The whole calculation, and the hand check
An amount carried forward by n years at rate r is multiplied by (1 + r) to the power of n. One hundred dollars in 1990 taken to 2026 is 36 years at 2.5 percent: 1.025 to the 36th power is 2.4325, so the answer is $243.25. Going backwards is the same expression with a negative exponent, so $243.25 in 2026 is $100.00 in 1990 dollars. Nothing else is involved. The reason the result feels authoritative and is not is entirely in the choice of that single rate.
Chained multiplication is also why the intuition fails at long spans. Doubling takes about 28 years at 2.5 percent and about 14 at 5 percent, so a rate twice as large does not produce twice the effect over a lifetime, it produces the square of it. Over 50 years, 2 percent multiplies prices by 2.7 and 4 percent multiplies them by 7.1.
Why a single average rate is a simplification
Real inflation arrives unevenly. A decade with one severe year and nine quiet ones ends up at the same average as a decade of steady moderate increases, and the two feel nothing alike and produce different intermediate values, even though the endpoint matches. This page draws a smooth curve between the two years, and reality is a jagged line that happens to pass through both ends.
If the number matters, take the two years from an official consumer price index instead and divide one by the other, which is what a statistical agency's own inflation calculator does. That result differs from this one, sometimes by a lot over a long span, and it is the one to cite. Use this page when you want to see the shape of the effect, test how sensitive an answer is to the rate you assume, or project forward into years no index covers yet, which is the one case where an assumed rate is the only option available.
What an average rate is even less good for
| What you are converting | Does an average consumer rate fit |
|---|---|
| A general household budget or a typical purchase | Reasonably, that is what the average describes |
| A house price or a rent | No, housing has its own indices and its own regional behaviour |
| Tuition or medical costs | No, both have run well above the general average for decades |
| Consumer electronics | No, quality-adjusted prices have fallen while the average rose |
| A salary or a wage | Only as a floor, wages track productivity and labour markets, not prices |
The salary case is the one people most often want and this page answers least well. Converting an old salary at an inflation rate tells you what it would buy, which is a real and useful thing, but it does not tell you how well off that person was relative to everyone around them. For that you want the salary as a fraction of the median wage in its own year.
The reverse direction, which is the useful one for savings
Run the years backwards and the calculator answers a different question: what a future amount is worth in today's money. Money that will arrive in 30 years at 2.5 percent inflation buys about half of what the same nominal amount buys now. That is the arithmetic behind treating a retirement target as a moving figure rather than a fixed one, and behind the distinction between a nominal return and a real one. A savings account paying 2 percent while prices rise 3 percent is losing about a percent a year in purchasing power, and the balance going up every month is precisely what disguises it.
Questions people ask
What average rate should I use?
For a general-purpose conversion over recent decades, something in the low single digits is the usual assumption, and the honest approach is to run the calculation two or three times across a plausible range and see how much the answer moves. If the conclusion changes between 2 and 3 percent, the conclusion was never solid enough to rest on a single number. For a specific historical span, do not guess an average at all — take both years from a published price index and divide.
Why does this differ from an official inflation calculator?
Because an official calculator divides two published index values and this one raises a single assumed rate to a power. The published index encodes what actually happened each year, including the years that were nothing like the average. Over a few years the two answers are close. Over 40 or 50 years they can separate substantially, and the index is the one to trust. This page is for the cases where an index is not available or not applicable: projecting into the future, or asking what a different rate assumption would imply.
Can I put in a negative rate?
Yes. A negative average rate means prices fall over the span, so an amount carried forward becomes smaller in nominal terms and money held as cash gains purchasing power. Sustained deflation is historically rare across a whole economy and common within individual categories, which is why the negative case is more useful for a single product line than for a general conversion. The calculator refuses rates of negative 100 percent or lower, since those imply prices reaching or passing zero.
Does this account for taxes or investment returns?
No. It converts a price into another year and nothing else. If you want to know whether savings kept up, compare the rate here against the after-tax return on the account: a 4 percent return taxed at 22 percent leaves about 3.1 percent, which is a real gain of roughly 0.6 percent against 2.5 percent inflation, and that gap is the entire return in economic terms. The compound interest and savings pages on this site handle the growth side of that comparison.