# Inflation calculator

Use our inflation calculator to check how prices in the UK have changed over time, from 1209 to 2020.

## What would goods and services costing

* Please only insert numbers (0 - 9)
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Data for 2021 will be available when the annual consumer price inflation time series is updated in January 2022.
• 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:

$\textit{Cost in 1985} = \textit{Cost in 1975} \times \frac{\textit{1985 price index}}{\textit{1975 price index}}$

$£65.33 = £23.60 \times \frac{373.2}{134.8}$

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

• 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:

$\textit{Average inflation} = \left( \left( \left( \frac{\textit{1985 price index}}{\textit{1975 price index}} \right) ^{0.1} \right) - 1 \right) \times 100$

$10.7\% = \left( \left( \left( \frac{373.2}{134.7} \right) ^{0.1} \right) -1 \right) \times 100$

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.

• 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.

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

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

We use several sources to create our calculator. For dates from 1750 until now we use the Office for National Statistics’ (ONS) composite price index. The ONS base their index on the Retail Price Index from 1947 onwards. But, before 1947 no single price index exists so the ONS use price data linked together from several different published sources. Every year we update our calculator using the ONS’s annual Long term indicator of prices of consumer goods and services.

For dates between 1209 to 1750, we use the cost of living index kindly supplied by Professor Greg Clark.

There are a number of other price indices available. You can find some alternatives in our A millennium of macroeconomic data spreadsheet and Professor Clark’s study The Macroeconomic Aggregates for England 1209-1869.

The website measuringworth.com has a calculator based on different measures of comparative value such as the Gross Domestic Product (GDP) deflator, average earnings, and GDP per head. These measures may be more useful depending on what you’re trying to do. For example, a calculator based on average earnings might be better if you want to compare wages, income or wealth over time.

• 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.