the easternmost province of Canada. Situated in the country's Atlantic region, it incorporates the island of Newfoundland and mainland Labrador with a combined area of . As of April 2011, the province's estimated population is 508,400...

in Canada; south tip of Greenland
Greenland
Greenland is an autonomous country within the Kingdom of Denmark, located between the Arctic and Atlantic Oceans, east of the Canadian Arctic Archipelago. Though physiographically a part of the continent of North America, Greenland has been politically and culturally associated with Europe for...

45° N France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

; Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

; Croatia
Croatia
Croatia , officially the Republic of Croatia , is a unitary democratic parliamentary republic in Europe at the crossroads of the Mitteleuropa, the Balkans, and the Mediterranean. Its capital and largest city is Zagreb. The country is divided into 20 counties and the city of Zagreb. Croatia covers ...

; Bosnia; Serbia
Serbia
Serbia , officially the Republic of Serbia , is a landlocked country located at the crossroads of Central and Southeast Europe, covering the southern part of the Carpathian basin and the central part of the Balkans...

; Romania
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...

; the Black sea
Black Sea
The Black Sea is bounded by Europe, Anatolia and the Caucasus and is ultimately connected to the Atlantic Ocean via the Mediterranean and the Aegean seas and various straits. The Bosphorus strait connects it to the Sea of Marmara, and the strait of the Dardanelles connects that sea to the Aegean...

; Ukraine
Ukraine
Ukraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...

; Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

; the Caspian sea
Caspian Sea
The Caspian Sea is the largest enclosed body of water on Earth by area, variously classed as the world's largest lake or a full-fledged sea. The sea has a surface area of and a volume of...

; Kazakhstan
Kazakhstan
Kazakhstan , officially the Republic of Kazakhstan, is a transcontinental country in Central Asia and Eastern Europe. Ranked as the ninth largest country in the world, it is also the world's largest landlocked country; its territory of is greater than Western Europe...

; Xinjiang
Xinjiang
Xinjiang is an autonomous region of the People's Republic of China. It is the largest Chinese administrative division and spans over 1.6 million km2...

(China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

); Mongolia
Mongolia
Mongolia is a landlocked country in East and Central Asia. It is bordered by Russia to the north and China to the south, east and west. Although Mongolia does not share a border with Kazakhstan, its western-most point is only from Kazakhstan's eastern tip. Ulan Bator, the capital and largest...

; Inner Mongolia
Inner Mongolia
Inner Mongolia is an autonomous region of the People's Republic of China, located in the northern region of the country. Inner Mongolia shares an international border with the countries of Mongolia and the Russian Federation...

and Manchuria
Manchuria
Manchuria is a historical name given to a large geographic region in northeast Asia. Depending on the definition of its extent, Manchuria usually falls entirely within the People's Republic of China, or is sometimes divided between China and Russia. The region is commonly referred to as Northeast...

(China); far east Russia; Hokkaido
Hokkaido
, formerly known as Ezo, Yezo, Yeso, or Yesso, is Japan's second largest island; it is also the largest and northernmost of Japan's 47 prefectural-level subdivisions. The Tsugaru Strait separates Hokkaido from Honshu, although the two islands are connected by the underwater railway Seikan Tunnel...

(Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...

); Kurils (Russia); Oregon
Oregon
Oregon is a state in the Pacific Northwest region of the United States. It is located on the Pacific coast, with Washington to the north, California to the south, Nevada on the southeast and Idaho to the east. The Columbia and Snake rivers delineate much of Oregon's northern and eastern...

to Michigan
Michigan
Michigan is a U.S. state located in the Great Lakes Region of the United States of America. The name Michigan is the French form of the Ojibwa word mishigamaa, meaning "large water" or "large lake"....

in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

; Lake Huron
Lake Huron
Lake Huron is one of the five Great Lakes of North America. Hydrologically, it comprises the larger portion of Lake Michigan-Huron. It is bounded on the east by the Canadian province of Ontario and on the west by the state of Michigan in the United States...

; Ontario
Ontario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....

Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

; Maine
Maine
Maine is a state in the New England region of the northeastern United States, bordered by the Atlantic Ocean to the east and south, New Hampshire to the west, and the Canadian provinces of Quebec to the northwest and New Brunswick to the northeast. Maine is both the northernmost and easternmost...

(USA); Nova Scotia
Nova Scotia
Nova Scotia is one of Canada's three Maritime provinces and is the most populous province in Atlantic Canada. The name of the province is Latin for "New Scotland," but "Nova Scotia" is the recognized, English-language name of the province. The provincial capital is Halifax. Nova Scotia is the...

30° N
30th parallel north
The 30th parallel north is a circle of latitude that is 30 degrees north of the Earth's equatorial plane. It stands one-third of the way between the equator and the North Pole and crosses Africa, Asia, the Pacific Ocean, North America and the Atlantic Ocean....

Morocco
Morocco
Morocco , officially the Kingdom of Morocco , is a country located in North Africa. It has a population of more than 32 million and an area of 710,850 km², and also primarily administers the disputed region of the Western Sahara...

; Algeria
Algeria
Algeria , officially the People's Democratic Republic of Algeria , also formally referred to as the Democratic and Popular Republic of Algeria, is a country in the Maghreb region of Northwest Africa with Algiers as its capital.In terms of land area, it is the largest country in Africa and the Arab...

; Libya
Libya
Libya is an African country in the Maghreb region of North Africa bordered by the Mediterranean Sea to the north, Egypt to the east, Sudan to the southeast, Chad and Niger to the south, and Algeria and Tunisia to the west....

; Egypt
Egypt
Egypt , officially the Arab Republic of Egypt, Arabic: , is a country mainly in North Africa, with the Sinai Peninsula forming a land bridge in Southwest Asia. Egypt is thus a transcontinental country, and a major power in Africa, the Mediterranean Basin, the Middle East and the Muslim world...

; Jordan
Jordan
Jordan , officially the Hashemite Kingdom of Jordan , Al-Mamlaka al-Urduniyya al-Hashemiyya) is a kingdom on the East Bank of the River Jordan. The country borders Saudi Arabia to the east and south-east, Iraq to the north-east, Syria to the north and the West Bank and Israel to the west, sharing...

; Saudi Arabia
Saudi Arabia
The Kingdom of Saudi Arabia , commonly known in British English as Saudi Arabia and in Arabic as as-Sa‘ūdiyyah , is the largest state in Western Asia by land area, constituting the bulk of the Arabian Peninsula, and the second-largest in the Arab World...

; Iraq
Iraq
Iraq ; officially the Republic of Iraq is a country in Western Asia spanning most of the northwestern end of the Zagros mountain range, the eastern part of the Syrian Desert and the northern part of the Arabian Desert....

; Kuwait
Kuwait
The State of Kuwait is a sovereign Arab state situated in the north-east of the Arabian Peninsula in Western Asia. It is bordered by Saudi Arabia to the south at Khafji, and Iraq to the north at Basra. It lies on the north-western shore of the Persian Gulf. The name Kuwait is derived from the...

; the Persian Gulf
Persian Gulf
The Persian Gulf, in Southwest Asia, is an extension of the Indian Ocean located between Iran and the Arabian Peninsula.The Persian Gulf was the focus of the 1980–1988 Iran-Iraq War, in which each side attacked the other's oil tankers...

; Iran
Iran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...

; Afghanistan
Afghanistan
Afghanistan , officially the Islamic Republic of Afghanistan, is a landlocked country located in the centre of Asia, forming South Asia, Central Asia and the Middle East. With a population of about 29 million, it has an area of , making it the 42nd most populous and 41st largest nation in the world...

; Pakistan
Pakistan
Pakistan , officially the Islamic Republic of Pakistan is a sovereign state in South Asia. It has a coastline along the Arabian Sea and the Gulf of Oman in the south and is bordered by Afghanistan and Iran in the west, India in the east and China in the far northeast. In the north, Tajikistan...

; India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

; Nepal
Nepal
Nepal , officially the Federal Democratic Republic of Nepal, is a landlocked sovereign state located in South Asia. It is located in the Himalayas and bordered to the north by the People's Republic of China, and to the south, east, and west by the Republic of India...

; southern China; south tip of Japan; northern Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...

; Texas
Texas
Texas is the second largest U.S. state by both area and population, and the largest state by area in the contiguous United States.The name, based on the Caddo word "Tejas" meaning "friends" or "allies", was applied by the Spanish to the Caddo themselves and to the region of their settlement in...

, Louisiana
Louisiana
Louisiana is a state located in the southern region of the United States of America. Its capital is Baton Rouge and largest city is New Orleans. Louisiana is the only state in the U.S. with political subdivisions termed parishes, which are local governments equivalent to counties...

and Florida
Florida
Florida is a state in the southeastern United States, located on the nation's Atlantic and Gulf coasts. It is bordered to the west by the Gulf of Mexico, to the north by Alabama and Georgia and to the east by the Atlantic Ocean. With a population of 18,801,310 as measured by the 2010 census, it...

(USA); Savage Islands
Savage Islands
The Savage Islands, also referred to as the Salvage Islands or the Selvagens Islands, of Sé. They are designated a Nature Reserve, comprising two areas: one on Selvagem Grande Island and the second on Selvagem Pequena Island.-Geography:...

(Portugal
Portugal
Portugal , officially the Portuguese Republic is a country situated in southwestern Europe on the Iberian Peninsula. Portugal is the westernmost country of Europe, and is bordered by the Atlantic Ocean to the West and South and by Spain to the North and East. The Atlantic archipelagos of the...

)
15° N
15th parallel north
The 15th parallel north is a circle of latitude that is 15 degrees north of the Earth's equatorial plane. It crosses Africa, Asia, the Indian Ocean, the Pacific Ocean, Central America, the Caribbean and the Atlantic Ocean....

Senegal
Senegal
Senegal , officially the Republic of Senegal , is a country in western Africa. It owes its name to the Sénégal River that borders it to the east and north...

; Mauritania
Mauritania
Mauritania is a country in the Maghreb and West Africa. It is bordered by the Atlantic Ocean in the west, by Western Sahara in the north, by Algeria in the northeast, by Mali in the east and southeast, and by Senegal in the southwest...

; Mali
Mali
Mali , officially the Republic of Mali , is a landlocked country in Western Africa. Mali borders Algeria on the north, Niger on the east, Burkina Faso and the Côte d'Ivoire on the south, Guinea on the south-west, and Senegal and Mauritania on the west. Its size is just over 1,240,000 km² with...

; Burkina Faso
Burkina Faso
Burkina Faso – also known by its short-form name Burkina – is a landlocked country in west Africa. It is surrounded by six countries: Mali to the north, Niger to the east, Benin to the southeast, Togo and Ghana to the south, and Côte d'Ivoire to the southwest.Its size is with an estimated...

; Niger
Niger
Niger , officially named the Republic of Niger, is a landlocked country in Western Africa, named after the Niger River. It borders Nigeria and Benin to the south, Burkina Faso and Mali to the west, Algeria and Libya to the north and Chad to the east...

Chad , officially known as the Republic of Chad, is a landlocked country in Central Africa. It is bordered by Libya to the north, Sudan to the east, the Central African Republic to the south, Cameroon and Nigeria to the southwest, and Niger to the west...

; Sudan
Sudan
Sudan , officially the Republic of the Sudan , is a country in North Africa, sometimes considered part of the Middle East politically. It is bordered by Egypt to the north, the Red Sea to the northeast, Eritrea and Ethiopia to the east, South Sudan to the south, the Central African Republic to the...

; Eritrea
Eritrea
Eritrea , officially the State of Eritrea, is a country in the Horn of Africa. Eritrea derives it's name from the Greek word Erethria, meaning 'red land'. The capital is Asmara. It is bordered by Sudan in the west, Ethiopia in the south, and Djibouti in the southeast...

; the Red sea
Red Sea
The Red Sea is a seawater inlet of the Indian Ocean, lying between Africa and Asia. The connection to the ocean is in the south through the Bab el Mandeb strait and the Gulf of Aden. In the north, there is the Sinai Peninsula, the Gulf of Aqaba, and the Gulf of Suez...

; Yemen
Yemen
The Republic of Yemen , commonly known as Yemen , is a country located in the Middle East, occupying the southwestern to southern end of the Arabian Peninsula. It is bordered by Saudi Arabia to the north, the Red Sea to the west, and Oman to the east....

; India; Myanmar
Myanmar
Burma , officially the Republic of the Union of Myanmar , is a country in Southeast Asia. Burma is bordered by China on the northeast, Laos on the east, Thailand on the southeast, Bangladesh on the west, India on the northwest, the Bay of Bengal to the southwest, and the Andaman Sea on the south....

; Thailand
Thailand
Thailand , officially the Kingdom of Thailand , formerly known as Siam , is a country located at the centre of the Indochina peninsula and Southeast Asia. It is bordered to the north by Burma and Laos, to the east by Laos and Cambodia, to the south by the Gulf of Thailand and Malaysia, and to the...

; Laos
Laos
Laos Lao: ສາທາລະນະລັດ ປະຊາທິປະໄຕ ປະຊາຊົນລາວ Sathalanalat Paxathipatai Paxaxon Lao, officially the Lao People's Democratic Republic, is a landlocked country in Southeast Asia, bordered by Burma and China to the northwest, Vietnam to the east, Cambodia to the south and Thailand to the west...

; Vietnam
Vietnam
Vietnam – sometimes spelled Viet Nam , officially the Socialist Republic of Vietnam – is the easternmost country on the Indochina Peninsula in Southeast Asia. It is bordered by China to the north, Laos to the northwest, Cambodia to the southwest, and the South China Sea –...

; Philippines
Philippines
The Philippines , officially known as the Republic of the Philippines , is a country in Southeast Asia in the western Pacific Ocean. To its north across the Luzon Strait lies Taiwan. West across the South China Sea sits Vietnam...

; Northern Mariana Islands
Northern Mariana Islands
The Northern Mariana Islands, officially the Commonwealth of the Northern Mariana Islands , is a commonwealth in political union with the United States, occupying a strategic region of the western Pacific Ocean. It consists of 15 islands about three-quarters of the way from Hawaii to the Philippines...

; southern Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...

; Guatemala
Guatemala
Guatemala is a country in Central America bordered by Mexico to the north and west, the Pacific Ocean to the southwest, Belize to the northeast, the Caribbean to the east, and Honduras and El Salvador to the southeast...

; Honduras
Honduras
Honduras is a republic in Central America. It was previously known as Spanish Honduras to differentiate it from British Honduras, which became the modern-day state of Belize...

; Nicaragua
Nicaragua
Nicaragua is the largest country in the Central American American isthmus, bordered by Honduras to the north and Costa Rica to the south. The country is situated between 11 and 14 degrees north of the Equator in the Northern Hemisphere, which places it entirely within the tropics. The Pacific Ocean...

; Caribbean Islands (between Dominica
Dominica
Dominica , officially the Commonwealth of Dominica, is an island nation in the Lesser Antilles region of the Caribbean Sea, south-southeast of Guadeloupe and northwest of Martinique. Its size is and the highest point in the country is Morne Diablotins, which has an elevation of . The Commonwealth...

and Martinique
Martinique
Martinique is an island in the eastern Caribbean Sea, with a land area of . Like Guadeloupe, it is an overseas region of France, consisting of a single overseas department. To the northwest lies Dominica, to the south St Lucia, and to the southeast Barbados...

); Cape Verde
Cape Verde
The Republic of Cape Verde is an island country, spanning an archipelago of 10 islands located in the central Atlantic Ocean, 570 kilometres off the coast of Western Africa...

Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

São Tomé and Príncipe
São Tomé and Príncipe
São Tomé and Príncipe, officially the Democratic Republic of São Tomé and Príncipe, is a Portuguese-speaking island nation in the Gulf of Guinea, off the western equatorial coast of Central Africa. It consists of two islands: São Tomé and Príncipe, located about apart and about , respectively, off...

; Gabon
Gabon
Gabon , officially the Gabonese Republic is a state in west central Africa sharing borders with Equatorial Guinea to the northwest, Cameroon to the north, and with the Republic of the Congo curving around the east and south. The Gulf of Guinea, an arm of the Atlantic Ocean is to the west...

; Republic of the Congo
Republic of the Congo
The Republic of the Congo , sometimes known locally as Congo-Brazzaville, is a state in Central Africa. It is bordered by Gabon, Cameroon, the Central African Republic, the Democratic Republic of the Congo , the Angolan exclave province of Cabinda, and the Gulf of Guinea.The region was dominated by...

; Democratic Republic of the Congo
Democratic Republic of the Congo
The Democratic Republic of the Congo is a state located in Central Africa. It is the second largest country in Africa by area and the eleventh largest in the world...

; Uganda
Uganda
Uganda , officially the Republic of Uganda, is a landlocked country in East Africa. Uganda is also known as the "Pearl of Africa". It is bordered on the east by Kenya, on the north by South Sudan, on the west by the Democratic Republic of the Congo, on the southwest by Rwanda, and on the south by...

; Lake Victoria
Lake Victoria
Lake Victoria is one of the African Great Lakes. The lake was named for Queen Victoria of the United Kingdom, by John Hanning Speke, the first European to discover this lake....

; Kenya
Kenya
Kenya , officially known as the Republic of Kenya, is a country in East Africa that lies on the equator, with the Indian Ocean to its south-east...

; Somalia
Somalia
Somalia , officially the Somali Republic and formerly known as the Somali Democratic Republic under Socialist rule, is a country located in the Horn of Africa. Since the outbreak of the Somali Civil War in 1991 there has been no central government control over most of the country's territory...

; Maldive Islands; Indonesia
Indonesia
Indonesia , officially the Republic of Indonesia , is a country in Southeast Asia and Oceania. Indonesia is an archipelago comprising approximately 13,000 islands. It has 33 provinces with over 238 million people, and is the world's fourth most populous country. Indonesia is a republic, with an...

; Kiribati
Kiribati
Kiribati , officially the Republic of Kiribati, is an island nation located in the central tropical Pacific Ocean. The permanent population exceeds just over 100,000 , and is composed of 32 atolls and one raised coral island, dispersed over 3.5 million square kilometres, straddling the...

; Galápagos Islands
Galápagos Islands
The Galápagos Islands are an archipelago of volcanic islands distributed around the equator in the Pacific Ocean, west of continental Ecuador, of which they are a part.The Galápagos Islands and its surrounding waters form an Ecuadorian province, a national park, and a...

Ecuador , officially the Republic of Ecuador is a representative democratic republic in South America, bordered by Colombia on the north, Peru on the east and south, and by the Pacific Ocean to the west. It is one of only two countries in South America, along with Chile, that do not have a border...

; Colombia
Colombia
Colombia, officially the Republic of Colombia , is a unitary constitutional republic comprising thirty-two departments. The country is located in northwestern South America, bordered to the east by Venezuela and Brazil; to the south by Ecuador and Peru; to the north by the Caribbean Sea; to the...

; northern Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...

15° S
15th parallel south
The 15th parallel south is a circle of latitude that is 15 degrees south of the Earth's equatorial plane. It crosses the Atlantic Ocean, Africa, the Indian Ocean, Australasia, the Pacific Ocean and South America....

Angola
Angola
Angola, officially the Republic of Angola , is a country in south-central Africa bordered by Namibia on the south, the Democratic Republic of the Congo on the north, and Zambia on the east; its west coast is on the Atlantic Ocean with Luanda as its capital city...

; Zambia
Zambia
Zambia , officially the Republic of Zambia, is a landlocked country in Southern Africa. The neighbouring countries are the Democratic Republic of the Congo to the north, Tanzania to the north-east, Malawi to the east, Mozambique, Zimbabwe, Botswana and Namibia to the south, and Angola to the west....

; Mozambique
Mozambique
Mozambique, officially the Republic of Mozambique , is a country in southeastern Africa bordered by the Indian Ocean to the east, Tanzania to the north, Malawi and Zambia to the northwest, Zimbabwe to the west and Swaziland and South Africa to the southwest...

; Malawi
Malawi
The Republic of Malawi is a landlocked country in southeast Africa that was formerly known as Nyasaland. It is bordered by Zambia to the northwest, Tanzania to the northeast, and Mozambique on the east, south and west. The country is separated from Tanzania and Mozambique by Lake Malawi. Its size...

The Republic of Madagascar is an island country located in the Indian Ocean off the southeastern coast of Africa...

; northern Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

; Vanuatu
Vanuatu
Vanuatu , officially the Republic of Vanuatu , is an island nation located in the South Pacific Ocean. The archipelago, which is of volcanic origin, is some east of northern Australia, northeast of New Caledonia, west of Fiji, and southeast of the Solomon Islands, near New Guinea.Vanuatu was...

; French Polynesia
French Polynesia
French Polynesia is an overseas country of the French Republic . It is made up of several groups of Polynesian islands, the most famous island being Tahiti in the Society Islands group, which is also the most populous island and the seat of the capital of the territory...

; Peru
Peru
Peru , officially the Republic of Peru , is a country in western South America. It is bordered on the north by Ecuador and Colombia, on the east by Brazil, on the southeast by Bolivia, on the south by Chile, and on the west by the Pacific Ocean....

; Bolivia
Bolivia
Bolivia officially known as Plurinational State of Bolivia , is a landlocked country in central South America. It is the poorest country in South America...

; Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...

30° S
30th parallel south
The 30th parallel south is a circle of latitude that is 30 degrees south of the Earth's equatorial plane. It crosses the Atlantic Ocean, Africa, the Indian Ocean, Australasia, the Pacific Ocean and South America....

South Africa
South Africa
The Republic of South Africa is a country in southern Africa. Located at the southern tip of Africa, it is divided into nine provinces, with of coastline on the Atlantic and Indian oceans...

; Lesotho
Lesotho
Lesotho , officially the Kingdom of Lesotho, is a landlocked country and enclave, surrounded by the Republic of South Africa. It is just over in size with a population of approximately 2,067,000. Its capital and largest city is Maseru. Lesotho is a member of the Commonwealth of Nations. The name...

The Kermadec Islands are a subtropical island arc in the South Pacific Ocean northeast of New Zealand's North Island, and a similar distance southwest of Tonga...

; Chile
Chile
Chile ,officially the Republic of Chile , is a country in South America occupying a long, narrow coastal strip between the Andes mountains to the east and the Pacific Ocean to the west. It borders Peru to the north, Bolivia to the northeast, Argentina to the east, and the Drake Passage in the far...

; Argentina
Argentina
Argentina , officially the Argentine Republic , is the second largest country in South America by land area, after Brazil. It is constituted as a federation of 23 provinces and an autonomous city, Buenos Aires...

; southern Brazil
Brazil
Brazil , officially the Federative Republic of Brazil , is the largest country in South America. It is the world's fifth largest country, both by geographical area and by population with over 192 million people...

45° S
45th parallel south
The 45th parallel south is a circle of latitude that is 45 degrees south of the Earth's equatorial plane. It is the line that marks the theoretical halfway point between the equator and the South Pole...

New Zealand
New Zealand
New Zealand is an island country in the south-western Pacific Ocean comprising two main landmasses and numerous smaller islands. The country is situated some east of Australia across the Tasman Sea, and roughly south of the Pacific island nations of New Caledonia, Fiji, and Tonga...

; Chile; Argentina
60° S
60th parallel south
The 60th parallel south is a circle of latitude that is 60 degrees south of the Earth's equatorial plane. No land lies on the parallel—it crosses nothing but ocean...

entirely ocean (slightly north of the South Orkney Islands
South Orkney Islands
The South Orkney Islands are a group of islands in the Southern Ocean, about north-east of the tip of the Antarctic Peninsula. They have a total area of about ....

); sometimes considered the northern boundary of the Southern ocean
Southern Ocean
The Southern Ocean comprises the southernmost waters of the World Ocean, generally taken to be south of 60°S latitude and encircling Antarctica. It is usually regarded as the fourth-largest of the five principal oceanic divisions...

75° S
75th parallel south
The 75th parallel south is a circle of latitude that is 75 degrees south of the Earth's equatorial plane in the Antarctic. The parallel passes through the Southern Ocean and Antarctica....

Dome C
Dome C
Dome C, also known as Dome Circe or Dome Charlie, located at Antarctica at an altitude of 3,233 m or 10,607 ft above sea level, is one of several summits or "domes" of the Antarctic Ice Sheet...

, Antarctica
90° S South pole
South Pole
The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is one of the two points where the Earth's axis of rotation intersects its surface. It is the southernmost point on the surface of the Earth and lies on the opposite side of the Earth from the North Pole...

## Subdivisions

A degree is divided into 60 minutes
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

. One minute can be further divided into 60 seconds. An example of a latitude specified in this way is 13°19'43″ N (for greater precision, a decimal fraction can be added to the seconds). An alternative representation uses only degrees and minutes, where the seconds are expressed as a decimal fraction of minutes: the above example would be expressed as 13°19.717' N. Degrees can also be expressed singularly, with both the minutes and seconds incorporated as a decimal number and rounded as desired (decimal degree notation): 13.32861° N. Sometimes, the north/south suffix is replaced by a negative sign for south (−90° for the South Pole).

## Effect of latitude

A region's latitude has a great effect on its climate
Climate
Climate encompasses the statistics of temperature, humidity, atmospheric pressure, wind, rainfall, atmospheric particle count and other meteorological elemental measurements in a given region over long periods...

and weather
Weather
Weather is the state of the atmosphere, to the degree that it is hot or cold, wet or dry, calm or stormy, clear or cloudy. Most weather phenomena occur in the troposphere, just below the stratosphere. Weather refers, generally, to day-to-day temperature and precipitation activity, whereas climate...

. Latitude more loosely determines prevailing winds, and other physical characteristics of geographic locations. Auroral
Aurora (astronomy)
An aurora is a natural light display in the sky particularly in the high latitude regions, caused by the collision of energetic charged particles with atoms in the high altitude atmosphere...

activity is common at high geomagnetic latitude
Geomagnetic latitude
Geomagnetic latitude is a parameter analogous to geographic latitude, except that bearing is with respect to the magnetic poles, as opposed to the geographic poles....

s.

Some observers have noted a correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

between the latitude of a country
Country
A country is a region legally identified as a distinct entity in political geography. A country may be an independent sovereign state or one that is occupied by another state, as a non-sovereign or formerly sovereign political division, or a geographic region associated with a previously...

and its economic
Economy
An economy consists of the economic system of a country or other area; the labor, capital and land resources; and the manufacturing, trade, distribution, and consumption of goods and services of that area...

activity; see North-South divide
North-South divide
The north–south divide is a socio-economic and political division that exists between the wealthy developed countries, known collectively as "the north", and the poorer developing countries , or "the south." Although most nations comprising the "North" are in fact located in the Northern Hemisphere ,...

.

## Elliptic parameters

Because most planets (including Earth) are ellipsoids of revolution, or spheroids, rather than sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

s, both the radius and the length of arc varies with latitude. This variation requires the introduction of elliptic parameters based on an ellipse's angular eccentricity
Angular eccentricity
In the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and eccentricity....

, (which equals , where and are the equatorial radius (6,378,137.0 m for Earth) and the polar radius (6,356,752.3142 m for Earth), respectively; is the first eccentricity
Eccentricity (mathematics)
In mathematics, the eccentricity, denoted e or \varepsilon, is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.In particular,...

squared, ; and or is the flattening
Flattening
The flattening, ellipticity, or oblateness of an oblate spheroid is a measure of the "squashing" of the spheroid's pole, towards its equator...

, . Utilized in creating the integrands for curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

is the inverse of the principal elliptic integrand, :

## Degree length

On the Earth's surface the length of an arcdegree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

of north–south latitude difference is about 60 nautical mile
Nautical mile
The nautical mile is a unit of length that is about one minute of arc of latitude along any meridian, but is approximately one minute of arc of longitude only at the equator...

s, 111 kilometre
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

s or 69 statute miles at any latitude. The length of an arcdegree of east-west longitude difference is about the same at the equator as the north-south, reducing to zero at the poles.

If the Earth were spherical a degree of latitude would cover exactly 60 nautical miles anywhere from the equator to the poles. In fact the Earth is slightly squashed — its "diameter" from pole to pole is slightly less than its equatorial diameter — making a north-south line on the Earth's surface more sharply curved near the equator than near the poles. Which means at the equator a degree of latitude covers 1% less north-south distance than it does at the poles.

On the WGS84 spheroid, the length in meters of a degree of latitude at latitude φ (that is, the distance along a north-south line from latitude (φ - 0.5) degrees to (φ + 0.5) degrees) is about

111132.954 - 559.822(cos 2φ) + 1.175(cos 4φ)

(Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.)
 Latitude N-S radiusof curvature Surface distance per 1° change in latitude E-W radius of curvature Surface distance per 1° change in longitude 0° 6335.44 km 110.574 km 6378.14 km 111.320 km 15° 6339.70 km 110.649 km 6379.57 km 107.551 km 30° 6351.38 km 110.852 km 6383.48 km 96.486 km 45° 6367.38 km 111.132 km 6388.84 km 78.847 km 60° 6383.45 km 111.412 km 6394.21 km 55.800 km 75° 6395.26 km 111.618 km 6398.15 km 28.902 km 90° 6399.59 km 111.694 km 6399.59 km 0.000 km

## Auxiliary latitudes

There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:
• geocentric latitude,
• reduced (or parametric) latitude,
• authalic latitude,
• rectifying latitude,
• conformal latitude,
• isometric latitude.

When the word 'latitude' is used without qualification it is to be taken as the geodetic latitude, sometimes called the geographic latitude.

All the auxiliary latitudes, except the isometric latitude, are numerically close to the geodetic latitude, the difference being zero at the poles and on the equator and attaining a maximum, between 5 and 10 minutes of arc, at a geodetic latitude a few arc minutes from 45 degrees. The geodetic latitude is greater than (or equal to) all auxiliary latitudes.

In the theory of map projections the auxiliary latitudes are typically employed as intermediate constructs in a transformation from geodetic coordinates to Eastings and Northings in the projection plane. The end user has no need of a numerical value such as the authalic latitude of the Eiffel tower.

The auxiliary latitudes defined below have been expressed in
terms of the semi-major axis, a, and the eccentricity, e, in forms which agree, apart from notational variants, with those given in the standard reference for map projections, namely Map projections — a working manual by Snyder. Derivations which assume some knowledge of the geometrical properties of the ellipsoid may be found in Adams. Pedagogical discussions of the geometry of the ellipsoid may be found in Rapp (Chapter 3) and Osborne (Chapters 5,6)

### Geocentric latitude

The geocentric latitude, denoted here by ψ, is the angle between the equatorial plane and the radius from the centre to a point on the surface. The relation between the geodetic latitude () and the geocentric latitude () is

The geodetic and geocentric latitudes are equal at the equator and poles. The value of the squared eccentricity is approximately 0.007 (depending on the choice of ellipsoid) and the maximum difference of is approximately 11.5 minutes of arc at a geodetic latitude of 45°6′.

### Reduced (or parametric) latitude

The reduced or parametric latitude, β, is defined by the radius drawn from the centre of the ellipsoid to that point on the surrounding sphere (of radius a) which is the vertical projection (parallel to Earth's axis of rotation) of a point on the ellipsoid at latitude . It was so-called by Bessel who solved problems for geodesics on the ellipsoid by reducing them to the equivalent problem on the sphere. It is widely used in the theory of projections. In terms of the geodetic latitude

The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p, the distance from the axis, and z, the distance above the equatorial plane, the equation of the ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

is

The Cartesian coordinates of the point are parameterized by

### Authalic latitude

The authalic latitude, ξ, gives an area-preserving transformation to a sphere.

where

and

and the radius of the sphere is taken as

Using the authalic latitude as a latitude on a sphere of the above radius defines an equal area mapping from the ellipsoid to the sphere. If the sphere is then projected to the plane with an area projection the result is an area-preserving double projection from the ellipsoid to the plane.

### Rectifying latitude

The rectifying latitude, μ, is the meridian distance scaled so that its value at the poles μ is equal 90 degrees or π/2 radians:

where the meridian distance from the equator to a latitude φ is (see Meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...

)

and the length of the meridian quadrant to the pole is

Using the rectifying latitude to define a latitude on a sphere of radius

defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an equirectangular projection
Equirectangular projection
The equirectangular projection is a very simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100...

to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale.

### Conformal latitude

The conformal latitude, χ, gives an angle-preserving (conformal
Conformal
Conformal may refer to:* Conformal map, in mathematics* Conformal geometry, in mathematics* Conformal map projection, in cartography* Conformal film on a surface* Conformal coating in electronics* Conformal hypergraph, in mathematics...

) transformation to the sphere.
.
This expression is sometimes given in the form
.
This kind of latitude defines a transformation from the ellipsoid to a sphere of arbitrary radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere (so that the shape of small elements is well preserved). A further conformal transformation from the sphere to the plane gives a conformal double projection from the ellipsoid to the plane. This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection
Transverse Mercator projection
The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM...

on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane).

### Isometric latitude

The isometric latitude, ψ (not to be confused with the geocentric latitude notation), is very important in the development of the ellipsoidal versions of the normal Mercator projection
Mercator projection
The Mercator projection is a cylindrical map projection presented by the Belgian geographer and cartographer Gerardus Mercator, in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as...

and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of ψ and longitude λ give rise to equal distance displacements along the meridians and parallels respectively. The graticule
Graticule
Graticule may refer to:* An oscilloscope graticule scale* Another name for the reticle pattern in an optical instrument* The grid used in the Geographic coordinate system...

defined by the lines of constant ψ and constant λ, divides the surface of the ellipsoid into a mesh of squares (of varying size). The isometric latitude is zero at the equator but rapidly diverges from the geodetic latitude, tending to infinity at the poles. The conventional notation is given in Snyder:

For the normal Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is E (units of length or pixels) then the distance, y, of a parallel of latitude φ from the equator is

### Comparison of selected types

The following plot shows the differences between the types of latitude. The data used are found in the table following the plot. Please note that the values in the table are in minutes, not degrees, and the plot reflects this as well. Also observe that the conformal symbols are hidden behind the geocentric due to being very close in value. Finally it is important to mention also that these differences don't mean that the use of one specific latitude will necessarily cause more distortions than the other (the real fact is that each latitude type is optimized for achieving a different goal).

Approximate difference from geographic latitude ("Lat")
Lat
Reduced
Authalic
Rectifying
Conformal
Geocentric
0.00′ 0.00′ 0.00′ 0.00′ 0.00′
1.01′ 1.35′ 1.52′ 2.02′ 2.02′
10° 1.99′ 2.66′ 2.99′ 3.98′ 3.98′
15° 2.91′ 3.89′ 4.37′ 5.82′ 5.82′
20° 3.75′ 5.00′ 5.62′ 7.48′ 7.48′
25° 4.47′ 5.96′ 6.70′ 8.92′ 8.92′
30° 5.05′ 6.73′ 7.57′ 10.09′ 10.09′
35° 5.48′ 7.31′ 8.22′ 10.95′ 10.96′
40° 5.75′ 7.66′ 8.62′ 11.48′ 11.49′
45° 5.84′ 7.78′ 8.76′ 11.67′ 11.67′
50° 5.75′ 7.67′ 8.63′ 11.50′ 11.50′
55° 5.49′ 7.32′ 8.23′ 10.97′ 10.98′
60° 5.06′ 6.75′ 7.59′ 10.12′ 10.13′
65° 4.48′ 5.97′ 6.72′ 8.95′ 8.96′
70° 3.76′ 5.01′ 5.64′ 7.52′ 7.52′
75° 2.92′ 3.90′ 4.39′ 5.85′ 5.85′
80° 2.00′ 2.67′ 3.00′ 4.00′ 4.01′
85° 1.02′ 1.35′ 1.52′ 2.03′ 2.03′
90° 0.00′ 0.00′ 0.00′ 0.00′ 0.00′

## Corrections for altitude

When converting from geodetic ("common") latitude to other types of latitude, corrections must be made for altitude for systems which do not measure the angle from the normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

of the spheroid
Spheroid
A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters....

. For example, in the figure at right, point H (located on the surface of the spheroid) and point H' (located at some greater elevation) have different geocentric latitudes (angles β and γ respectively), even though they share the same geodetic latitude (angle α). Note that the flatness of the spheroid and elevation of point H' in the image is significantly greater than what is found on the Earth, exaggerating the errors inherent in such calculations if left uncorrected. Note also that the reference ellipsoid
Reference ellipsoid
In geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body....

used in the geodetic system is itself just an approximation of the true geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...

, and therefore introduces its own errors, though the differences are less severe. (See Astronomical latitude, below.)

## Astronomical latitude

A fundamentally different measure of latitude is the astronomical latitude, which is the angle between the equatorial plane and the normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...

to the geoid
Geoid
The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest , and extended through the continents . According to C.F...

(i.e. a plumb line). This is the only "latitude" that is not based on the spheroid being used to approximate the Earth's surface. It differs from the geodetic latitude only slightly (usually not more than a few thousandths of a degree) due to the slight deviations of the geoid from the reference ellipsoid.

Astronomical latitude is not to be confused with declination
Declination
In astronomy, declination is one of the two coordinates of the equatorial coordinate system, the other being either right ascension or hour angle. Declination in astronomy is comparable to geographic latitude, but projected onto the celestial sphere. Declination is measured in degrees north and...

, the coordinate astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...

s use to describe the locations of stars north/south of the celestial equator
Celestial equator
The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earth's equator. In other words, it is a projection of the terrestrial equator out into space...

(see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to describe the locations of stars and solar system bodies north/south of the ecliptic
Ecliptic
The ecliptic is the plane of the earth's orbit around the sun. In more accurate terms, it is the intersection of the celestial sphere with the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun...

(see ecliptic coordinates).

## Paleolatitude

Continents move over time, due to continental drift
Continental drift
Continental drift is the movement of the Earth's continents relative to each other. The hypothesis that continents 'drift' was first put forward by Abraham Ortelius in 1596 and was fully developed by Alfred Wegener in 1912...

, taking whatever fossils and other features of interest they may have with them. Particularly when discussing fossils, it is often more useful to know where the fossil was when it was laid down, than where it is when it was dug up: this is called the paleolatitude of the fossil. The paleolatitude can be constrained by paleomagnetic
Paleomagnetism
Paleomagnetism is the study of the record of the Earth's magnetic field in rocks. Certain minerals in rocks lock-in a record of the direction and intensity of the magnetic field when they form. This record provides information on the past behavior of Earth's magnetic field and the past location of...

data. If tiny magnetisable grains are present when the rock is being formed, these will align themselves with Earth's magnetic field like compass needles. A magnetometer
Magnetometer
A magnetometer is a measuring instrument used to measure the strength or direction of a magnetic field either produced in the laboratory or existing in nature...

can deduce the orientation of these grains by subjecting a sample to a magnetic field, and the magnetic declination
Magnetic declination
Magnetic declination is the angle between magnetic north and true north. The declination is positive when the magnetic north is east of true north. The term magnetic variation is a synonym, and is more often used in navigation...

of the grains can be used to infer the latitude of deposition.