Inflation is compound growth pointed at prices instead of balances. It uses the same arithmetic as compound interest, which is why the same small annual figures produce the same surprisingly large results over decades.
The difference is direction. Compounding on savings raises what you have. Compounding on prices lowers what it buys.
Two questions, one calculation
There are two ways to ask about inflation, and they are reciprocals of each other. What will something costing a fixed amount today cost in the future, and what will a fixed amount of money buy in the future.
Both come from the same growth factor: multiply for the future price, divide for the future purchasing power. The inflation calculator reports both, along with the number of years it takes prices to double at a given rate.
The real return is the one that matters
A savings account paying 3 per cent while prices rise 4 per cent leaves you with more money and less buying power. The balance is going up, the statement looks fine, and the position is worsening.
This is why the real return, the return after inflation, is the figure worth tracking. Nominal returns describe the number on the screen; real returns describe what the number can do.
Long horizons are where it bites
Over a year or two the effect is small enough to ignore for most purposes. Over the twenty or thirty years of a retirement or a mortgage, it dominates. A target set in today's money and left unadjusted quietly shrinks for the entire period.
Any long dated goal is best set in real terms first, then converted to a nominal target, rather than picking a round nominal number and hoping. As covered in the piece on savings goals, that adjustment often changes which lever needs to move.
Where a single rate stops describing your life
A published inflation rate is an average across a basket of goods, weighted for a typical household. Your own rate depends on what you actually buy: someone paying rent in a tight market and someone with a fixed mortgage face very different figures, whatever the headline says.
That is a good reason to treat the rate in any calculation as an assumption you choose rather than a fact you look up once. Running a projection at a couple of different rates shows how sensitive the answer is to a number nobody can know in advance, which is usually more informative than any single result.