## Growth Rate Definition

We will determine the definition of growth rate by first understanding what economists mean by growth. Growth refers to an increase in any given value. In macroeconomics, we often look at growth in employment or the gross domestic product (GDP). By this, we are simply looking at whether employment or GDP has increased. In other words, **growth** refers to a **change in the level** of a given economic value.

**Growth** refers to an increase in the level of a given economic value over a given period.

We will now make this definition clearer using a simple example.

The GDP of Country A was $1 trillion in 2018 and $1.5 trillion in 2019.

From the simple example above, we can see that the level of Country A's GDP increased from $1 trillion in 2018 to $1.5 trillion in 2019. This means that the GDP of Country A grew by $0.5 trillion from 2018 to 2019.

The **growth rate**, on the other hand, refers to the **rate of increase** in the level of an economic value. It was important for us to first understand growth because growth and growth rate are closely related, as we can find the growth rate if we know the growth. However, unlike growth, the growth rate is measured as a percentage.

**Growth rate** refers to the percentage rate of increase in the level of an economic value over a given period.

- Take note of the difference between growth and growth rate.Whereas growth refers to
**an increase in the level**of an economic value over a given period,growth rate refers to the**percentage rate of increase**in the level of an economic value over a given period.

## How to Calculate Growth Rate?

The growth rate is a fundamental concept economics. It's a measure of how a specific variable or quantity expands over time—a simple yet powerful tool for understanding and predicting changes. Let's delve into the specifics of its calculation.

### Growth Rate Formula

The growth rate formula is straightforward to understand and apply. It revolves around transforming the change in a certain value into a percentage of the initial value. Here's how it's written:

The formula for growth rate is simple; you just convert the change in level into a percentage of the initial level. Let's write out the equation.

\(\text{Growth Rate} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%\)

In this formula, the "Final Value" and "Initial Value" represent the final and starting points of the value we're interested in, respectively.

Or

\(\hbox{Growth Rate}=\frac{\Delta\hbox{V}}{\hbox{V}_1}\times100\%\)

Where:

\(\Delta\hbox{V}=\text{Final Value}-\text{Initial Value}\)

\(V_1=\text{Initial Value}\)

Let's make this clearer with an example.

The GDP of Country A was $1 trillion in 2020 and $1.5 trillion in 2021. What is the growth rate of Country A's GDP?

Now, all we have to do is use the following:

\(\hbox{Growth Rate}=\frac{\Delta\hbox{V}}{\hbox{V}_1}\times100\)

We have:

\(\hbox{Growth Rate}=\frac{1.5-1}{1}\times100=50\%\)

There you have it! It's that simple.

### Tips for calculating the growth rate

Understanding how to calculate the growth rate is crucial, and here are some tips to help remember the equation and calculation process:

**Identify the Values:**Clearly distinguish the initial and final values. These are the starting and ending points of what you're studying.**Calculate the Change:**Subtract the initial value from the final value to find the total change.**Normalize to the Initial Value:**Divide the change by the initial value. This normalizes the growth to the size of the original quantity, giving you the growth "rate".**Convert to Percentage:**Multiply by 100 to convert the growth rate to a percentage.

## Economic Growth Rate

When economists talk about economic growth, it typically refers to a change in the level of GDP over a given period, and the economic growth rate builds on this. The economic growth rate refers to the percentage rate of change in the level of GDP over a given period. Note the difference. However, economists are often referring to the economic growth rate when they talk about economic growth.

**Economic growth **refers to an increase in the level of GDP over a given period.

**Economic growth rate **refers to the percentage rate of increase in the level of GDP over a given period.

Now, let's look at an example.

The GDP of Country A in 2020 was $500 million. The GDP of Country A grew by $30 million in 2021. What is the economic growth rate of Country A?

We can then use this formula to calculate the economic growth rate:

\(\hbox{Economic Growth Rate}=\frac{\Delta\hbox{GDP}}{\hbox{GDP}_1}\times100\)

We get:

\(\hbox{Economic Growth Rate}=\frac{30}{500}\times100=6\%\)

It is important to note that economic growth is not always positive, even though it is positive most times. In cases where the economic growth is negative, this means that the GDP in the initial year is higher than the current year, and the output is contracting. If the economic growth rate is negative, then the economy has declined since the previous year. However, the economic growth rate can reduce from year to year but remain positive, and this means that the economy still grew but at a lower rate. Let's have a look at Figure 2 which shows the economic growth rate in the USA from 2012 to 2021^{1}.

As figure 2 shows, the growth rate reduced at certain points. For example, from 2012 to 2013, there was a reduction in the growth rate, but it stayed positive. However, the growth rate in 2020 was negative, showing that the economy declined that year.

## How to Calculate Per Capita Growth Rate?

The per capita growth rate is a way for economists to compare the living standards of people between different periods. But, we must first understand what the **real GDP per capita** is. Simply put, this is the real GDP of the country distributed across the population.

**Real GDP per capita** refers to the real GDP of the country distributed across the population.

It is calculated using the following formula:

\(\hbox{Real GDP per capita}=\frac{\hbox{Real GDP}}{\hbox{Population}}\)

The **per capita growth** is the increase in the real GDP per capita over a given period. This is simply the new real GDP per capita minus the old GDP per capita.

The **per capita growth** is the increase in the real GDP per capita over a given period.

The **per capita growth rate** is the percentage rate of increase in the real GDP per capita over a given period. This is what economists refer to when they make statements regarding per capita growth.

The per capita growth rate is the percentage rate of increase in the real GDP per capita over a given period.

It is calculated as:

\(\hbox{Per capita growth rate}=\frac{\Delta\hbox{Real GDP per capita}}{\hbox{Real GDP per capita}_1}\times100\)

Shall we look at an example?

Country A had a Real GDP of $500 million in 2020 and a population of 50 million. However, in 2021, the Real GDP increased to $550 million, whereas the population increased to 60 million. What is the per capita growth rate of country A?

First, let's find the real GDP per capita for both years. Using:

\(\hbox{Real GDP per capita}=\frac{\hbox{Real GDP}}{\hbox{Population}}\)

For 2020:

\(\hbox{2020 Real GDP per capita}=\frac{\hbox{500}}{\hbox{50}}=\$10\)

For 2021:

\(\hbox{2021 Real GDP per capita}=\frac{\hbox{550}}{\hbox{60}}=\$9.16\)

The per capita growth rate can be calculated using the following:

\(\hbox{Per capita growth rate}=\frac{\Delta\hbox{Real GDP per capita}}{\hbox{Real GDP per capita}_1}\times100\)

We have:

\(\hbox{Per capita growth rate of Country A}=\frac{9.16-10}{10}\times100=-8.4\%\)

As you can see, the real GDP increased from 2020 to 2021. However, when the population growth was accounted for, we realized that the real GDP per capita actually saw a decline. This shows how important the per capita growth rate is and how easily misleading it can be to only look at economic growth.

## How to Calculate Annual Growth Rate?

The **annual growth rate** is the yearly percentage rate of increase of real GDP. This is simply telling us the extent to which the economy grew from year to year. The annual growth rate is particularly important in calculating how long it takes a gradually growing variable to double. This is done by applying the **rule of 7****0**, and economists usually apply this to the real GDP or real GDP per capita.

The **annual growth rate** is the yearly percentage rate of increase of real GDP.

The **rule of 70** is the formula used in calculating how long it takes a gradually growing variable to double.

The rule of 70 is presented as follows:

\(\hbox{Years to double}=\frac{\hbox{70}}{\hbox{Annual Growth Rate of the Variable}}\)

Let's look at an example now.

Country A has an annual per capita growth rate of 3.5%. How long will it take country A to double its real GDP per capita?

Using:

\(\hbox{Years to double}=\frac{\hbox{70}}{\hbox{Annual Growth Rate of the Variable}}\)

We have:

\(\hbox{Years to double}=\frac{70}{3.5}=20\)

This means it will take approximately 20 years for country A to double its real GDP per capita.

Read our article on Economic Growth to understand more about what the numbers we calculated mean.

## Growth Rate - Key takeaways

- Growth rate refers to the percentage rate of increase in the level of an economic variable over a given period.
- Economic growth refers to an increase in the level of GDP over a given period.
- Economic growth rate refers to the percentage rate of increase in the level of GDP over a given period.
- The per capita growth rate is the percentage rate of increase in the real GDP per capita over a given period.
- The rule of 70 is the formula used in calculating how long it takes a gradually growing variable to double.

## References

- World Bank, GDP growth (annual %) - United States, https://data.worldbank.org/indicator/NY.GDP.MKTP.KD.ZG?locations=US

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##### Frequently Asked Questions about Growth Rate

What is the formula for growth rate?

Growth Rate = [(Change in a value)/(the initial value)]*100

What is an example of growth rate?

If the GDP of a country increases from $1million to $1.5 million. Then the growth rate is:

Growth Rate = [(1.5-1)/(1)]*100=50%

What is growth rate of economy?

Economic growth rate refers to the percentage rate of increase in the level of GDP over a given period.

What's the difference between growth and growth rate?

Whereas growth refers to an increase in the level of an economic value over a given period, growth rate refers to the percentage rate of increase in the level of an economic value over a given period.

How do you calculate economic growth rate?

Economic Growth Rate = [(Change in real GDP)/(the initial real GDP)]*100

What is growth rate of GDP?

GDP growth rate refers to the percentage rate of increase in the level of GDP over a given period.

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