Your salary goes up 5%. Prices, according to the inflation figure in the news that month, went up 3%. It is tempting to subtract and call it a 2% real raise. That subtraction is close enough to be useful as a rough gut check, but it is not actually correct — and the size of the error grows with the numbers involved.
What inflation actually does to money
The inflation calculator makes the asymmetry concrete: at 100% inflation, prices double — but your money’s buying power does not fall 100%, it falls 50%. The same $100 that bought one unit of something now buys half a unit, because the price doubled, not because the money vanished. Buying power and prices move on different bases: prices are measured against where they started, buying power is measured against what the new prices can still purchase. At the modest, ordinary end of the range — 3% inflation over ten years — prices rise about 34% while buying power falls about 26%. Those two numbers describe the same underlying change and are not equal, and they diverge further as either the rate or the time horizon grows.
Applying that to a raise
The subtraction trick — 5% raise minus 3% inflation equals a “2% real raise” — is a linear approximation of a relationship that is not actually linear. The more precise version divides rather than subtracts: your new purchasing power relative to your old purchasing power is (1 + raise) / (1 + inflation), minus one. At 5% and 3% that is 1.05 / 1.03 − 1 ≈ 1.94%, close enough to the subtraction’s 2% that it barely matters at these small numbers. But the two methods pull apart fast once either number grows — at a 20% raise against 15% inflation, subtraction says 5%; division says 1.05/1.15 − 1 ≈ −0.09 loss, a member of the wrong sign for the same raise.
Where this actually bites
Multi-year comparisons are where the subtraction habit does the most damage, because errors that are small in any single year compound the same way compound interest does. A string of raises that each barely account for inflation are not “roughly keeping pace” over five years — the small annual shortfalls compound into a real, and often surprising, loss of purchasing power, even while every individual year’s raise number looked positive on the payslip.
The same ratio question shows up in investment returns
This is not only a payslip issue. Any nominal percentage — a savings account’s advertised rate, an investment’s reported annual return — is subject to the identical correction before it tells you anything about real purchasing power. A savings account paying 4% during a year of 3% inflation is not “up 4%” in any sense that matters for what that money can buy; by the same ratio logic used above, it is barely ahead in real terms, and during periods where inflation exceeds the nominal rate entirely, a balance can grow in dollar terms while still losing purchasing power in real terms — a genuinely counterintuitive outcome that only becomes visible once nominal and real figures are separated rather than conflated.
The practical habit this suggests: whenever you see a percentage attached to money — a raise, a return, an interest rate — ask what it is being compared against before deciding whether it represents real progress. A number with no stated comparison point is not yet telling you anything about whether you are actually ahead.
Why the inflation figure in the news is an average, not your inflation
The headline inflation rate is a weighted average across a broad basket of goods and services that the average household buys — it is not a personal figure. If your own spending skews toward categories rising faster than that average (housing in a tight local market, say) or slower (categories where prices have been flat or falling), your personal experience of “how much further my money goes” can differ meaningfully from the published national figure in either direction. This is one reason two people can look at the same published inflation number and reasonably disagree about whether it “feels right” — they are both correct about their own experience, and both describing something genuinely different from the national average.
None of this means a raise below the inflation rate is worthless — it still slows the rate at which purchasing power erodes compared to no raise at all. The point is narrower: comparing the two numbers by simple subtraction, rather than by the ratio, systematically misstates how far ahead or behind a given raise actually leaves you, and the size of that misstatement grows with both numbers involved.
How to use this
- Do not compare a raise percentage to an inflation percentage by eye across several years — run the actual figures through the inflation calculator, since the gap between subtraction and the correct ratio widens with time and with size.
- A raise that exactly equals the published inflation rate keeps you flat, not ahead — the reference point for “getting ahead” is inflation, not zero.
- The same logic applies to investment returns discussed in the ROI calculator: a nominal return has to clear inflation before any of it counts as real growth in what that money can actually buy.
