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. If a year after is entered,
the index using an calculated by interpolating the last 3 years.
Normalisation of the consumer price index (CPI) as the basis for calculation
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)
The amount related to the end of the last year (A_{2}) is calculated from the product of the amount at the beginning of the first year (B_{1})
and the ratio of the consumer price index at the end of the last year (CPI_{2}) to the consumer price index at the beginning of the first year (CPI_{1}):
A_{2} = A_{1} * CPI_{2} / CPI_{1}.
For example, an amount of 1000 € in 2000 would have a value in 2021 of:
A_{2} = 1000 * 109,1 / 79,9 = 1365,46 €.
The percentage price increase P is calculated from the consumer price index of the last year (CPI_{2}) and the consumer price index of the first
year (CPI_{1}) as follows:
P = (CPI_{2} / VPI_{1} - 1) * 100.
For example, a CPI of 79.9 € in 2000 and a CPI of 109.1 in 2021 results in a percentage price increase of:
P = (109,1 / 79,9 - 1) * 100 = 36,55 %.
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 P 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}
P = ((x_{1} * x_{2} * ... * x_{n}) ^{1/n}) - 1) * 100.
For the years 2017 to 2020, for example, n = 3 results in a percentage price increase P 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
P = (m^{1/n} - 1) * 100 = 1,23 %