Inflation Calculator: Method

Inflation Calculator: How It Works

What it does

The page answers one question: what is an amount of U.S. dollars from one year worth in the dollars of another year? It looks up a price index for both years, takes the ratio and reports the equivalent amount, the total inflation between the two dates, the average yearly rate and what the original amount still buys. Every step is printed as formula, numbers put in, answer.

The method

The index. A price index is the cost of a fixed basket of goods and services, scaled so that a base period equals 100. The page uses the Consumer Price Index for All Urban Consumers (CPI-U) of the U.S. Bureau of Labor Statistics: all items, U.S. city average, not seasonally adjusted, with the average of 1982–84 equal to 100. It is published every month from January 1913, and for every finished year as an annual average of the twelve months.

Symbols. A₁ is the amount entered, in dollars of the From date; I₁ and I₂ are the index values at the From and To dates; N is the number of years from the first date to the second.

Equivalent amount. An amount keeps its buying power when it changes in the same proportion as prices:

A₂ = A₁ I₂ / I₁

The ratio k_p = I₂ / I₁ is how many times the price level changed. The same formula works in both directions: with an earlier To date the ratio is below one and the amount shrinks.

Cumulative inflation. The total percent change of the price level: Cum = 100 (I₂ / I₁ − 1).

Average yearly rate. The one rate g_a that, compounded every year for N years, gives the same total change, (1 + g_a)^N = I₂ / I₁:

g_a = (I₂ / I₁)^{1 / N} − 1

It is smaller than the cumulative figure divided by the years, because each year's rise is applied to a price level that has already risen.

Buying power. PP = A₁ I₁ / I₂ is the amount A₁, counted in To-date dollars, restated in From-date dollars. For a later To date it is what cash kept the whole time still buys.

Annual averages and months. In Simple mode both dates are annual averages. In Advanced mode a month can be chosen for both dates; the years between are then counted in twelfths. A month is not compared with a whole year.

The unfinished year. The current year has no annual average until December is published. The page uses the average of the months published so far and labels it "so far".

Real return (Advanced). A nominal return r_n is the growth of an amount in dollars; the real return is the growth of its buying power. The Fisher relation links them through the inflation rate:

1 + r_real = (1 + r_n) / (1 + g_a)

The shortcut r_real ≈ r_n − g_a leaves out the small product of the two rates.

A date after the data (Advanced). For a date beyond the last published value the index is carried forward at the inflation rate h you enter: I = B (1 + h)^f, where B is the last published figure (the latest year for annual dates, the latest month for monthly dates) and f the years from it to the date.

What it assumes

That the CPI-U basket describes the prices that matter for the amount. That the dollars are U.S. dollars spent in the United States. For annual dates, that the amount was spread over the year; for a single purchase on a known date, a month is closer. For a future date, that inflation runs at the one rate you entered every year. The index values are those on file on the retrieval date shown in the results; the not-seasonally-adjusted CPI-U is rarely revised, but new months are added only when the file is refreshed.

When it misleads

Your basket is not the average basket. The CPI-U weighs housing, food, transport, medical care and everything else as the average urban household spends. Rent in one city, tuition, a new car or a computer can each move very differently, so the equivalent amount for one particular good may be far from the result.

Long spans compare different worlds. The basket of 1913 held no air travel or telephones worth the name, and many of today's goods did not exist. The index is chained across such changes with care, but over a century the comparison is a broad guide, not a precise measure.

The average rate hides the path. A 3 % average over forty years can contain years above 10 % and years of falling prices; the yearly chart shows them.

A projection is not a forecast. A future result depends entirely on the inflation rate typed in. Nobody knows that rate in advance.

Other indexes give other answers. Wages, house prices, asset prices and the indexes used for pensions or for the national accounts each follow their own path. This page reports the CPI-U only.

Early values are coarse. Index values before 2007 are published to one decimal. In 1913, when the index is near 10, that rounding alone is about half a percent.

Worked example

The default case: $100.00 from 2000 restated in 2025 dollars.

Index values (annual averages): I₁ = 172.2 for 2000 and I₂ = 321.943 for 2025.

Price ratio: k_p = 321.943 / 172.2 = 1.8696.

Equivalent amount: A₂ = 100 × 1.8696 = $186.96.

Cumulative inflation: 100 (1.8696 − 1) = 86.96 %.

Average yearly rate over N = 25 years: 1.8696^1/25 − 1 = 0.0253, or 2.53 % a year (86.96 / 25 = 3.48 % would overstate it).

Buying power: PP = 100 × 172.2 / 321.943 = $53.49. Cash of $100.00 kept from 2000 buys in 2025 what $53.49 bought in 2000.

In Advanced mode with a nominal return of 7 % a year: real return = 1.07 / 1.02534 − 1 = 4.36 % a year; $100.00 grows to $542.74 in 2025 dollars, which is $290.30 in 2000 dollars.

A calculator for education and analysis, not investment advice.