Population density

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Arithmetic Rounding numbers Compound Measures Standard form

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GCSE Maths Ratio and Proportion Compound Measures

Population Density

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

There are also population density worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is population density?

Population density is a compound measure that tells us how many people live in an area of a specified size.

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 a mountainous region.

To work out population density we need to know the relationship between population density, population (the number of people) and land area.

\text{Population density}=\frac{\text{population}}{\text{land area}}

We can turn this into a formula triangle,

Population density can be used to make population estimates. The units are often $people/km^2$ (people per square kilometre). Occasionally the units might be people per square mile.

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

What is population density?

How to use population density

In order to solve problems involving population density:

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

Explain how to use population density

Population density worksheet

Get your free population density worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Population density worksheet

Get your free population density worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Related lessons on compound measures

Population density is part of our series of lessons to support revision on compound measures. You may find it helpful to start with the main compound measures lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Population density examples

Example 1: calculating population density

Malta has a population of $440 \ 000$ and an area of $316 \ km^{2}.$ Calculate the population density of Malta. Give your answer to the nearest integer.

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

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

2Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

\text{Population density}=\frac{\text{population}}{\text{land area}}=\frac{440 \ 000}{316}=1392.405…

3Write down the final answer.

The population density of Malta is $\bf{1392}$ $people \ per \ km^{2}$ (to the nearest integer).

Example 2: calculating population density

Australia has a population of $24 \ 900 \ 000$ and an area of $7 \ 690 \ 000 \ km^{2}.$ Calculate the population density of Australia. Give your answer to $3$ significant figures.

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

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

Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

$\text{Population density}=\frac{\text{population}}{\text{land area}}=\frac{24\ 900 \ 000}{7 \ 690 \ 000}=3.2379…$

Write down the final answer.

The population density of Australia is $\bf{3.24}$ $people \ per \ km^2$ (to $3$ significant figures).

Example 3: calculating population

Hong Kong has a population density of $6700 \ people/km^2$ and an area of $1100 \ km^{2}.$ Calculate the population of Hong Kong.

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

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

Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

$\begin{aligned} \text{Population density}&=\frac{\text{population}}{\text{land area}}\\\\ 6 \ 700 &=\frac{\text{population}}{1 \ 100}\\\\ \text{Population}&=6 \ 700 \times 1 \ 100\\\\ \text{Population}&=7 \ 370 \ 000 \end{aligned}$

Write down the final answer.

The population of Hong Kong is $7 \ 370 \ 000$ people.

Example 4: calculating population

Rwanda has a population density of $470 \ people/km^2$ and an area of $26 \ 000 \ km^{2}.$ Calculate the population of Rwanda.

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

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

Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

$\begin{aligned} \text{Population density}&=\frac{\text{population}}{\text{land area}}\\\\ 470 &=\frac{\text{population}}{26 \ 000}\\\\ \text{Population}&=470 \times 26 \ 000 \\\\ \text{Population}&=12 \ 220 \ 000 \end{aligned}$

Write down the final answer.

The population of Rwanda is $\bf{12 \ 220 \ 000}$ people.

Example 5: calculating land area

New York has a population density of $11 \ 300 \ people/km^2$ and a population of $8.8$ million people. Calculate the land area of New York. Give your answer to $3$ significant figures.

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

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

Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

$\begin{aligned} \text{Population density}&=\frac{\text{population}}{\text{land area}}\\\\ 11 \ 300 &=\frac{8 \ 800 \ 000}{\text{land area}}\\\\ \text{Land area}&=8 \ 800 \ 000\div 11 \ 300\\\\ \text{Land area}&=778.76… \end{aligned}$

Write down the final answer.

The land area of New York is $\bf{779}$ $km^2$ (to $3$ significant figures).

Example 6: calculating land area

Pakistan has a population density of $267 \ people/km^2$ and a population of $2.12 \times 10^8$ people. Calculate the land area of Pakistan. Give your answer in standard form to $3$ significant figures.

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

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

Use the formula.

The formula is

$\text{Population density}=\frac{\text{population}}{\text{land area}}$ .

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

$\begin{aligned} \text{Population density}&=\frac{\text{population}}{\text{land area}}\\\\ 267 &=\frac{2.12\times 10^8}{\text{land area}}\\\\ \text{Land area}&=2.12\times 10^8\div 267\\\\ \text{Land area}&=794 \ 007.49… \end{aligned}$

Write down the final answer.

\text{Land area}=794\ 007.49…=794\ 000=7.94\times 10^5

The land area of Pakistan is $7.94 \times 10^5 \ km^2$ (to $3$ significant figures).

Common misconceptions

Make sure you use the formula wisely

Make sure you divide or multiply appropriately. When dividing, make sure the population is the dividend (the number being divided).

Check the units

The units usually involve $km^{2},$ but another square unit may be used such as $miles^2$ or $m^{2}.$

Check what form the final answer needs to be in

You may be asked to round your answer. You may be asked to write your final answer in standard form, as the numbers involved can be very large.

Practice population density questions

193 \ people/km^2

191 \ people/km^2

192 \ people/km^2

194 \ people/km^2

Population density $=\frac{\text{population}}{\text{land area}}=\frac{28 \ 100 \ 00}{147 \ 000}=191.156…$

The answer needs rounding to $3$ significant figures.

$191.156\dots=191$ to $3$ significant figures.

So the population density of Nepal is $191 \ people/km^2$ .

19 \ 300 \ people/km^2

1 \ 940 \ people/km^2

19 \ 400 \ people/km^2

194 \ people/km^2

$\text{Population density}=\frac{\text{population}}{\text{land area}}=\frac{3.87\times 10^4}{2}=19 \ 350$ .

The answer needs rounding to $3$ significant figures.

$19 \ 350=19 \ 400$ to $3$ significant figures.

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

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

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

$2$ million is the number of people who live in Nigeria.

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

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

$\text{Population}=\text{population density}\times \text{land area}= 212\times 924 \ 000=19 \ 588 \ 000$ .

The answer needs giving to the nearest million.

$19 \ 588 \ 000$ is $20$ 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 we need to write the final answer in standard form and round to $3$ significant figures.

$29 \ 184 \ 000= 2.9184\times 10^7=2.92\times 10^7$ to $3$ significant figures.
So, the population of Venezuela is $2.92\times 10^7.$

$36 \ 200 \ km^2$ is the land area of Taiwan.

$36 \ 200 \ miles^2$ is the land area of Taiwan.

$3 \ 620 \ miles^2$ is the land area of Taiwan.

$3 \ 620 \ km^2$ is the land area of Taiwan.

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

$\text{Land area}=\frac{\text{population}}{\text{population density}}=\frac{23 \ 600 \ 000}{652}=36 \ 196.3…$ .

Then we need to write the final answer rounded to $3$ significant figures.

$36 \ 196.3…=36 \ 200$ to $3$ significant figures.
The units for the land area will be $km^2$ since $km^2$ was part of the units for the population density.

$1.92\times 10^5 \ km^2$ 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}=\frac{\text{population}}{\text{population density}}=\frac{2.68\times 10^8}{140}=1 \ 914 \ 285.7…

Then we need to write the final answer in standard form and round to $3$ significant figures.

$1 \ 914 \ 285.7… = 1.9142857…\times 10^6=1.91\times 10^6$ to $3$ significant figures.

Population density GCSE questions

1. Bangladesh has a population of $161 \ 000 \ 000$ people. The population density is $1000$ people per $km^2.$ Calculate the area of Bangladesh.

(2 marks)

Show answer

161 \ 000 \ 000 \div 1000

(1)

161 \ 000 \ km^2

(1)

2. Here is some information about the populations and areas of $3$ different towns.

Which country has the highest population density? You must show your workings.

(2 marks)

Show answer

\begin{aligned} &\text{Spain:}\ 4.67\times 10^7 \div 5.06\times 10^5=92.292… \\\\ &\text{Laos:}\ 7.06\times 10^6 \div 2.37\times 10^5=29.789… \\\\ &\text{Netherlands:}\ 1.71\times 10^7 \div 3.74\times 10^4=457.219… \end{aligned}

(1)

Netherlands has the highest population density.

(1)

3. (a) A village has an area of $5 \ km^2$ and a population density of $600 \ people \ per \ km^{2}.$

Calculate the number of people living in the village.

(b) A new estate is built. It has a population density of $800 \ people \ per \ km^{2}. \ 500$ people live in the new estate.

Calculate the overall population density of the village and the new estate.

(5 marks)

Show answer

(a)

5 \times 600

(1)

$3000$ people

(1)

(b)

500 \div 800=0.625

(1)

\frac{3000+500}{5+0.625}

(1)

=622.222… = 622 \ people \ per \ km^2

(1)

Learning checklist

You have now learned how to:

Calculate the population density

Solve problems involving population density

The next lessons are

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Introduction

What is population density?

How to use population density

Population density worksheet

Population density examples

↓

Example 1: calculating population density Example 2: calculating population density Example 3: calculating population Example 4: calculating population Example 5: calculating land area Example 6: calculating land area

Common misconceptions

Practice population density questions

Population density GCSE questions

Learning checklist

Next lessons

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