Consumer price index (CPI) for Germany
The consumer price index (CPI) is a key indicator of price development. The percentage change in the CPI is referred to as an
inflation rate or price increase rate. A time period with a rising price index is called inflation, a falling price index deflation.
The CPI for Germany —
long series from 1948
- is published monthly as a table by the
Federal Statistical Office.
This table contains various price indices for the period 1948 to 1991, and since 1991, a unified CPI and an index of retail prices.
The index refers in each case as a percentage value compared to a base year. For the years 1948 to 1990 the price index for the cost of living is shown with base
year 1995 (index = 100) and from 1991 the consumer price index with base year 2015 (index = 100).
In this inflation calculator 2022, to calculate the consumer price index (CPI), the price index for the standard of living from 1948 to 1961 is taken from the column
"4-Personenhaushalt von Arbeitern und Angestellten" and from 1962 to 1990 from the column "Alle privaten Haushalte"
and from 1991 from the column "Verbraucherpreisindex" for Germany. The Federal Statistical Office publishes both annual and monthly values for the various key figures.
In this inflation calculator 2022 only the current average annual values for the consumer price index (JD indices) are taken into account.
The last updated annual values therefore refer to the year 2021.
Conversion of the consumer price index (CPI) to the base year 2015
In the published table of the Federal Statistical Office, the index for the years 1948 to 1990 is related to the base year 1995 (index = 100). In this
inflation calculator 2022
all indices from this period are normalised to the currently valid reference year 2015 and displayed as the CPI:
CPI = Index_{1995} * Index_{year} / 100.
For the year 1948, for example, the normalized consumer price index (CPI), rounded to one decimal place, is calculated as follows:
CPI = 75.1 * 28.5 / 100 = 21.4.
Calculation of the price rise from the consumer price index (CPI)
Inflation causes prices to rise. This means that the same goods and services get a higher monetary value.
The amount A_{2} related to the end of the last year is calculated from the product of the amount A_{1} at the end of the first year
and the ratio of the consumer price index CPI_{2} at the end of the last year to the consumer price index CPI_{1} at the end of the first year:
A_{2} = A_{1} * CPI_{2} / CPI_{1}.
For example, an amount of € 1,000 in 2017 would have a value in 2020 of:
A_{2} = 1,000 * 105.8 / 102.0 = € 1,037.25.
For goods and services worth € 1000 in 2017, € 1037.25 is payable for the same goods and services in 2020.
The percentage price increase P is calculated from the consumer price index CPI_{2} of the last year and the consumer price index CPI_{1} of the first
year as follows:
P = (CPI_{2} / CPI_{1} - 1) * 100.
For example, a CPI of 102.0 in 2017 and a CPI of 105.8 in 2020 results in a percentage price increase P of:
P = (105.8 / 102.0 - 1) * 100 = 3.725 %.
Calculation of purchasing power from the consumer price index (CPI)
Inflation reduces the value of money, which means that money has less purchasing power. Purchasing power and price increase are reciprocal to each other.
The purchasing power P related to the end of the last year is calculated from the product of the amount A at the end of the first year and the ratio of
the consumer price index CPI_{1} of the first year to the consumer price index CPI_{2} of the last year:
P = A * CPI_{1} / CPI_{2}.
For example, a value of € 1000 at the end of 2017 would have a purchasing power P at the end of 2020 of:
P = 1000 * 102.0 / 105.8 = € 964.08.
For € 1,000, only goods and services can be bought in 2020 that had a value of € 964.08 in 2017.
Average inflation per year
The average inflation rate spent per year applied to the amount in the first year and in each case to the resulting price increases of all subsequent years results
in the amount spent in the last year. The average inflation rate per year I is calculated from the
geometric mean of all consumer price indices (CPI) in the period
under consideration over n years with i = 1 ... n:
x_{i} = CPI_{i+1} / CPI_{i}
I = ((x_{1} * x_{2} * ... * x_{n}) ^{1/n}) - 1) * 100.
For the years 2017 to 2020, for example, n = 3 results in an average inflation rate I of:
x_{1} = CPI_{2018} / CPI_{2017} = 103.8 / 102.0 = 1.0176
x_{2} = CPI_{2019} / CPI_{2018} = 105.8 / 103.8 = 1.0145
x_{3} = CPI_{2020} / CPI_{2019} = 105.8 / 105.3 = 1.0047
m = x_{1} * x_{2} * x_{3} = 1.0372
I = (m^{1/n} - 1) * 100 = 1.23 %
The average inflation rate of 1.23% applied to the value of € 1,000 in the first year and to each of the following 2 years results in a price increase of € 1,037.35
in the last year:
2018: 1.23 % von € 1,000.00 = € 12.30
2019: 1.23 % von € 1,012.30 = € 12.45
2020: 1.23 % von € 1,024.75 = € 12.60
This results in a price increase of € 1,037.35. Due to rounding errors, a small deviation occurs compared to the result from the
calculation of the price rise from the consumer price index (CPI).
Estimation of the inflation rate for coming years
If the last year entered in the inflation calculator is later than the last published year
2021, the inflation rate for the coming years is estimated.
For this purpose, the historical consumer price indices (CPI) of the past years are used according to the number of future years. For this past period,
the average inflation rate per year and the consumer price index (CPI) calculated from this for the
latest year are output. The latest valid year is 2093.
In the case of estimated data, the inflation calculator outputs the year figures for the estimation as an additional remark.