How inflation compounds
Inflation is compound growth applied to prices. If prices rise at rate i each year, a basket that costs A today costs A x (1 + i)^n after n years. Running it backwards gives purchasing power: a fixed sum A received n years from now buys A / (1 + i)^n worth of today's goods. Those two formulas are the whole calculator, and the second one is the one people underestimate.
The rule of 70 is a useful shortcut: divide 70 by the inflation rate to get the years it takes for prices to double. At 3% that is about 23 years; at 7% it is ten. The exact figure is ln(2) / ln(1 + i), which at 3% is 23.4 years.
A worked example
Take $1,000 and 3% inflation over 25 years. The growth factor is 1.03^25 = 2.0938, so the basket that costs $1,000 today will cost $2,093.78 - you need $1,093.78 more just to stand still.
Now hold $1,000 in cash for those 25 years. It still says $1,000, but it buys $1,000 / 2.0938 = $477.61 of today's goods. You lost 52.2% of your purchasing power without a single dollar leaving the account. That is the argument for not parking long-term money in a checking account.
For a retirement-sized example, a $60,000 annual budget at 3% needs about $125,600 a year after 25 years. A pension or annuity with no cost-of-living adjustment loses more than half its real value over a typical retirement.
What inflation has actually done
The Bureau of Labor Statistics publishes the Consumer Price Index each month. US CPI inflation has averaged roughly 2.5% to 3% a year over the past several decades, with a long calm stretch from the mid-1990s to 2020 when it mostly sat between 1% and 3%. Then it jumped: about 4.7% in 2021, 8.0% in 2022 - the highest annual figure since 1981, peaking at 9.1% year-over-year in June 2022 - and 4.1% in 2023 before easing back toward 3%. The Federal Reserve targets 2% on a different measure, the PCE price index, which typically runs a few tenths below CPI.
Your personal inflation rate is not the headline number. CPI weights a basket for the average urban consumer; if you rent in a hot market, pay for childcare or buy health insurance on your own, you have probably experienced more. College tuition and medical care have outpaced the index for decades, while electronics and clothing have gotten cheaper.
Two protections are worth knowing about. Social Security benefits get an annual cost-of-living adjustment tied to CPI-W. And Treasury Inflation-Protected Securities and Series I savings bonds adjust their principal or rate with CPI, so they preserve purchasing power rather than a dollar amount - useful for money that must hold real value over decades.