Population Density

GCSELevel 4-5WJEC

Population Density

Population density tells us how many people are living in a given location. It is often given in people per $\text{km}^2$ , which means in an area, approximately how many people live in each $\text{km}^2$

Calculating Population Density

To calculate population density, you need to know the population of an area and the size of an area.

The equation for population density is:

$\text{Population density} = \dfrac{\text{Population}}{\text{Land Area}}$

If somewhere is crowded, it will have a high population density, and if somewhere is sparsely populated, it will have a low population density.

Example 1: Calculating Population Density

Calculate the population density of Boston given that it has a population of $650000$ and an area of $230\text{ km}^2$ .

[2 marks]

To calculate this, we will use the equation.

$\text{Population density} = \dfrac{\text{Population}}{\text{Land Area}}$

$\text{Population density} = \dfrac{650000}{230}$

$\text{Population density} = 2826\text{ people}/\text{km}^2$ to the nearest whole number.

Example 2: Using the Equation

San Francisco has a population density of $1350\text{ people}/\text{km}^2$ and a population of $810000$ .

Work out the area of San Francisco.

[3 marks]

We will use the equation again, but will have to rearrange it:

$\text{Population density} = \dfrac{\text{Population}}{\text{Land Area}}$

$1350 = \dfrac{810000}{\text{Land Area}}$

Rearrange:

$\text{Land Area} = \dfrac{810000}{1350}$

$\text{Land Area} = 600\text{ km}^2$

Population Density Example Questions

Question 1: York has an area of $270\text{ km}^2$ and a population of $210000$

Work out the population density of York to the nearest whole number.

[2 marks]

\text{Population Density}=210000\div270\\

= 778\text{ people}/\text{km}^2

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Question 2: Birmingham has a population of $1.2\text{ million}$ and a size of $270\text { km}^2$ whereas Manchester has a population of $500000$ and an area of $115\text{ km}^2$ .

Work out which area has a higher population density.

[4 marks]

Birmingham:

Population density $= 1200000\div270\\$

Population density $=4444\text{ people}/\text{km}^2$

Manchester:

Population density $= 500000\div115\\$

Population density $=4347\text{ people}/\text{km}^2$

Therefore, Birmingham has a higher population density.

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Question 3: The population density of Liverpool is $4546\text{ people}/\text{km}^2$ , and the area is $110\text{ km}^2$ . Work out the population of Liverpool.

[2 marks]

Put the figures we know into the equation:

4546=\dfrac{\text{Population size}}{110}

Rearrange:

\text{Population size}=4546\times110

\text{Population size}=500060

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Specification Points Covered

WJEC

Using compound measures including speed, density and population density. Using compound measures such as $m/s$ , $km/h$ , $mph$ , $mpg$ , $kg/m^{3}$ , $g/cm^{3}$ , population per $km^{2}$ .