# Center of population

The point on earth closest to everyone in the world on average is in the north of South Asia, with a mean distance of 5,000 kilometers (3,000 mi). Its antipodal point is correspondingly the farthest point from everyone on earth, and is located in the South Pacific near Easter Island, with a mean distance of 15,000 kilometers (9,300 mi). The data used by this figure is lumped at the country level, and is therefore precise to only a few hundred kilometers.

In demographics, 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 different ways of defining such a "center point", leading to different geographical locations; these are often confused.[1]

## Definitions

Three commonly used (but different) center points are:

1. the mean center, also known as the centroid or center of gravity;
2. the median center, which is the intersection of the median longitude and median latitude;
3. the geometric median, 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.

### 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 the 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 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) and a meridian (a line of longitude). In that case, this center is easily found by taking separately the medians of the population's latitude and longitude coordinates.

### 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 for the geometric median; it is typically computed using iterative methods.

## 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 Brasilia, Astana or Austin. 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. As described in INED (Institut national d'études démographiques),[2] the solution methodology deals only with the globe. As a result, the answer is independent of which 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 distances as the metric, and a granularity of 1,000 kilometers (600 mi), 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 somewhere north of South Asia[3] with an average distance of 5,200 kilometers (3,200 mi) to all humans.[2] 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.

## By country

### Australia

Australia's population centroid is in central New South Wales. By 1996 it had moved only a little, to the north-west, since 1911.[4]

In Canada, a 1986 study placed the point of minimum aggregate travel just north of Toronto in the city of Richmond Hill, and moving westward at a rate of approximately 2 metres per day.[5]

### China

China's population centroid has wandered within southern Henan from 1952 to 2005. Incidentally, the two end point dates are remarkably close to each other.[6] China also plots its economic centroid or center of economy/GDP, which has also wandered, and is generally located at the eastern Henan borders.

### Finland

In Finland, the point of minimum aggregate travel is located in the municipality of Hauho.[7] It is moving slightly to the south-west-west every year because people are moving out of the periphery areas of northern and eastern Finland.

### Germany

In Germany, the centroid of the population is located in Spangenberg, Hesse, close to Kassel.[8]

### Great Britain

The centre of population in Great Britain did not move much in the 20th century. In 1901, it was in Rodsley, Derbyshire and in 1911 in Longford. In 1971 it was at Newhall, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire.[9][10][11][need quotation to verify]

### Japan

The centroid of population of Japan is in Gifu Prefecture, almost directly north of Nagoya city, and has been moving east-southeast for the past few decades.[12] More recently, the only large regions in Japan with significant population growth have been in Greater Nagoya and Greater Tokyo.

### New Zealand

In June 2008, New Zealand's median centre of population was located near Taharoa, around 100 km (65 mi) southwest of Hamilton on the North Island's west coast.[13]

### Sweden

The demographical center of Sweden (using the median center definition) is Hjortkvarn in Hallsberg Municipality, Örebro 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.[14]

### Russia

The place closest to everyone in Russia, as of 2010, is calculated to be in Izhevsk, 175 miles east of Kazan, or at the coordinates 53.727345202945 latitude 54.047898583217 longitude. Because of urban population growth in Russia the point has been moving to the west.

### United States

The mean center of United States population (using the centroid definition) has been calculated for each U.S. Census since 1790. In 2010 this point was located near Plato, Missouri, in the central part of the state. However, when Washington, D.C. was chosen as the federal capital of the United States in 1790, the center of the U.S. population was in Kent County, Maryland, a mere 47 miles (76 km) east-northeast of the new capital. Over the last two centuries, the mean center of United States population has progressed westward and, since 1930, southwesterly, reflecting population drift.

## Sources

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

## References

1. Kumler, Mark P.; Goodchild, Michael F. (1992). "The population center of Canada – Just north of Toronto?!?". In Janelle, Donald G. (ed.). Geographical snapshots of North America: commemorating the 27th Congress of the International Geographical Union and Assembly. pp. 275–279.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
2. Claude Grasland and Malika Madelin (May 2001). "The unequal distribution of population and wealth in the world" (PDF). Population Et SociétéS. Institut national d'études démographiques. 368: 1–4. ISSN 0184-7783.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
3. exact phrase in the paper is "at the crossroads between China, India, Pakistan and Tajikistan"
4. "Figure 15: Shifts in the Australian Population Centroid*, 1911–1996". Parliament of Australia Parliamentary Library. Archived from the original on 19 August 2000. Retrieved 7 January 2009.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
5. "The Population Center of Canada – Just North of Toronto?!?" (PDF). Retrieved 21 April 2012.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
6. http://sourcedb.igsnrr.cas.cn/zw/lw/201007/P020100706529106697457.pdf
7. Uusirauma.fi Kaupunkilehti Uusi Rauma 03.08.2009 Päivän kysymys? Missä Rauman keskipiste? (Finnish)
9. "News Item:". University of Leeds. Retrieved 25 November 2007.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
10. "Population Centre". Appleby Magna & Appleby Parva. Archived from the original on 23 November 2007. Retrieved 25 November 2007.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
11. "Coffee Break: The movable Midlands; ANSWERS TO CORRESPONDENTS". The Daily Mail. London. 7 February 2002. p. 64.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
12. "Our Country's Center of Population (我が国の人口重心)". Stat.go.jp. Retrieved 21 April 2012.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
13. "Subnational Population Estimates: At 30 June 2008 -- Commentary". Statistics New Zealand. Retrieved 11 November 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
14. "Sweden's demographic centre, SCB.se, 2008-03-18". Scb.se. 18 March 2008. Retrieved 21 April 2012.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
15. https://www.ptt.cc/man/Geography/D1F0/DD1E/M.1105123514.A.427.html