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### Glossary of Terms

Annualized Growth Rate
The average growth rate measured over a year. For short periods, it is the extrapolation of the increase continuing for a year's time. For long periods, it is the hypothetical constant per-year rate that takes the beginning-date value of a series to the ending-date value of the series during the time span.

Growth rates depend on the compounding rate used. With one exception, the rates reported here are compounded annually. For the DJIA, the rate is compounded daily. See how the Annualized Growth Rates are constructed.

Average Earnings
"Earnings" represent an estimate of the total monetary value of the compensation an average worker in full time employment would get each year. Earnings consist of wages plus non-cash (in-kind) payments plus bonuses plus commissions plus remuneration per output accomplished ("piece-rate payments") plus payment for overtime (hours exceeding the normal number per time period).

British Official Price of Gold
The price at which gold was coined at the Royal Mint, expressed as number of British pounds per fine (pure) ounce. See Gold Price in the glossary to learn more.

Commodity
Commodities are (usually consumer) goods and services. Examples include bread, attending a rock concert, visiting the dentist, and personal computers.

Computation of Annualized Growth Rates
There are several different ways in which the annualized rate of growth can be calculated. None of these ways is "the" correct way, but we believe that the method we adopted is the most appropriate for the users of this calculator. To outline the alternative methods, consider the following notation:

B = value of variable in beginning year.
E = value of variable in ending year.
N = number of years between beginning and ending year.
For example, if the beginning year is 1950 and the ending year is 1965, then N = 15.

Consumer Bundle
The value of the consumer bundle (VCB) is the average annual expenditures of consumer units. Expenditures are for goods and services; also included are gifts and charitable contributions, as well as insurance premiums and pension contributions. The value of the consumer bundle is expressed in dollars; it is not corrected for inflation.

Consumer Price Index
The CPI in any year is the cost in that year of a bundle of goods and services purchased by a typical urban consumer compared to the cost of that bundle of goods and services in a base period. The CPI provides a narrow measure of inflation, because it is confined to consumer goods and services.

For this series, the base period is the 1982-84 annual average. The series used in MeasuringWorth extends the United States Bureau of Labor Statistics CPI-U (consumer price index for all urban consumers) series back in time. The official CPI series begins in 1913, but improvements to the official series are made here, so the CPI series here is identical to the BLS series only from 1978 onward.

For further discussion of the limitations of the CPI, and for detailed exposition of development of this CPI series, please read What Was the Consumer Price Index Then? A Data Study (360K PDF).

Contemporary Opportunity Costs
Contemporary Opportunity Costs measures a subject (always a project) relative to the VCB (value of the consumer bundle). Because the VCB, the average expenditure of households, is the measure, the project-item may pertain to business/government, to a person/household, or to a nonprofit institution.

Contemporary Standard of Living
Contemporary Standard of Living measures a subject (income or wealth) against the value of the consumer bundle (VCB).

Daily DJA
The first Dow Jones Index was composed of 12 stocks, 10 of which were railroads. It was published daily until 1896, when Dow started publishing the first Dow Jones Industrial Average (DJIA.) In 1916 there was a new DJIA published that was similar to the first index, but a smaller value. That index has been published continually up today. The three indexes are merged on this site.

The numbers use in the Annualized Growth Calculator are the average for the year of the daily closing. For more information see Daily Closing Values of the Dow Jones Average in the United States, May 2, 1885 to Present and Source Note for DJA.

Economic Power
Economic Power measures a subject (income or wealth) against the total output of the economy, measured by GDP. The economic power of the person to whom the item pertains addresses the ability to influence the composition or total-amount of production in the economy (GDP).

Economic Status
Economic Status measures a subject (income or wealth) relative to a wage or more general income, such as the wage rate of workers in manufacturing or per-capita GDP. Note that the specific measures are identical labor value or income value, but the kinds of subjects differ.

Gross Domestic Product (GDP)
GDP is a measure of the total market value of all final goods and services produced in a country during one year. In other words, GDP is total spending on newly produced goods and services. In the United States, the annual GDP is about 15 trillion dollars, meaning that amount is spent on U.S output in one year.

Four general groups are buying what is produced. The households buying food, HDTVs, medical care and whatever else they want and can afford to spend constitute about 70 percent of GDP. Another 15 percent of GDP consists of spending by business firms to purchase new capital equipment, buildings, and inventories. Taking up about 19 percent of GDP is spending of government on items such as schools, highways, and Air Force F-16s. Finally, the production of goods and services for export comprises 12 percent of GDP. This total adds up to more than 100 percent, because 17 percent of U.S. spending on goods and services are produced overseas.

See Nominal GDP and Real GDP also.

GDP Deflator
The GDP deflator is an index number that represents the "average price" of all the goods and services produced in the economy. It a weighted number based on what is paid for the entirety of GDP, that is, for everything from a gallon of milk to a new Army helicopter. Changes in the deflator are a broad measure of inflation.

The GDP deflator is calculated by dividing Nominal GDP by Real GDP.

GDP per capita
GDP divided by Population. This ratio is the "average" per-person output of the economy. GDP per-capita is greater than per-capita personal income, because GDP includes consumption of fixed capital and undistributed corporate profits -- flows that are not part of national personal income. See Nominal GDP per capita and Real GDP per capita.

Gold Price
Expressed as number of currency units (for example, U.S. dollars or British pounds) per fine (pure) Troy ounce. A Troy ounce is about ten-percent heavier than the "avoirdupois" ounce, the latter measure commonly used domestically in the United States.

Gold/ Silver Price Ratio
The "silver price" of gold, meaning the number of ounces of silver per ounce of gold computed as a ratio of the market price of gold to the market price of silver: MeasuringWorth covers the Hamburg market, 1687-1832, the London market, 1833-1914, and the New York market, 1915 to present.

Graphing Using a Log Scale
Many economic variables tend to change exponentially rather than arithmetically over time. That is, the variable increases and sometime decreases as a percent of its value. Thus if GDP is 100 it might increase by 2, and if GDP is 1,000 the increase is likely to be 20. Both situations involve a two-percent increase in GDP.

Consider a time series (for example, an annual time series, X) that has experienced significant growth. On a normal (arithmetic) graph, which plots X against time (year), earlier values would be close to the horizontal (time, year) axis and later values far above the horizontal axis. On a logarithmic graph, which plots log X against time, the same percentage change in X will look that same, regardless of the size of the observations. This means that the slope of the graph (year-to-year change in log X) is the year-to-year growth rate of X itself. Thus the log graph makes it easy to see how a series growth rate changes over time.

Historic Opportunity Costs
Historic Opportunity Costs measures a subject (generally a project) against a bundle of consumer goods and services (via the CPI or RPI) or a bundle of all goods and services (using the GDP deflator). For a project of a person or household, the CPI or RPI is preferred. For investment and government projects, the GDP deflator is more appropriate.

Historic Standard of Living
Historic Standard of Living measures a subject (income or wealth) against the cost of a "fixed" bundle of consumer goods and services (the CPI or RPI) or the cost of all goods and services (the GDP deflator).

Income or Wealth
Income is a flow of earnings, while wealth is a stock of assets. The 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 it can involve a physical asset, such as real estate.

Labor Value or Income Value
Labor Value or Income Value measures a subject (commodity or project) against a specific wage or more-general income, such as the average wage rate or per capita GDP.

London Market Price of Gold
From 1968 onward, "PM fix" quote; of London Bullion Market Association, annual average of monthly averages of daily data. Earlier data from diverse sources; see What Was the Price of Gold Then? Importance, Measurement, and History (29K PDF), and Was the Price of Gold Then? A Data Study (119K PDF). Expressed in British pounds per fine (pure) ounce 1718-1949, and in U.S. dollars per fine (pure) ounce 1950 onward.

Measures of Worth
Clearly, intrinsic values, objects, or events are difficult, if not impossible, to measure in money terms. There is probably no objective way of assessing the worth of freedom of speech, the love of your life, or a beautiful sunset. Such items lack a well-defined monetary amount associated with them. Therefore we do not attempt to measure the worth of such items. Also, we cannot measure the worth even of an item associated with a money amount, if the time period (say, year) of that money amount is not clearly established. What is the worth today of "a loaf of bread produced or consumed sometime in the past"? Such an incompletely phrased question cannot be answered.

Nominal GDP
GDP expressed in current market prices, which is GDP not corrected for inflation. The nominal GDP may also be called "money GDP", "current-price GDP" or "GDP at current prices". Nominal GDP over time incorporates both real-output change and price change (inflation).

Nominal GDP per capita
Nominal GDP divided by Population, which measures the "average" per-person output of the economy in the prices of the current year. See GDP per capita.

New York Market Price of Gold
Price of gold in over-the-counter market in New York City, expressed as number of U.S. dollars per fine (pure) ounce. Until 1968 (with the exception of episodic periods during which New York banks and/or the U.S. Treasury "suspended specie payments", that is, they refused to provide gold in exchange for currency) it is identical to U.S. official price of gold. See Gold Price.

Population
Generally means resident population. Although it is sometimes restricted to meaning civilian population and sometimes extended to include armed forces overseas. Expressed in number (usually thousands or millions) of persons.

Project
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.

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 computation, whereas a complete purchasing power calculator, such as found on this website, uses various prices, wages, output, etc., depending on the context.

Real GDP
The output of the current GDP valued in the prices of a base year, sometimes referred to as "GDP corrected for inflation". It may also be called "deflated GDP", "constant-price GDP" or "GDP at constant prices". The base year changes from time to time.

Real GDP per capita
Real GDP divided by Population. This is the "average" output of the economy per person measured in a base year prices. This ratio is often used as a measure of standard of living in comparisons over time of one country, or between different countries when measured in the same currency. The measure is expressed in currency units per person (for example, U.S. dollars per person, or British pounds per person). See GDP per capita.

Real Price
Real Price measures a subject (a commodity) against the cost of a bundle of goods and services that in principle is fixed though in practice varies over time.

Real Value
Real Value measures a subject (a commodity) relative to the "value of the consumer bundle" (VCB).

Retail Price Index
This is an index used in the United Kingdom that measures the cost in a given period of the goods and services purchased by a typical consumer in a base period. The Retail Price Index provides a narrow measure of inflation, because it is confined to consumer goods and services. The series used in MeasuringWorth incorporates the official retail-price-index series only from 1948 onward. For earlier years- from 1947 all the way back to 1264- we utilize the series of various economic historians. The component series are linked so that a consistent retail-price-index series is obtained continuously from 1264 to the present.

Share of GDP
Share of GDP measures the consumption or production of a subject (commodity or project) against the output of the economy, that is, the given monetary amount is computed as a percent of GDP. This measure indicates opportunity cost in terms of the total output of the economy. The viewpoint is the importance of the item to society as a whole, and thismeasure is the most aggregate of all the measures.

One would rarely use this measure for a commodity. The exception would be if the amount (of the commodity) was a significant share of GDP, such as potatoes in Ireland in the mid-19th century.

Unskilled Wage
Payment (wage rate) per time period for unskilled labor, expressed either in number of currency units per time period (for example, U.S. dollars per hour), or as index number.

U.S. Official Price of Gold
Expressed as number of U.S. dollars per fine (pure) ounce. See Gold Price.

Some of your series go back to 1774, but wasn't the the British pound the currency of that time?
The American dollar evolved from the Spanish dollar, which, with its fractional parts, was the principal circulating coin of the American colonies and then the American states. The original U.S. dollar, established in 1792, contained the same amount of pure silver as the average weight of the Spanish dollars then in circulation in the United States. So when one considers dollar amounts in the 1774-1792 period, while, strictly speaking, the reference is to the Spanish dollar, one can treat the Spanish dollar as equal in value to the future American dollar.

The British pound was not the circulating currency of the colonies and states. Rather, each colony had its own pound (and shilling and pence), which had a value less than British pound. For example, a British shilling was equal to one shilling and six pence in Massachusetts but two shillings in New York. This British-type monetary system was a unit of account rather than a circulating coin.

Why not present a "weighted" average of the results?
A user has suggested that the calculators also present a "weighted" average combining the different conversion techniques. Our reply is that this would destroy the main value of the calculators that show there is no one answer to the question of what was something worth in the past.

As we explain in the essay "Measures of Worth" and our examples, measuring relative worth must have a context to measure against. In one case it may be the cost relative to a bundle of consumer goods. The next, it may be the average income of the country. This is why we give many choices.

How can the answers be so precise?
They cannot. The calculators report answers to the last cent or pence, but in truth, it would make more sense if we reported that results with only two-digit accuracy. So if the answer is \$427.32, it would be better to say \$430.

Most historical data must be measured by making certain assumptions about the relationship between the variable that is being reported and an observation that is available. For example, a price index is based on representative items. The price of potatoes might be assumed to be 3% of the cost of food and yet it could be 2.6 or 3.4% instead. So when the price of potatoes goes up, the true cost of the increase in food may be under or over estimated.

So why do we report the results the way we do? Partly it is easier and partly it is because we think (you) the users prefer it this way.

What is the convention for reporting pounds per dollar?
Comment: In the Dollar-Pound Exchange Rate data set, the exchange rate is expressed in the opposite way, that is, the price of the British pound in U.S. dollars. But this reverses standard quotation conventions.

Answer: You can find the exchange rate between the pound and the dollar both ways. The dollar-pound exchange rate series expresses it in the historical and conventional way of number of dollars per pound. The multiple-country data set expresses the exchange rate as number of pounds per dollar, for consistency with the other series.

What are my old dollars worth?
Question: I have these old dollars and I'm trying to see how much they are worth. I have some from 1928 and others are from 1934.

Answer: Your old dollar is only 'worth' a dollar today if you spend it, but you might be able to sell it as a collector's item to a currency site for more. You might google "selling old currency" to find a dealer.

How do I cite your site?
Question: I am listing your calculator in a bibliography, and I cannot find on your URL a citation for your publisher. May I have the city of your publisher and your publisher's business name?

Answer: We are a WWW site. We do not have a city of a publisher or a publisher's business address. At the bottom of all the calculators and data sets there is a citation listed. There are many different ways to cite a WWW site. This website gives many examples.

Why does the price of gold differ so much over time compared to the dollar?
Question: According to your website \$1 in 1960 has a relative worth from \$7.60 using the CPI to \$16.20 using the nominal GDP per capita in 2010. But between the same years the price of gold has increased from \$35 an once to \$1,224 an once, or by a factor of 35 to 1. Are your calculations wrong?

Answer:Gold is not money, but a commodity the same as oil or corn. Sometimes it increases faster than the average of all prices or incomes, sometimes not. A different set of years gives a very different result. A \$1 in 1980 has a relative worth from \$1.86 using the GDP deflator to \$2.88 using the nominal GDP per capita in 2000. During that period, the price of gold decreased from \$613 an once to \$280 an once, a drop of almost 65%.

Can you really compare relative value over time?
Question: When I was thirty, in 1971, a house cost about five times my income (5 x \$5000); today it's the same (5 x \$40,000 for a thirty-something). But in 1971 there were no home computers or internet, no cell phones, no cars that could get 50mpg and run for 200,000 miles with minimal care. The wealth of a thirty year old today seems vastly greater, and yet everyone is saying that young people today are behind the eight ball. How is that kind of relative value to be calculated?

Answer:The sophisticated answer is that economists have fancy formulas that compute the value of a new good relative existing ones. They are used in the construction of indexes such as the CPI. So the "value" or price of a cell phone is (somewhat) comparable to a wired phone, which was comparable to the telegraph. The technique uses the concept of "hedonic" prices, income substitution, and other manipulations. The straight answer is you can't. This is a very subjective question and in my view, your opinion is correct and we greatly understate how much better off we are today than in the past.

Please let us know if and how this discussion has assisted you in using our calculators.