Real Value from a Nominal Value (Deflating by an Index)

Comparing amounts of money across years without adjusting for prices is comparing two different units and calling them the same. This page does the adjustment: multiply by the ratio of the two index values, and you have restated the amount in the prices of whichever year you chose as the base.

The direction is where people go wrong. To bring an OLD amount into TODAY'S prices, multiply by today's index over the old one — a number bigger than one, so the amount gets bigger. To bring a modern amount back into an old year's prices, the ratio inverts and the amount shrinks. It helps to say out loud which year the answer is in: "$50 in 1975 is $291 in 2024 prices" and "$291 in 2024 is $50 in 1975 prices" are the same sentence, and both name their year.

The honest warning on this page is that the question has several defensible answers and no single right one. "What is $50 in 1975 worth today" sounds like a question with a fact for an answer. It is not. It depends entirely on which index you deflate by, and the reputable choices disagree substantially:

A consumer price index answers "what would it cost to buy the 1975 basket today", and is the usual default. A chained index answers the same question while letting the basket shift as people substitute, and gives a systematically lower inflation figure over long spans — over fifty years the two diverge by a great deal. A GDP deflator covers everything produced rather than what households buy, and is the right choice for comparing outputs rather than living costs. An index of average earnings answers a completely different and often more relevant question — what share of a typical income the amount represented — and over long periods gives much larger numbers than any price index, because real wages grew. Comparing the cost of a public work in 1900 to today by prices and by wages can differ by a factor of several.

Over a few years these choices barely matter. Over fifty they are the dominant term in the answer, larger than any reasonable disagreement about the arithmetic. So state which index you used, and treat a single headline figure that does not name its index as unfinished work rather than as wrong.

Two further limits. Long index chains accumulate every measurement problem of each link — the substitution, quality and new-goods issues of the inflation page compound across a century. And the further back you go, the less the basket resembles anything a modern household buys: a basket dominated by food, coal and cloth is not comparable to one dominated by housing, health care and services, and no ratio of index numbers repairs that. The comparison stops being a measurement and becomes an illustration, which is fine as long as it is offered as one.