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Home > Education and Museum > How the inflation calculator works

# How the inflation calculator works

​Our inflation calculator works for amounts between £1 and £1,000,000,000,000 (£1 trillion).

For example, imagine you want to know what goods and services costing £23.60 in 1975 would have cost in 1985:

The price index for 1975 = 134.8
The price index for 1985 = 373.2

The calculator increases the cost in 1975 by the change in prices between 1975 and 1985 with this formula:

Cost in 1985 = Cost in 1975 x (1985 price index / 1975 price index)

£65.33 = £23.60 x (373.2 / 134.8)

So the cost in 1985 of the same goods and services has risen to £65.33.

#### Average inflation

The inflation calculator also tells you the average yearly inflation rate between two years. The formula for this, again using the example of 1975 to 1985, is:

Average inflation = ( ( ( 1985 price index / 1975 price index ) ^ 0.1 ) – 1 ) x 100

The answer is:

10.7% = ( ( ( 373.2 / 134.8 ) ^ 0.1 ) -1 ) x 100

This looks a bit complicated, but it just shows that on average prices rose by 10.7% a year between 1975 and 1985. By the way, “^ 0.1” means that the change in prices is ‘raised to the power of one tenth’ to calculate the average inflation rate over ten years.

#### Deflation

If prices fell between the two years you put into the calculator, average inflation will be negative. This is called deflation.

For example, say you input the dates 1920 and 1933. The calculator reveals that inflation averaged -3.5%, because prices fell in almost every year between 1920 and 1933.

#### Calculator caveats and limitations

Our inflation calculator is designed for illustrative and general reference purposes only.

The calculations are approximate, and give a rough guide to the buying power of the pound for goods and services purchased in the UK.

In order to make comparisons possible over long periods of time, the calculator uses the composite price index published by the Office for National Statistics (ONS). Since there is no single price index available all the way back to 1750, the composite index is produced by linking together price data from several different published sources – both official and unofficial. We update this annually based on the ONS’s annual Consumer Price Inflation (CPI) figure.

#### Accuracy of inflation data

Over long periods, the definitions of goods and services included in the price index have changed. For example, a family’s food and clothes today are very different to those of a typical family a hundred years ago.

Changes in household spending also reflect higher incomes and the wider range of goods and services available to buy today. These new goods and services are included in today’s price index, but not in earlier versions.

Overall, these features of the data mean that comparisons of prices further back in time and over long periods are less accurate than comparisons over short periods in recent years.

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