Center of population

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Three commonly used (but different) center points are:



Map projection Systematic representation of the surface of a sphere or ellipsoid onto a plane

A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. There is no limit to the number of possible map projections.

Mean centre




Median centre


Circle of latitude Geographic notion

A circle of latitude on Earth is an abstract east–west circle connecting all locations around Earth at a given latitude.

Latitude The angle between zenith at a point and the plane of the equator

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the geodetic latitude as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six auxiliary latitudes which are used in special applications.

Meridian (geography) line between the poles with the same longitude

A (geographic) meridian is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points of equal longitude, as measured in angular degrees east or west of the Prime Meridian. The position of a point along the meridian is given by that longitude and its latitude, measured in angular degrees north or south of the Equator. Each meridian is perpendicular to all circles of latitude. Each is also the same length, being half of a great circle on the Earth's surface and therefore measuring 20,003.93 km.

Geometric median


In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations. It may contain constants, variables, certain "well-known" operations, and functions, but usually no limit. The set of operations and functions admitted in a closed-form expression may vary with author and context.




Practical uses for finding the center of population include locating possible sites for forward capitals, such as Brasília, Nur-Sultan 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.

Brasília Federal capital in Central-West, Brazil


Nur-Sultan Capital of Kazakhstan

Nur-Sultan, previously Astana, is the capital city of Kazakhstan. It is located on the banks of the Ishim River in the northern portion of Kazakhstan, within the Akmola Region, though administered separately from the region as a city with special status. The 2017 official estimate reported a population of 1,029,556 within the city limits, making it the second-largest city in Kazakhstan, behind Almaty, the capital from 1991 to 1997.

Austin, Texas Capital of Texas

Austin is the capital of the U.S. state of Texas and the seat of Travis County, with portions extending into Hays and Williamson counties. It is the 11th-most populous city in the United States and the 4th-most populous city in Texas. It is also the fastest growing large city in the United States, the second most populous state capital after Phoenix, Arizona, and the southernmost state capital in the contiguous United States. As of the U.S. Census Bureau's July 1, 2017 estimate, Austin had a population of 950,715 up from 790,491 at the 2010 census. The city is the cultural and economic center of the Austin–Round Rock metropolitan statistical area, which had an estimated population of 2,115,827 as of July 1, 2017. Located in Central Texas within the greater Texas Hill Country, it is home to numerous lakes, rivers, and waterways, including Lady Bird Lake and Lake Travis on the Colorado River, Barton Springs, McKinney Falls, and Lake Walter E. Long.



By country










In Finland, the point of minimum aggregate travel is located in the former municipality of Hauho. [11] 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.



Great Britain



The mean center of the India lies at the Lat 22.49 N, Long 80.10 E near the town of Nainpur in the state of Madhya Pradesh.





New Zealand

New Zealand's median centre of population over time NZ median centre of population 2017.png
New Zealand's median centre of population over time





The center of population in the Russian Federation is calculated by A. K. Gogolev to be at 56°34′N53°30′E﻿ / ﻿56.567°N 53.500°E﻿ / 56.567; 53.500 , 42 km (26 mi) south of Izhevsk. [22]


Heping District, Taichung. [23]

United States



Related Research Articles


In statistics, a central tendency is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.



Mercator projection map projection

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects, the Mercator projection distorts the size of objects as the latitude increases from the Equator to the poles, where the scale becomes infinite. So, for example, landmasses such as Greenland and Antarctica appear much larger than they actually are, relative to landmasses near the equator such as Central Africa.

Centroid mean ("average") position of all the points in the shape; mean position of all the points in all of the coordinate directions; point at which a cutout of the shape could be perfectly balanced on the tip of a pin

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the figure. Informally, it is the point at which a cutout of the shape could be perfectly balanced on the tip of a pin.

Mean center of the United States population

The mean center of the United States population is determined by the United States Census Bureau from the results of each national census. The Bureau defines it as follows:

The concept of the center of population as used by the U.S. Census Bureau is that of a balance point. The center of population is the point at which an imaginary, weightless, rigid, and flat surface representation of the 50 states and the District of Columbia would balance if weights of identical size were placed on it so that each weight represented the location on one person. More specifically, this calculation is called the mean center of population.

Centre points of the United Kingdom

There has long been debate over the exact location of the geographical centre of the United Kingdom, and its constituent countries, due to the complexity and method of the calculation, such as whether to include offshore islands, and the fact that erosion will cause the position to change over time. There are two main methods of calculating this "centre": either as the centroid of the two-dimensional shape made by the country, or as the point farthest from the boundary of the country. These two methods give quite different answers.

Geographical midpoint of Europe


<i>k</i>-means clustering Vector quantization algorithm minimizing the sum of squared deviations


Medoids are representative objects of a data set or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images and 3-D trajectories and gene expression. These are also of interest while wanting to find a representative using some distance other than squared euclidean distance.

Lloyds algorithm

In computer science and electrical engineering, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced sets of points in subsets of Euclidean spaces and partitions of these subsets into well-shaped and uniformly sized convex cells. Like the closely related k-means clustering algorithm, it repeatedly finds the centroid of each set in the partition and then re-partitions the input according to which of these centroids is closest. However, Lloyd's algorithm differs from k-means clustering in that its input is a continuous geometric region rather than a discrete set of points. Thus, when re-partitioning the input, Lloyd's algorithm uses Voronoi diagrams rather than simply determining the nearest center to each of a finite set of points as the k-means algorithm does.

Geographic center of the contiguous United States Point considered to be the center of the 48 contiguous American states

The geographic center of the contiguous United States is the center of 48 U.S. states. It has been regarded as such by the U.S. National Geodetic Survey (NGS) since the 1912 additions of New Mexico and Arizona to the United States.

Two-point equidistant projection type of map projection

The two-point equidistant projection is a map projection first described by Hans Maurer in 1919. It is a generalization of the much simpler azimuthal equidistant projection. In this two-point form, two locus points are chosen by the mapmaker to configure the projection. Distances from the two loci to any other point on the map are correct: that is, they scale to the distances of the same points on the sphere.

Statistical geography is the study and practice of collecting, analysing and presenting data that has a geographic or areal dimension, such as census or demographics data. It uses techniques from spatial analysis, but also encompasses geographical activities such as the defining and naming of geographical regions for statistical purposes. For example, for the purposes of statistical geography, the Australian Bureau of Statistics uses the Australian Standard Geographical Classification, a hierarchical regionalisation that divides Australia up into states and territories, then statistical divisions, statistical subdivisions, statistical local areas, and finally census collection districts.

The spectral centroid is a measure used in digital signal processing to characterise a spectrum. It indicates where the "center of mass" of the spectrum is located. Perceptually, it has a robust connection with the impression of "brightness" of a sound.

In geography, the centroid of the two-dimensional shape of a region of the Earth's surface is known as its geographical centre or geographical center. There has long been debate over the methods of calculation of the geographical centres of various countries and regions, proposed methods include:

3D reconstruction


Centre points of Australia

Centre points of Australia are those geographical locations that have been considered to be centre of Australia, as distinct from the extreme points of Australia.


  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.
  5. exact phrase in the paper is "at the crossroads between China, India, Pakistan and Tajikistan"
  6. "Center of World Population". City Extremes. 2017. Retrieved 21 August 2017.
  10. Haav, Mihkel (2010) - "Eesti dünaamika 1913-1999"
  11. [ permanent dead link ] Kaupunkilehti Uusi Rauma 03.08.2009 Päivän kysymys? Missä Rauman keskipiste? (in Finnish)
  12. Archived 24 October 2007 at the Wayback Machine (in German)
  13. "News Item:". University of Leeds . Retrieved 25 November 2007.
  22. Сайт "Встарь, или Как жили люди"