Inflation Calculator

Purchasing power factor = 1 ÷ (1 + rate)^years; what the money will buy = amount × factor; what the same goods will cost = amount ÷ factor; cumulative inflation = (amount ÷ factor ÷ amount − 1) × 100

Amount

The sum you are following, in today's money. It can be a cash balance, a pension, a salary, or the price of one specific thing — the arithmetic does not care which, because everything is measured in the same currency at the same starting moment.

Inflation rate

The annual rate you assume, held constant for the whole period. This is the page's one real assumption: a published index gives you last year's rate, not next year's, and a single number for twenty years is a simplification the calculator cannot check for you.

Years

How long the money sits there, in whole years. The rate is applied once per year and compounded, so the effect is not linear — doubling the years slightly more than doubles the loss, which is the reason a 30-year span looks so much worse than a 10-year one.

Purchasing power factor

The single number both answers come from. It is below 1 whenever the rate is positive, and multiplying by it moves you from today's money to tomorrow's; dividing by it moves you the other way, from tomorrow's price back to today's.

Use it when you want to know what a fixed sum becomes, not what it earns. That distinction is where this page is most often reached for the wrong job: a savings account, a bond or a pension pays you interest, and the question of whether you are ahead is the difference between the interest you earn and the inflation you suffer, which is a real return and a different calculation. What this page answers is narrower and still useful — what the cost of living does to money that is not invested at all: cash under a mattress, a fixed pension, a deposit earmarked for a house, a budget set years ago and never revisited. Two things to hold on to when reading the result. The rate is the whole answer, so a run at two percent and a run at five percent are not two versions of one fact but two different futures. And the two money figures are the same factor used in opposite directions, so they always move against each other: when the purchasing power figure falls, the future cost figure rises by the same proportion, and the third figure is just that movement expressed as a percentage.

1. 1,000 left alone for ten years at 3 percent

   1. Purchasing power factor: 1 ÷ 1.03^10 = 0.744094
   2. What the money will buy: 1,000 × 0.744094 = 744.09
   3. What the same goods will cost: 1,000 ÷ 0.744094 = 1,343.92
   4. Cumulative inflation: 1,343.92 ÷ 1,000 − 1 = 34.39 percent

   The two money figures are the same fact told twice: spending 1,343.92 in ten years' time feels like spending 1,000 today, which is the same statement as saying today's 1,000 will feel like 744.09. Multiply them and you get a million — 1,343.92 × 744.09 ≈ 1,000,000 — because each is the other's reciprocal once the original 1,000 is accounted for. If that relationship ever fails to hold on screen, one of the two has been computed from the wrong number.

2. The same 1,000 over thirty years

   1. Purchasing power factor: 1 ÷ 1.03^30 = 0.411987
   2. What the money will buy: 1,000 × 0.411987 = 411.99
   3. What the same goods will cost: 1,000 ÷ 0.411987 = 2,427.26
   4. Cumulative inflation: 2,427.26 ÷ 1,000 − 1 = 142.73 percent

   Tripling the years nearly doubles the loss again: ten years costs 25.6 percent of the money's value, thirty years costs 58.8 percent. That is compounding working against you rather than for you, and it is why a retirement horizon and a five-year horizon cannot be reasoned about with the same intuition. The 3 percent here is the same 3 percent as in the previous example; only the exponent changed.

3. A house deposit of 100,000 over twenty years at 2.5 percent

   1. Purchasing power factor: 1 ÷ 1.025^20 = 0.610271
   2. What the money will buy: 100,000 × 0.610271 = 61,027.09
   3. What the same goods will cost: 100,000 ÷ 0.610271 = 163,861.64
   4. Cumulative inflation: 163,861.64 ÷ 100,000 − 1 = 63.86 percent

   A lower rate over a longer period can do more damage than a higher rate over a shorter one, which is the kind of comparison this page exists to make: 2.5 percent for twenty years removes 39 percent of the deposit's value, while 5 percent for ten years removes 39 percent as well. Only running both makes that visible, and the reason they land in the same place is that what matters is the total exponent, not either factor on its own.

4. Prices falling — 2 percent a year for ten years

   1. Purchasing power factor: 1 ÷ 0.98^10 = 1.223876
   2. What the money will buy: 1,000 × 1.223876 = 1,223.88
   3. What the same goods will cost: 1,000 ÷ 1.223876 = 817.07
   4. Cumulative inflation: 817.07 ÷ 1,000 − 1 = −18.29 percent

   A negative rate is sustained deflation, and the page handles it the same way as any other input rather than refusing it: the factor rises above 1, the money buys more, and the cumulative figure comes back negative. This is not a curiosity. Japan has spent long stretches with prices broadly flat or falling, and a page that silently rejected a minus sign would tell you nothing about those years. The one input that is refused is −100 percent or below, because the factor would divide by zero or invert the sign of everything downstream.

5. One cent, ten years, 3 percent — where rounding takes over

   1. Purchasing power factor: 1 ÷ 1.03^10 = 0.744094
   2. What the money will buy: 0.01 × 0.744094 = 0.0074, which displays as 0.01 at two decimal places
   3. What the same goods will cost: 0.01 ÷ 0.744094 = 0.0134, which also displays as 0.01
   4. Cumulative inflation: 0.01 ÷ 0.01 − 1 = 0

   The third figure is computed from the two displayed above it, not from the unrounded numbers behind them, and on an amount this small that makes it zero. It looks wrong and it is deliberate: recomputing from the rounded pair is what keeps the three figures on the panel agreeing with each other. Every derived figure on this page is built that way, so the percentage always equals the relationship between the two money amounts you can actually see.

The rate is constant, and real inflation is not. A single figure applied for thirty years cannot show a spike, a decade of near-zero prices, or the way the things you personally buy move differently from the things in the index. It is also the same rate for every kind of spending: food, rent and electronics do not inflate together, so a household that spends more of its income on housing than the average basket does will feel a rate this page cannot represent. This is a projection, not a forecast — it shows what follows from the rate you chose, not what will happen. And nothing here accounts for interest, so it says nothing about whether money in an account is keeping up; that comparison needs a real return.

What is the difference between purchasing power and the cost of living?

They are the same movement measured from opposite ends. Purchasing power is what your money can buy, so it falls; the cost of living is what the things you buy cost, so it rises. At 3 percent for ten years a thousand becomes 744.09 of purchasing power and the same goods become 1,343.92, and those two numbers are reciprocals of each other rather than independent results. This page shows both because people arrive with either question in mind, but there is only one calculation underneath.

What inflation rate should I use?

There is no correct answer, and the page will not pretend there is. A published index measures the change in the price level of an average basket over a period that has already ended; what you need is a rate for a period that has not started. Many central banks target 2 percent over the longer run, which is a policy aim rather than a forecast, and long-run averages of the index are a common stand-in. One thing worth knowing before you pick: a statistical office will tell you plainly that a consumer price index is not the same thing as an inflation rate. It is a measure used as one. Run the calculator at two rates and look at the spread rather than trusting either.

Does this include the interest my money earns?

No, and that omission is the single most common way this page is misread. A balance in an account earning 4 percent while prices rise 3 percent has gained purchasing power, and nothing on this page will show it, because no interest is entered or applied. The figure this page gives is what happens to money that sits still. If you want the net effect, the quantity you need is the real return — the interest rate adjusted for inflation — and that is a different calculation on a different page.

Is this the same as asking whether my pay is keeping up?

No. This page follows the price side only, so it can tell you what a sum of money loses, but it has nothing to say about what you earn. A salary that rises faster than prices leaves you ahead even though the purchasing power of any fixed sum has fallen — those two statements are not in conflict, because one is about a stock of money and the other about a flow of income. Questions about whether a raise beats inflation, and what a pay rise is worth after it, belong on the salary page.

Can the inflation rate be negative?

Yes, and the page accepts rates down to just above minus 100 percent. A negative rate is deflation: prices fall, the purchasing power factor rises above 1, and the money buys more at the end than at the start. The cumulative figure comes back negative, which is the correct sign rather than a bug. Rates at or below minus 100 percent are refused, because the factor would divide by zero or turn negative and every figure downstream would lose its meaning.

Why do the two money figures multiply to about a million on a thousand?

Because they are the same factor in both directions. If the factor is 0.744094, one figure is 1,000 times it and the other is 1,000 divided by it, so their product is 1,000 squared. This is a useful check when you are reading the panel: 1,343.92 and 744.09 are not two measurements that happen to agree, they are one measurement written twice, and a change in the rate moves them in opposite directions by construction.

Why does a very small amount show zero inflation?

Rounding, and it is intentional. The cumulative figure is worked out from the two money amounts as they are displayed, not from the unrounded values behind them, so on an amount where both round to the same cent the difference is zero. The alternative — computing the percentage from full-precision numbers — would give a non-zero figure that disagrees with the two amounts printed next to it. Every derived result on this page is built from the displayed figures so that the panel is internally consistent, and this is the case where that choice becomes visible.

• Why does the Federal Reserve aim for inflation of 2 percent over the longer run? — the central bank's own statement of its target and the reasoning behind it, which is the origin of the figure most people put in the rate field — Board of Governors of the Federal Reserve System (United States)
• Harmonised Index of Consumer Prices (HICP) — the euro area's measure of the change in the price level, with the current rate and the method behind it — European Central Bank
• Real Return — the glossary definition of a return adjusted for inflation, which is the calculation this page deliberately does not do — Investor.gov, U.S. Securities and Exchange Commission (United States)