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In 2023, the relative value of £10,000   0s   0d from 1823 ranges from £1,095,000.00 to £64,730,000.00.

A simple Purchasing Power Calculator would say the relative value is £1,145,000.00. This answer is obtained by multiplying £10,000.00 by the percentage increase in the RPI from 1823 to 2023.

This may not be the best answer.

The best measure of the relative value over time depends on if you are interested in comparing the cost or value of a Commodity , Income or Wealth , or a Project . For more discussion on how to pick the best measure, consult the Tutorials.

If you want to compare the value of a £10,000 0s 0d Commodity in 1823 there are four choices. In 2023 the relative:
real price of that commodity is £1,145,000.00
labour value of that commodity is £11,420,000.00
income value of that commodity is £15,240,000.00
economic share of that commodity is £64,730,000.00


If you want to compare the value of a £10,000 0s 0d Income or Wealth , in 1823 there are four choices. In 2023 the relative:
real wage or real wealth value of that income or wealth is £1,145,000.00
labour earnings of that income or wealth is £11,420,000.00
relative income value of that income or wealth is £15,240,000.00
relative output value of that income or wealth is £64,730,000.00


If you want to compare the value of a £10,000 0s 0d Project in 1823 there are three choices. In 2023 the relative:
real cost of that project is £1,095,000.00
labour cost of that project is £11,420,000.00
economic cost of that project is £64,730,000.00

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Citation

"Five Ways to Compute the Relative Value of a UK Pound Amount, 1270 to Present," MeasuringWorth, .

URL: www.measuringworth.com/ukcompare/

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A Project is either an investment, such as construction of a canal or installation of a cable network; or a government expenditure, such as the financing of Medicare or a war. Also within this category are such items as the size of a government budget deficit, and the total assets or net worth of a company.
Income is a flow of earnings, while Wealth is a stock of assets. Earnings might be of a specific type of labor, such as a plumber or professional athlete, or the (average) earnings of a broad group of labor, such as unskilled workers. Wealth can be a financial asset such as bank deposits or a stock portfolio, or can involve a physical asset, such as real estate.
Commodities are (usually consumer) goods and services. Examples are bread, attending a rock concert, buying hamburgers, a visit to the dentist, and personal computers.

Real Price is measured as the relative cost of a (fixed over time) bundle of goods and services such as food, shelter, clothing, etc., that an average household would buy. In theory the size of this bundle does not change over time, but in practice adjustments are made to its composition. This measure uses the RPI.

Labour Value is measured as the multiple of the average wage that a worker would need to use to buy the commodity. This measure uses one of the wage indexes.

Income Value is measured as the multiple of average income that would be needed to buy a commodity. This measure uses the index of GDP per capita.

Real Wage or Real Wealth measures the purchasing power of an income or wealth by its relative ability to buy a (fixed over time) bundle of goods and services such as food, shelter, clothing, etc. This bundle does (in theory) not change over time. This measure uses the RPI.

Relative Income measures an amount of income or wealth relative to per capita GDP. When compared to other incomes or wealth, it shows the economic status or relative "prestige value" the owners of this income or wealth because of their rank in the income distribution. This measure uses GDP per capita.

Relative Output measures the amount of income or wealth relative to the total output of the economy. When compared to other incomes or wealth, it shows the relative "influence" of the owner of this income or wealth has in controlling the composition or total-amount of production in the economy. This measure uses the share of GDP.

Real Cost of a project is measured by comparing its cost to the cost index of all output in the economy. This measure uses the GDP Deflator.

Labor Cost of a project is measured as a multiple of the average wage of the workers that might be used to build the project. This measure uses one of the wage indexes.

Labour Earnings measures the amount of income or wealth relative to the wage of the average worker. This measure uses one of the wage indexes.

Economy Cost of a project is measured as the cost of the project as a percent of the output of the economy. This measure indicates the opportunity cost in terms of the total output of the economy. It can be interpreted as the importance of the item to society as a whole. This measure uses the share of GDP.

Economic Share is the worth of a commodity in a particular time period divided by GDP; it is its share of total output. This is helpful in measuring the relative value of aggregate consumption items such as all the cars made in a year.

The RPI is most often used to make comparisons partly because it is the series with which people are most familiar. This series tries to compare the cost of things the average household buys such as food, housing, transportation, medical services, etc. For earlier years, it is the most useful series for comparing the cost of consumer goods and services. It can be interpreted as how much money you would need today to buy an item in the year in question if its price had changed the same percentage as the average price change.
A Purchasing Power Calculator compares the relative value of a past amount of dollars to a present amount. A simple calculator uses only the prices of consumer purchases to do this whereas a complete purchasing power calculator, such as found in this website, uses various prices, wages, output, etc., depending on the context.