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Population D F

Population density formula

Here you will learn about the population density formula, including how to calculate population density and how to solve problems involving population density.

Students will first learn about the population density formula as part of algebra in high school.

What is the population density formula?

The population density formula is a formula used to calculate population density. Population density is a compound measure that tells us how many people live in an area of a specified size. It expresses the number of people per unit of area, such as per square mile or square kilometer.

If an area has a high population density, it is crowded; for example, in a city.

If an area has a low population density, it is sparsely populated; for example, in a mountainous region.

To use the population density formula, you need to know the relationship between population density, population (the number of people), and land area.

The population density formula is:

\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}

You can turn this into a formula triangle:

Population density can be used to make population estimates. The units are often $\text{people/km}$ $^2$ (people per square kilometer) or $\text{people/mi}$ $^2$ (people per square mile).

You may study more about world population, population growth, urbanization, and demographics in geography.

What is the population density formula?

Common Core State Standards

How does this relate to high school math?

High School – Algebra – Creating Equations (HSA.CED.A.4)
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law $V=IR$ to highlight resistance $R.$

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Use this quiz to check your grade 6 to 7 students’ understanding of ratios. 10+ questions with answers covering a range of 6th and 7th grade ratio topics to identify areas of strength and support!

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How to use the population density formula

In order to solve problems involving the population density formula:

Check what information you have been given and what you are finding.
Use the population density formula.
Write down the final answer.

Population density formula examples

Example 1: calculating population density

New York City has a population size of $8,336,000$ and an area of $302.6$ square miles. Calculate the population density of New York City. Give your answer to the nearest integer.

Check what information you have been given and what you are finding.

You have been given the population and the land area. You need to find the population density.

2Use the population density formula.

The formula is:

\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}

You can substitute in the values and work out the population density.

\text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }}=\cfrac{8,336,000}{302.6}=27,547.918 \ldots

3Write down the final answer.

The population density of New York City is $\bf{27,548} \text{ people per mi}$ $^{2}$ (to the nearest integer).

Example 2: calculating population density

Australia has a total population of $24,900,000$ and an area of $7,690,000 \, km^{2}.$ Calculate the population density of Australia. Give your answer to the nearest hundredth.

Check what information you have been given and what you are finding.

You have been given the population and the land area. You need to find the population density.

Use the population density formula.

The formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

You can substitute in the values and work out the population density.

$\text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }}=\cfrac{24,900,000}{7,690,000}=3.2379 \ldots$

Write down the final answer.

The population density of Australia is $\bf{3.24} \text{ people per km}$ $^{2}$ (to the nearest hundredth).

Example 3: calculating population

Hong Kong has a population density of $6,700 \text{ people/km}$ $^{2}$ and an area of $1,100 \, km^{2}.$ Calculate the population of Hong Kong.

Check what information you have been given and what you are finding.

You have been given the population density and the land area. You need to find the population.

Use the population density formula.

The formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

You can substitute in the values and work out the population density.

$\begin{aligned}& \text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }} \\\\ & 6700=\cfrac{\text { Population }}{1,100} \\\\ & \text { Population }=6,700 \times 1100 \\\\ & \text { Population }=7,370,000 \end{aligned}$

Write down the final answer.

The human population of Hong Kong is $\bf{7,370,000}$ people.

Example 4: calculating population

San Francisco has a population density of $18,790$ people per square mile and a total area of $47$ square miles. Calculate the population of San Francisco.

Check what information you have been given and what you are finding.

You have been given the population density and the land area. You need to find the population.

Use the population density formula.

The formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

You can substitute in the values and work out the population density.

$\begin{aligned}& \text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }} \\\\ & 18,790=\cfrac{\text { Population }}{47} \\\\ & \text { Population }=18,790 \times 47 \\\\ & \text { Population }=883,130 \end{aligned}$

Write down the final answer.

The population, or total number of people, of San Francisco is $\bf{883,130}.$

Example 5: calculating land area

Boston, Massachusetts has a population density of $13,900$ people per square mile and a population of $675,000$ people. Calculate the land area of Boston. Give your answer to the nearest tenth.

Check what information you have been given and what you are finding.

You have been given the population density and the population. You need to find the land area.

Use the population density formula.

The formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

You can substitute in the values and work out the population density.

$\begin{aligned}& \text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }} \\\\ & 13,900=\cfrac{675,000}{\text { Land Area }} \\\\ & \text { Land Area }=675,000 \div 13,900 \\\\ & \text { Land Area }=48.561 \ldots \end{aligned}$

Write down the final answer.

The land area of Boston is $\bf{48.6}$ $mi^{2}$ (to the nearest tenth).

Example 6: calculating land area

Pakistan has a population density of $267 \text{ people/km}$ $^{2}$ and a population of $2.12 \times 10^{8}$ people. Calculate the land area of Pakistan. Give your answer in scientific notation to the nearest hundredth.

Check what information you have been given and what you are finding.

You have been given the population density and the population. You need to find the land area.

Use the population density formula.

The formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

You can substitute in the values and work out the population density.

$\begin{aligned}& \text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }} \\\\ & 267=\cfrac{2.12 \times 10^8}{\text { Land Area }} \\\\ & \text { Land Area }=2.12 \times 10^8 \div 267 \\\\ & \text { Land Area }=794,007.49 \ldots \end{aligned}$

Write down the final answer.

\text { Land Area }=794,007.49 \ldots=794,000=7.94 \times 10^5

The land area of Pakistan is $7.94 \times 10^5 \, km^{2}$ (to the nearest hundredth).

Teaching tips for population density formula

Have students calculate the population density of different areas using square grids on a map and real population data from the U.S. Census Bureau. This can be done with graph paper where each square represents a given area size, and students can place dots or stickers to represent the population.

Use online tools like population density calculators where students can adjust population and area sizes to see how the density changes. Interactive elements help reinforce the mathematical relationships.

Tie the lesson to human geography, history, and social studies by discussing why certain areas have higher or lower population densities (for example, economic factors, natural resources on earth, climate, historical events).

Make sure students understand that population density is an average measure and does not account for clustering or sparse areas. Use examples on worksheets that include urban areas versus rural areas to illustrate this point.

Easy mistakes to make

Incorrectly using the formula
Reinforce the correct formula to calculate density:

$\text { Population density }=\cfrac{\text { population }}{\text { area }}$

Use plenty of population density examples to practice this.

Confusing population with population density
Emphasize that population density is a measure of the total number of individuals per unit of area (for example, per square mile or square kilometer), not the total number of people altogether.

Mixing up different measures
Students may confuse population density with other measures like total population, urban density, population growth rate, or carrying capacity.

Tip: Clarify the differences between these terms and provide examples to highlight what each measure represents.

Check what form the final answer needs to be in
You may be asked to round your answer or to write your final answer in scientific notation, as the numbers involved can be very large.

Practice population density formula questions

$8,000 \text{ people/mi}$ $^2$

$7,952 \text{ people/mi}$ $^2$

$800 \text{ people/mi}$ $^2$

$795 \text{ people/mi}$ $^2$

\text { Population Density }=\cfrac{\text { Population }}{\text { Land Area }}=\cfrac{4,000,000}{503}=7,952.286 \ldots

The answer needs rounding to the nearest integer.

$7,952.286..=7,952$ to the nearest integer.

So the population density of Los Angeles is $7,952 \text{ people/mi}$ $^2.$

$19,300 \text{ people/km}$ $^2$

$1,940 \text{ people/km}$ $^2$

$19,400 \text{ people/km}$ $^2$

$194 \text{ people/mi}$ $^2$

\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}=\cfrac{3.87\times 10^4}{2}=19,350

The answer needs rounding to the nearest hundred.

$19,350=19,400$ to the nearest hundred.

The population density of Monaco is $19,400 \text{ people/km}$ $^2.$

$4$ million is the number of people who live in Nigeria.

$40$ million is the number of people who live in Nigeria.

$20$ million is the number of people who live in Nigeria.

$200$ million is the number of people who live in Nigeria.

To find the population, multiply the population density by the land area.

\text { Population }=\text { Population Density } \times \text { Land Area }=212 \times 924,000=195,888,000

The answer needs to be given to the nearest million.

$195,888,000$ is $200$ million to the nearest million.

$2.91 \times 10^6$ is the number of people living in Venezuela.

$2.91 \times 10^7$ is the number of people living in Venezuela.

$2.92 \times 10^7$ is the number of people living in Venezuela.

$2.92 \times 10^6$ is the number of people living in Venezuela.

To find the population, multiply the population density by the land area.

\text{Population}=\text{Population Density}\times \text{Land Area}=32\times (9.12\times 10^5)=29,184,000

Then you need to write the final answer in scientific notation and round to the nearest hundredth.

$29,184,000=2.9184 \times 10^7=2.92 \times 10^7$ to the nearest hundredth.

So, the population of Venezuela is $2.92 \times 10^7.$

$76.7 \, mi^2$ is the land area of Cleveland.

$76,700 \, mi^2$ is the land area of Cleveland.

$70 \, mi^2$ is the land area of Cleveland.

$7 \, million^2$ is the land area of Cleveland.

To find the land area, divide the population by the population density.

\text { Land Area }=\cfrac{\text { Population }}{\text { Population Density }}=\cfrac{368,000}{4,800}=76.66 \ldots

Then you need to write the final answer rounded to the nearest tenth.

$76. 66\dots=76.7$ to the nearest tenth.

$1.92\times 10^5 \, km^2$ is the land area of Indonesia.

$1.92\times 10^6 \, km^2$ is the land area of Indonesia.

$1.91\times 10^6 \, km^2$ is the land area of Indonesia.

$1.91\times 10^5 \, km^2$ is the land area of Indonesia.

To find the land area, divide the population by the population density.

\text{Land Area}=\cfrac{\text{Population}}{\text{Population Density}}=\cfrac{2.68\times 10^8}{140}=1,914,285.7…

Then you need to write the final answer in scientific notation and round to the nearest hundredth.

$1,914,285.7… = 1.9142857…\times 10^6=1.91\times 10^6$ to the nearest hundredth.

Population density formula FAQs

What is population density?

Population density is a compound measure that tells us how many people live in an area of a specified size. It expresses the number of people per unit of area, such as per square mile or square kilometer.

What is the population density formula?

The population density formula is:

$\text{Population Density}=\cfrac{\text{Population}}{\text{Land Area}}$

What is the quadrat method?

The quadrat method is a sampling technique used in ecology to estimate the abundance and distribution of organisms in an area. It involves placing a grid or square (quadrat) at random locations within a study area and counting the number of organisms within each quadrat to estimate population density.

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