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The growth rate is an important analytical indicator that allows you to answer the question: how did this or that indicator increase/decrease and how many times did it change over the analyzed period of time.

Correct calculation

Calculation using an example

Objective: the volume of Russian grain exports in 2013 amounted to 90 million tons. In 2014, this figure was 180 million tons. Calculate the growth rate as a percentage.

Solution: (180/90)*100%= 200% That is: the final indicator is divided by the initial indicator and multiplied by 100%.

Answer: the growth rate of grain exports was 200%.

Rate of increase

The growth rate shows how much a particular indicator has changed. It is very often confused with the growth rate, making annoying mistakes that can be easily avoided by understanding the difference between the indicators.

Calculation using an example

Problem: in 2010, the store sold 2,000 packs of washing powder, in 2014 - 5,000 packs. Calculate the growth rate.

Solution: (5000-2000)/2000= 1.5. Now 1.5*100%=150%. The base year is subtracted from the reporting period, the resulting value is divided by the base year indicator, then the result is multiplied by 100%.

Answer: the growth rate was 150%.

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In various areas of social life, a number of sciences and research methods, formulas for growth rates and growth rates are used. They are most often used in economics and statistics to identify trends and results of activities. This article discusses situations where these formulas are needed, their definitions, and how they are calculated.

Growth rate

Calculating the growth rate begins with defining a series of numbers between which you need to find a percentage relationship. The control number is usually compared either with the previous indicator or with the base number at the beginning of the number series. The result is expressed as a percentage.

The growth rate formula is as follows:

Growth Rate = Current/Baseline*100%. If the result is more than 100%, growth is noted. Accordingly, less than 100 is a decrease.

An example is the option of increasing and decreasing wages. The employee received a monthly salary: in January - 30,000, in February - 35,000. The growth rate was:

Rate of increase

The growth rate formula allows you to calculate the percentage of how much the value of an indicator has increased or decreased over a certain period. In this case, a more specific figure is visible, allowing one to judge the efficiency of work over time. That is, by calculating the ratio of wages (or other characteristic) using the growth rate formula, we will see by what percentage this amount has changed.

There are two calculation options:

1. Growth rate = current value / base value * 100% - 100%:

35 000/30 000*100%-100%=16,66%;

1. Growth rate = (current value - base value) / base value * 100%:

(35 000-30 000)/30 000*100%=16,66%.

Both calculation methods are identical. A negative mathematical result indicates a decrease in the indicator for the period under review. In our example, the employee’s salary in February was 16.66% higher than in January.

Growth and gain formulas: basic, chain and average

The rate of growth and increment can be found in several ways, depending on the purpose of the calculation. There are formulas for obtaining basic, chain and average growth and increment rates.

Base rate of growth and gain shows the ratio of the selected series indicator to the indicator taken as the main one (calculation base). Usually it is at the beginning of the row. The formulas for calculation are as follows:

• Growth rate (B) = Selected indicator/Baseline indicator*100%;
• Growth rate (B) = Selected indicator/Base indicator*100%-100.

Chain rate of growth and gain shows the change in the indicator over time along the chain. That is, the difference in time between each subsequent indicator and the previous one. The formulas look like this:

• Growth Rate (G) = Selected Indicator/Previous Indicator*100%;
• Growth rate (G) = Selected indicator / Previous indicator * 100% -100.

There is a relationship between the chain and base growth rates. The ratio of the result of dividing the current indicator by the base one to the result of dividing the previous indicator by the base one is equal to the chain growth rate.

Average growth and gain rate used to determine the average change in indicators for a year or other reporting period. In order to determine this value, you need to determine the geometric mean of all indicators in the period or find it by determining the ratio of the final value to the initial one:

Nuances of calculations

The formulas presented are very similar and can be confusing and confusing. To do this, let us explain the following.

DEFINITION

Growth rate represents the ratio of the value of any economic indicator for a certain time to its initial value, which is taken as the basis (base) of reference.

Growth rate is measured as a percentage or relative value.

The rate of economic growth is directly dependent on type of economic growth. There are 2 types of economic growth in economics – extensive growth and intensive.

At extensive growth an increase in production volumes occurs due to the introduction of a larger number of factors (raw materials, fuel, labor, equipment, etc.).

At intensive type of growth an increase in production volume can be achieved by improving quality indicators (qualifications, technologies, achievements of scientific and technological progress). That is, growth occurs due to an improvement in quality, and not quantity, as with extensive growth.

If the intensive type begins, then the pace may even decrease slightly compared to the extensive type of growth. But this fact does not mean that there has been a decline in economic development or that it has slowed down.

Features of growth types:

• With an extensive type of growth, the economy can maintain proportions, structural characteristics and development in breadth.
• With an intensive type of growth, the economy becomes dynamic due to the expansion of production, as well as due to progressive structural adjustments.

Growth Rate Formula

In general, the growth rate formula is as follows:

Tr=Pnp/Pkp

Here Tp is the growth rate,

Pnp – indicator of the beginning of the period,

Pkp is an indicator of the end of the period.

To obtain a more visual result, the resulting answer is multiplied by 100% and the growth rate formula is expressed as a percentage.

What does the growth rate formula show?

The growth rate shows how many percent the growth of the statistical indicator of the current period was in comparison with the previous period.

At different values ​​of the growth rate formula, three scenarios can be observed:

1) A growth rate of more than 100% means positive dynamics.

2) A growth rate of 100% means that no changes have occurred.

3) A growth rate of less than 100% means negative dynamics.

Difference between growth rate and growth rate

Students often confuse the concepts of growth rate and growth rate, since their formulas are slightly similar.

To determine the growth rate, the indicator of the base period is subtracted from the indicator of the calculation period, then the resulting result is divided by the indicator of the base period and multiplied by 100%. As a result, you can obtain the growth rate as a percentage.

In order not to confuse these concepts, it should be noted that the growth rate reflects the growth of the indicator itself, that is, how many times it changes in the period of time under consideration.

And the growth rate, in turn, reflects how much the indicator grows over this period of time in comparison.

Examples of problem solving

EXAMPLE 1

EXAMPLE 1

Many people are interested in how to calculate the growth rate for a certain period. When examined in detail, this issue can cause many problems, because the growth rate can be calculated taking into account basic, chain and average indicators with different nuances. We will consider this issue in a simpler context.

Growth Rate Calculation: Formula

In general, the scheme for calculating the growth rate looks like this: growth rate = data at the end of the period / data at the beginning of the period. For a more visual result, the answer is multiplied by 100%, thus the growth rate will be expressed as a percentage.

Let's look at the application of the growth rate scheme using a specific example. Let's say we need to calculate the growth rate over several years. We have an indicator for 2005 - 240 and we have an indicator for 2013 - 480. In order to calculate the growth rate over these years as a percentage, we 480/240 * 100%. Result: 200%. The growth rate was 200%, which means that the indicator we are considering doubled from 2005 to 2013.

The growth rate is often confused with the growth rate, since their formulas are similar, but these indicators are still different. In order to find the growth rate, you need to subtract the indicator in the base period from the indicator in the billing period, then divide the result by the indicator in the base period and multiply by 100. The result is the growth rate as a percentage. Let's look at the example above. Let's assume that 240 is the indicator for the base period, and 480 is the indicator for the reporting period. So, (480-240)/240 * 100% = 100%. The growth rate was 100%.

As you can see, the growth rate and the growth rate are different indicators. The growth rate shows how the indicator grows, how many times it changes over the period under review, and the growth rate shows how much the indicator under consideration increases over a certain period. Each of them is calculated differently, so do not confuse them.

The growth rate is one of the dynamic, that is, changing indicators of the economic system. To calculate dynamics indicators, you need to set a base level - that is, the one with which all further indicators will be compared.

In economics, the variable base principle is often used. This means that each subsequent indicator is compared with the previous one. To understand how to calculate the growth rate, you need to be able to calculate basic indicators.

Quick navigation through the article

Absolute increase

First of all, we need such a concept as absolute growth. Calculating absolute growth is quite simple: to do this, calculate the difference between the latest economic indicators and the previous ones.

For example, if the selected indicator in the reporting period amounted to X rubles, and in the previous reporting period Y rubles, then the absolute increase will be X-Y rubles.

Absolute growth can be positive or negative. Using this indicator, you can immediately see the increase or decrease of the selected indicator for the selected period.

Rate of increase

The growth rate indicates relative growth. This is a relative value and is calculated as a percentage or fraction, as a growth factor. In order to calculate the growth rate for a selected indicator, you need to divide the absolute growth for the selected period by the indicator for the initial period. We multiply the resulting value by 100 to obtain a percentage.

Let's look at the example already given:

• For the reporting period, revenue is X rubles, and for the previous one - Y rubles.
• The absolute increase is X-Y.
• The growth rate can now be calculated from the available data: (X-Y)/Y *100. This indicator can also be positive or negative.

To calculate the growth rate for the entire period, you need to select an initial, base level (for example, the year the company was founded). Then the absolute increase is calculated as the difference between the indicators of the last year and the first year. By dividing this difference by the indicator for the first year, you can calculate the growth rate for the entire period.

Dynamic indicators of the economic system show its viability and profitability. One of these indicators is the growth rate, which shows the percentage of growth in indicators.