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In
demographics Demography () is the statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analysis examin ...
, the center of population (or population center) of a region is a geographical point that describes a centerpoint of the region's population. There are several ways of defining such a "center point", leading to different geographical locations; these are often confused.


Definitions

Three commonly used (but different) center points are: # the ''
mean A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...
center'', also known as the ''
centroid In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the figure. The same definition extends to any object in n-d ...
'' or ''
center of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For ...
''; # the ''
median The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...
center'', which is the intersection of the median
longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...
and median
latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
; # the ''
geometric median In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances or absolute ...
'', also known as ''Weber point'', ''Fermat–Weber point'', or ''point of minimum aggregate travel''. A further complication is caused by the curved shape of the Earth. Different center points are obtained depending on whether the center is computed in three-dimensional space, or restricted to the curved surface, or computed using a flat
map projection In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...
.


Mean center

The mean center, or centroid, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of equal mass. Mathematically, the centroid is the point to which the population has the smallest possible ''sum of squared distances''. It is easily found by taking the arithmetic mean of each coordinate. If defined in three-dimensional space, the centroid of points on the Earth's surface is actually inside the Earth. This point could then be projected back to the surface. Alternatively, one could define the centroid directly on a flat map projection; this is, for example, the definition that the
US Census Bureau The United States Census Bureau, officially the Bureau of the Census, is a principal agency of the U.S. federal statistical system, responsible for producing data about the American people and economy. The U.S. Census Bureau is part of the U ...
uses. Contrary to a common misconception, the centroid does ''not'' minimize the average distance to the population. That property belongs to the geometric median.


Median center

The median center is the intersection of two perpendicular lines, each of which divides the population into two equal halves. Typically these two lines are chosen to be a parallel (a line of
latitude In geography, latitude is a geographic coordinate system, geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at t ...
) and a meridian (a line of
longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...
). In that case, this center is easily found by taking separately the
median The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...
s of the population's latitude and longitude coordinates.
John Tukey John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...
called this the ''cross median''.


Geometric median

The geometric median is the point to which the population has the smallest possible ''sum of distances'' (or equivalently, the smallest ''average distance''). Because of this property, it is also known as the ''point of minimum aggregate travel''. Unfortunately, there is no direct
closed-form expression In mathematics, an expression or equation is in closed form if it is formed with constants, variables, and a set of functions considered as ''basic'' and connected by arithmetic operations (, and integer powers) and function composition. ...
for the geometric median; it is typically computed using
iterative method In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an " ...
s.


Determination

In practical computation, decisions are also made on the granularity (coarseness) of the population data, depending on population density patterns or other factors. For instance, the center of population of all the cities in a country may be different from the center of population of all the states (or provinces, or other subdivisions) in the same country. Different methods may yield different results. Practical uses for finding the center of population include locating possible sites for forward capitals, such as
Brasília Brasília ( ; ) is the capital city, capital of Brazil and Federal District (Brazil), Federal District. Located in the Brazilian highlands in the country's Central-West Region, Brazil, Central-West region, it was founded by President Juscelino ...
,
Astana Astana is the capital city of Kazakhstan. With a population of 1,423,726 within the city limits, it is the second-largest in the country after Almaty, which had been the capital until 1997. The city lies on the banks of the Ishim (river), Ishim ...
or
Austin Austin refers to: Common meanings * Austin, Texas, United States, a city * Austin (given name), a list of people and fictional characters * Austin (surname), a list of people and fictional characters * Austin Motor Company, a British car manufac ...
, and, along the same lines, to make tax collection easier. Practical selection of a new site for a capital is a complex problem that depends also on population density patterns and transportation networks.


World

It is important to use a method that does not depend on a two-dimensional projection when dealing with the entire world. In a study from the
Institut national d'études démographiques The French Institute for Demographic Studies (, ; INED) is a French research institute specializing in demography and population studies in general. History Before 1945 In 1941, Nobel Prize winner Alexis Carrel, an early proponent of eugenics ...
, the solution methodology deals only with the globe. As a result, the answer is independent of which
map projection In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...
is used or where it is centered. As described above, the exact location of the center of population will depend on both the granularity of the population data used, and the distance metric. With
geodesic In geometry, a geodesic () is a curve representing in some sense the locally shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a conn ...
distances as the metric, and a granularity of , meaning that two population centers within 1000 km of each other are treated as part of a larger common population center of intermediate location, the world's center of population is found to lie "at the crossroads between China, India, Pakistan and Tajikistan" with an average distance of to all humans. The data used in the reference support this result to a precision of only a few hundred kilometers, hence the exact location is not known. Another analysis, using city-level population data, found that the world's center of population is close to
Almaty Almaty, formerly Alma-Ata, is the List of most populous cities in Kazakhstan, largest city in Kazakhstan, with a population exceeding two million residents within its metropolitan area. Located in the foothills of the Trans-Ili Alatau mountains ...
, Kazakhstan.


By country


Antigua and Barbuda

In 2011, the center of population of
Antigua Antigua ( ; ), also known as Waladli or Wadadli by the local population, is an island in the Lesser Antilles. It is one of the Leeward Islands in the Caribbean region and the most populous island of the country of Antigua and Barbuda. Antigua ...
(excluding
Barbuda Barbuda (; ) is an island and dependency located in the eastern Caribbean forming part of the twin-island state of Antigua and Barbuda as an autonomous entity. Barbuda is located approximately north of Antigua. The only settlements on the i ...
) was located in St. Claire.


Australia

Australia's population centroid is in central
New South Wales New South Wales (commonly abbreviated as NSW) is a States and territories of Australia, state on the Eastern states of Australia, east coast of :Australia. It borders Queensland to the north, Victoria (state), Victoria to the south, and South ...
. By 1996, it had moved only a little to the north-west since 1911. It moved only 1.4 km north in 2022 from the previous year and in 2023 moved 1.9 km west compared to 2022, located 40 km east of
Ivanhoe ''Ivanhoe: A Romance'' ( ) by Walter Scott is a historical novel published in three volumes, in December 1819, as one of the Waverley novels. It marked a shift away from Scott's prior practice of setting stories in Scotland and in the more ...
.


Canada

In Canada, a 1986 study placed the point of minimum aggregate travel just north of
Toronto Toronto ( , locally pronounced or ) is the List of the largest municipalities in Canada by population, most populous city in Canada. It is the capital city of the Provinces and territories of Canada, Canadian province of Ontario. With a p ...
in the city of Richmond Hill, and moving westward at a rate of approximately 2 meters per day.


China

China's population centroid has wandered within southern
Henan Henan; alternatively Honan is a province in Central China. Henan is home to many heritage sites, including Yinxu, the ruins of the final capital of the Shang dynasty () and the Shaolin Temple. Four of the historical capitals of China, Lu ...
from 1952 to 2005. Incidentally, the two end point dates are remarkably close to each other. China also plots its economic centroid or center of economy/GDP, which has also wandered, and is generally located at the eastern Henan borders.


Estonia

The center of population of Estonia was on the northwestern shore of Lake Võrtsjärv in 1913 and moved an average of 6 km northwest with every decade until the 1970s. The higher immigration rates during the late Soviet occupation to mostly
Tallinn Tallinn is the capital city, capital and List of cities in Estonia, most populous city of Estonia. Situated on a Tallinn Bay, bay in north Estonia, on the shore of the Gulf of Finland of the Baltic Sea, it has a population of (as of 2025) and ...
and
Northeastern Estonia Between 57.3 and 59.5 latitude and 21.5 and 28.1 longitude, Estonia lies on the eastern coast of the Baltic Sea on the level northwestern part of the rising East European Platform. Estonia's continental mainland is bordered to the north by the ...
resulted the center of population moving faster towards north and continuing urbanization has seen it move northwest towards Tallinn since the 1990s. The center of population according to the 2011 census was in Jüri, just 6 km southeast from the border of Tallinn.


Finland

In Finland, the point of minimum aggregate travel is located in the former municipality of
Hauho Hauho is a former municipality of Finland. It was situated in the province of Southern Finland and is today a part of the region of Tavastia Proper (Kanta-Häme / Egentliga Tavastland). Hauho was amalgamated with the municipality of Hämeenlinna ...
. It is moving slightly to the south-west-west every year because people are moving out of the peripheral areas of northern and eastern Finland.


Germany

In Germany, the centroid of the population is located in
Spangenberg Spangenberg is a small town in northeastern Hesse, Germany. Geography Spangenberg lies in the Schwalm-Eder district some southeast of Kassel, west of the Stölzinger Gebirge, a low mountain range. Spangenberg is the demographic centrepoint of ...
,
Hesse Hesse or Hessen ( ), officially the State of Hesse (), is a States of Germany, state in Germany. Its capital city is Wiesbaden, and the largest urban area is Frankfurt, which is also the country's principal financial centre. Two other major hist ...
, close to
Kassel Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in North Hesse, northern Hesse, in Central Germany (geography), central Germany. It is the administrative seat of the Regierungsbezirk Kassel (region), Kassel and the d ...
.


Great Britain

The center of population in Great Britain did not move significantly in the 20th century. In 1901, it was in Rodsley, Derbyshire and in 1911 in
Longford Longford () is the county town of County Longford in Ireland. It had a population of 10,952 at the 2022 census. It is the biggest town in the county and about one third of the county's population lives there. Longford lies at the meeting of ...
. In 1971 it was at Newhall,
Swadlincote Swadlincote is a historic mining town in the district of South Derbyshire, in the county of Derbyshire, England. It lies within The National Forest (England), The National Forest area. It borders the counties of Leicestershire and Staffordshire ...
, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire. Using the 2011 census the population center can be calculated at
Snarestone Snarestone is a small rural village in North West Leicestershire, England.OS Explorer Map 245: The National Forest :(1:25 000) :
, Swadlincote.


Ireland

The center of population of the entire
island of Ireland Ireland (, ; ; Ulster-Scots: ) is an island in the North Atlantic Ocean, in Northwestern Europe. Geopolitically, the island is divided between the Republic of Ireland (officially named Irelanda sovereign state covering five-sixths of th ...
is located near Kilcock,
County Kildare County Kildare () is a Counties of Ireland, county in Ireland. It is in the Provinces of Ireland, province of Leinster and is part of the Eastern and Midland Region. It is named after the town of Kildare. Kildare County Council is the Local gove ...
. This is significantly further east than the
Geographical centre of Ireland The Geographical Centre of Ireland, according to an investigation and calculation carried out by the Official Irish Government Mapping Agency, Ordnance Survey Ireland (OSI) published on the official OSI website on 24 February 2022 is near the ...
, reflecting the disproportionately large cities of the east of the island (
Belfast Belfast (, , , ; from ) is the capital city and principal port of Northern Ireland, standing on the banks of the River Lagan and connected to the open sea through Belfast Lough and the North Channel (Great Britain and Ireland), North Channel ...
and
Dublin Dublin is the capital and largest city of Republic of Ireland, Ireland. Situated on Dublin Bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, and is bordered on the south by the Dublin Mountains, pa ...
). The center of population of the
Republic of Ireland Ireland ( ), also known as the Republic of Ireland (), is a country in Northwestern Europe, north-western Europe consisting of 26 of the 32 Counties of Ireland, counties of the island of Ireland, with a population of about 5.4 million. ...
is located southwest of
Edenderry Edenderry (; ) is a town in east County Offaly, Republic of Ireland, Ireland. It is near the borders with Counties County Kildare, Kildare, County Meath, Meath and County Westmeath, Westmeath. The Grand Canal of Ireland, Grand Canal runs along ...
,
County Offaly County Offaly (; ) is a Counties of Ireland, county in Republic of Ireland, Ireland. It is part of the Eastern and Midland Region and the Provinces of Ireland, province of Leinster. It is named after the Ancient Ireland, ancient Kingdom of Uí ...
.


Japan

The centroid of population of Japan is in
Gifu Prefecture is a Prefectures of Japan, prefecture of Japan located in the Chūbu region of Honshu. Gifu Prefecture has a population of 1,910,511 () and has a geographic area of . Gifu Prefecture borders Toyama Prefecture to the north; Ishikawa Prefecture ...
, almost directly north of
Nagoya is the largest city in the Chūbu region of Japan. It is the list of cities in Japan, fourth-most populous city in Japan, with a population of 2.3million in 2020, and the principal city of the Chūkyō metropolitan area, which is the List of ...
city, and has been moving east-southeast for the past few decades. Since 2010, the only large regions in Japan with significant population growth have been in
Greater Tokyo The Greater Tokyo Area is the most populous metropolitan area in the world, consisting of the Kantō region of Japan (including Tokyo Metropolis and the prefectures of Chiba, Gunma, Ibaraki, Kanagawa, Saitama, and Tochigi) as well as the p ...
and
Okinawa Prefecture is the southernmost and westernmost prefecture of Japan. It consists of three main island groups—the Okinawa Islands, the Sakishima Islands, and the Daitō Islands—spread across a maritime zone approximately 1,000 kilometers east to west an ...
.


New Zealand

In June 2008, New Zealand's median center of population was located near Taharoa, around 100 km (65 mi) southwest of
Hamilton Hamilton may refer to: * Alexander Hamilton (1755/1757–1804), first U.S. Secretary of the Treasury and one of the Founding Fathers of the United States * ''Hamilton'' (musical), a 2015 Broadway musical by Lin-Manuel Miranda ** ''Hamilton'' (al ...
on the
North Island The North Island ( , 'the fish of Māui', historically New Ulster) is one of the two main islands of New Zealand, islands of New Zealand, separated from the larger but less populous South Island by Cook Strait. With an area of , it is the List ...
's west coast. In 1900 it was near
Nelson Nelson may refer to: Arts and entertainment * ''Nelson'' (1918 film), a historical film directed by Maurice Elvey * ''Nelson'' (1926 film), a historical film directed by Walter Summers * ''Nelson'' (opera), an opera by Lennox Berkeley to a lib ...
and has been moving steadily north (towards
Auckland Auckland ( ; ) is a large metropolitan city in the North Island of New Zealand. It has an urban population of about It is located in the greater Auckland Region, the area governed by Auckland Council, which includes outlying rural areas and ...
, the country's most populous city) ever since.


Sweden

The demographical center of Sweden (using the median center definition) is Hjortkvarn in
Hallsberg Municipality Hallsberg Municipality () is a municipality in Örebro County in central Sweden. Its seat is located in the town of Hallsberg, which is the main railway hub for the central Swedish interior. The present municipality was created in 1971 when the m ...
,
Örebro Örebro ( ; ) is the seventh-largest city in Sweden, the seat of Örebro Municipality, and capital of Örebro County. It is situated by the Närke Plain, near the lake Hjälmaren, a few kilometers inland along the small river Svartån, and ...
county. Between the 1989 and 2007 census the point moved a few kilometres to the south, due to a decreasing population in northern Sweden and immigration to the south.


Russia

The center of population in the Russian Federation is calculated by A. K. Gogolev to be at as of 2010, south-southwest of
Izhevsk Izhevsk or Ijevsk (, ; , or ) is the capital city of Udmurtia, Russia. It is situated along the Izh River, west of the Ural Mountains in Eastern Europe. It is the 21st-largest city in Russia, and the most populous in Udmurtia, with over 600,000 ...
.


Taiwan

The center of population of Taiwan is located in Heping District, Taichung.


United States

The mean center of the United States population (using the centroid definition) has been calculated for each U.S. Census since 1790. Over the last two centuries, it has progressed westward and, since 1930, southwesterly, reflecting population drift. For example, in 2010, the mean center was located near Plato, Missouri, in the south-central part of the state, whereas, in 1790, it was in
Kent County, Maryland Kent County is a county located in the U.S. state of Maryland. As of the 2020 census, its population was 19,198, making it the least populous county in Maryland. Its county seat is Chestertown. The county was named for the county of Kent in ...
, east-northeast of the future federal capital, Washington, D.C.


See also

*
Extremes on Earth This article lists extreme locations on Earth that hold geographical records or are otherwise known for their geophysical or meteorological superlatives. All of these locations are Earth-wide extremes; extremes of individual continents or count ...


References

{{reflist, colwidth=30em


Sources

* Bellone F. and Cunningham R. (1993). "All Roads Lead to... Laxton, Digby and Longford." Statistics Canada 1991 Census Short Articles Series.


External links


Australian parliamentary research paper with map of population centroids


Lists of coordinates Demography
Population Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...