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Arithmetic Population Density

Arithmetic Population Density

You wouldn't think that underpopulation would be an important issue in the world these days, would you? Turns out, it is. If you come from a rural area, you probably know just what we're talking about. Every year, more people leave for the cities. Arithmetic population density keeps dropping, and it gets harder and harder to keep schools open and grocery stores from closing their doors.

At the other end of the spectrum, perhaps you live in a small town being overwhelmed by an expanding metropolitan area. Every year, land values go up, taxes rise, more subdivisions get built, wild habitat disappears, and arithmetic population density increases. The local government can barely keep up with the roads and schools that need to be built or expanded. Sound like a case of overpopulation? Despite some negative changes, the local economy is likely to improve as arithmetic population density increases.

Arithmetic Population Density Definition

Arithmetic Population Density (APD) is a basic, important, and easy-to-understand demographic statistic.

Arithmetic Population Density: The ratio of human population to land area.

Arithmetic Population Density Formula

To calculate arithmetic population density, find the total land area. This is usually expressed in square miles or square kilometers (there are 2.59 square kilometers in a square mile).

Second, find the total population for that land area.

Then, divide the population by the land area. It's as simple as that!

Country A has a population of 23,547,657 and is 53,467 square miles. Its arithmetic population density is 440 people per square mile and 170 (440/2.59) people per square km.

Some things to keep in mind:

  • Population figures can vary based on whether they are from estimates or censuses, and what year they are considered accurate for.

  • Some areas contain many temporary residents (such as college students or migrant laborers) that may or may not be included in APD calculations.

  • APD should be based on land area only but may also be based on total area, which includes water surfaces enclosed by land areas.

arithmetic population density APD world map StudySmarterFig. 1 - Arithmetic population density of the world. Darker shades indicate higher densities, typically places that are highly urbanized. The lightest shade, found in deserts, sub-Arctic, and Arctic regions, cannot be farmed and/or have little or no freshwater.

Arithmetic Density vs Physiological Density

Arithmetic population density does not take into account factors like where people live across a space. This is important because people often cluster in cities and agricultural areas while having much lower densities in grazing areas and non-productive regions.

Physiological density is therefore a better measure for areas with cropland, because it is the ratio of people to cropland rather than people to total area. Knowing a country's physiological population density can tell you how many people need to be fed by each unit of area in crops.

Importance of Arithmetic Population Density

Why do we need to know arithmetic population density? Because it gives us the ability to make comparisons between countries, cities, states, and other geographical regions.

Knowing arithmetic population density can help urban planners and city officials better understand how to apportion goods and services and design infrastructure. Two neighborhoods of a city, we'll call them Happyville and Niceville, with the same physical size, may have quite different APDs. If they have the same level of infrastructure, the higher-density area, Happyville, may be disadvantaged: its streets will be far more clogged than Niceville. Its health clinics and hospitals will be more crowded. Its police stations and fire stations will be much busier.

Dot-Density Maps

To get by the skewed figures of APD that don't show where people are clustered and where they are more dispersed, thematic maps like dot-density maps (or dot distribution maps) are useful. They give a much better picture of arithmetic population density than regional averages do.

arithmetic population density Illinois map StudySmarterFig. 2 - Dot-density map shows the arithmetic population density of Illinois

Rural Areas

Arithmetic population density in relationship to infrastructure is a critically important factor in rural areas as well, but for the opposite reason to cities. Rural areas, which are often important for their agricultural production, tourism services, mining, and other economic activities, tend to have low APDs, particularly in developed nations like the US.

Low APDs are largely a result of mechanization in primary sector activities: far fewer people are needed to do what were once labor-intensive tasks like farming. This means that fewer jobs are available, so people need to move to places that can provide them with jobs.

Nevertheless, because the people who remain are critically important to the economic activities that take place, they must be provided the same services that people in urban areas receive: public schools, healthcare, grocery stores, paved roads, electricity, wireless Internet, and so forth. The problem is that many services rely on the tax base, and with fewer people, less tax money is available. Fewer consumers are available as well, making it cost-ineffective for companies to provide sufficient grocery stores and shops selling other necessary goods.

With fewer goods and services available and fewer jobs, rural areas also have a hard time competing with urban areas when it comes to job creation. People are unwilling to move to "remote" areas without the level of goods and services they are accustomed to closer to cities. Wages and salaries tend to be lower as well.

As APD decreases, the underpopulation crisis is exacerbated, and this is what much of the rural US has been facing for decades. While the economic activities rural people engage in are critically important, fewer and fewer people want to live there, so it gets more and more difficult and expensive to maintain roads, schools, mail services, healthcare, and so on.

Arithmetic Population Density Example

The above discussion puts into perspective the idea that crowded places are "overpopulated" and need fewer people. This is completely contextual. The US is not the only country with large areas that suffer from underpopulation. Rural areas across the world are neglected because there are fewer consumers, and it is more expensive to provide for them.

Depending on the type of government, rural people may even be neglected because they have relatively few votes compared to urban areas.

Top Ten Most Dense Populations

The countries with the highest population densities (per square mile) are:

  1. Monaco (47,508)

  2. Singapore (19,727)

  3. Bahrain (4,828)

  4. Maldives (4,502)

  5. Malta (4,317)

  6. Bangladesh (2,955)

  7. Vatican City (2,701)

  8. Palestine (2,209)

  9. Barbados (1,694)

  10. Lebanon ( 1,386)

arithmetic population density monaco StudySmarterFig. 3 - Monaco (foreground; background is France) is a city-state with the highest population density of any country. Manhattan, by virtue of its much taller buildings, is far more crowded, for example.

By way of comparison, Manhattan, one of the most affluent places on Earth, has a population density of 72,918 people per square mile. There simply is not a relationship between how crowded a place is and how affluent it is, though the top three above are all affluent (Monaco and Singapore are city-states). Places with high population densities may attract more jobs and thus more people, have higher tax bases, and thus more money to spend.

Bangladesh (#6 above) is an example of an extremely crowded country that happens to have the highest percentage of arable land of any country in the world. Though it has some large cities, most of its 166 million people are farmers. With so much labor and so much arable land available, Bangladesh has become self-sufficient in rice and is a leading world producer of various vegetables. Once the poster child for famine and overpopulation, Bangladesh has shown the world that "overcrowding" does not necessarily spell gloom and doom.

Top Ten Lowest APDs

Now let's turn to the other end of the spectrum. Here are the sovereign countries with the lowest population densities (per square mile) and the biomes that permit little or no habitation due to lack of water and/or extreme weather conditions that allow little or no agriculture:

  1. Australia (9). Deserts

  2. Canada (11). Arctic, sub-Arctic

  3. Kazakhstan (18). Deserts

  4. Russia (22). Arctic, sub-Arctic (tundra and taiga)

  5. Bolivia (28). High-altitude deserts (Altiplano)

  6. Chad (35). Sahara

  7. Saudi Arabia (42). Arabian Desert

  8. Argentina (42). Sub-Arctic (Patagonia)

  9. Mali (46). Sahara

  10. Niger (52). Sahara

Again, we can't derive a rule from the above list that relates underpopulation to affluence, because it includes some of the least developed (Chad, Mali, Niger) AND most developed or wealthy (Saudi Arabia, Canada, Australia) countries in the world.

What we DO know is that they all have problems providing goods and services to their rural populations. Remember that the APD divides total people by land area, and in some of these countries, 90% or more of the population lives in cities. Those who do not may live in tiny communities hundreds of miles apart from each other.

For the AP Human Geography exam, you should know the differences between Agricultural Population Density Arithmetic Population Density, and Physiographic Population Density!

In much of the Canadian Arctic, Sahara, Siberia, and Australian bush, weather conditions make roads difficult or impossible. People may lose access to the outside world for months at a time, and during most or all of the year they as well as the goods they need have to come in and go out by plane. This raises the prices of consumer goods considerably.

Should places with extremely low APDs have people at all if it is so difficult and expensive to provide for them? Who are these people, in the first place?

As mentioned above, many are associated with critically important primary economic sector activities, which include grazing, mining, fishing, and timber extraction. On top of that, they may be Indigenous people, as is almost entirely the case in the Canadian Arctic and Sahara, for example. Their very cultural identity and way of life are tied to the land, but they also deserve to receive all the benefits of the modern world that people in cities enjoy.

Arithmetic Population Density - Key takeaways

  • Arithmetic Population Density is a statistic that measures the ratio of human residents to land area.
  • The highest-density places in the world are cities.
  • The lowest density places in the world are Arctic regions and deserts, where lack of water and the impossibility of agriculture limit human populations.
  • Rural areas with low arithmetic population density face many challenges associated with underpopulation, such as insufficient tax bases for the provision of services.
  • Urban areas with high population densities may require higher densities of provision of goods, services, and infrastructure than urban areas with lower population densities.


  1. Fig. 2: Illinois population density map (https://commons.wikimedia.org/wiki/File:Population_Density_of_Illinois_2010_Wikipediamap.svg) by Wandresen22 is licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/deed.en)
  2. Fig. 3: Monaco (https://commons.wikimedia.org/wiki/File:Monaco_from_a_bof.jpg) by Subaaa is licensed by CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/deed.en)

Frequently Asked Questions about Arithmetic Population Density

Arithmetic population density is the ratio of human residents to land area for any given region.

 An example of arithmetic density is Manhattan, with a density of 72,918 people per square mile. 

You find the arithmetic population density of an area by dividing the total number of human residents by the land area. 

Arithmetic density is important for comparison purposes between areas of the same physical size, when considering what goods and services are needed; it is also important when it indicated underpopulation of rural areas and the challenges that presents to governments.

Australia, at nine people per square mile, has the lowest arithmetic population density.

Final Arithmetic Population Density Quiz


A region with a low arithmetic population density is most likely to be:

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The region with the highest arithmetic population density is most likely to be:

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An urban neighborhood with highrise apartments.

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The world's least densely populated country is

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The world's most densely populated country is:

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Which population density measure is most useful for urban areas?

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What type of map is most useful for portraying arithmetic population density?

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Dot density map (dot distribution map).

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Overpopulated places as a rule suffer the most from poverty and other socioeconomic problems.

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Underpopulated places have more and better jobs and overall better economies, as a rule.

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Bangladesh's overpopulation and amount of arable land means it has abundant labor availability and can feed itself.

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You find two widely varying figures for population density of the same region. This is likely because: 

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One is from a census and the other from a population estimate; one includes temporary residents and the other doesn't; they are from different years.

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