Inflation calculator

Inflation is a rise in the general price level. The same money gradually buys less, not because euros disappear from the account but because each euro buys fewer goods than before. That loss is what is meant by a fall in purchasing power.

The loss of purchasing power is the heart of the matter. Not one euro leaves your account; what shrinks is what those euros get you. If a basket costs €100 today and €103 in a year, your hundred buys less in a year than it does now, even though it is still a hundred. Inflation does not shrink money, it shrinks what money can buy.

That is where the difference between nominal and real value comes from. The nominal value is the count of euros, what you see on the statement. The real value is that same amount expressed in today's prices, what it will actually buy. At zero inflation the two are identical; the moment prices rise, the nominal value stays put and the real one falls.

Prices do not rise in a straight line; they compound exactly as compound interest does. At 3% inflation, goods costing €100 cost €103 after a year, and after two years not €106 but €106.09, because the second rise starts from the higher level. Over n years prices are multiplied by a factor of (1 + i)^n. The same factor works the other way too: dividing today's amount by it gives its real value.

So why will €100 today not be worth the same in twenty years? Because the rise in prices compounds. At 3% a year, prices over twenty years do not rise by 60% but by 81%, since each year the price level climbs from an already higher base. That same €100 then carries the purchasing power of roughly €55. Not because the money disappeared, but because everything around it grew dearer.

The whole calculation rests on a single number: the cumulative factor (1 + i)^n, which says how many times over the price level is multiplied across n years. Whether you multiply by it or divide by it decides which of two questions you are answering.

Multiplying answers the question of how many euros you will have to hold in n years to buy exactly what the amount P buys today. This number is always above today's amount, and it is the one planning needs: a target for retirement or for a reserve only means something when it is stated in future prices.

Dividing answers the opposite question: if you leave today's amount sitting, what purchasing power will it carry in n years. This number is always lower, and it is precisely what idle money gives up. Both figures come out of the same factor, so they are two views of one phenomenon rather than two separate ones.

It is worth noticing that the fall in purchasing power does not mirror the rise in prices. If prices go up by 50%, purchasing power does not fall by 50% but by 33%: the same money buys two thirds of what it did. The difference arises because the rise is measured against the old price while the fall is measured against the new one.

The units matter. The most common mistake is confusing a percentage with a decimal; the second most common is multiplying the rate by the number of years instead of raising it to a power.

The terms used in this calculation are explained in more depth in the encyclopedia.