Real Interest Rate Calculator

A subtraction that has a name

Your bank offers 9 percent. Prices are rising at 6 percent. So you are earning 3 percent, and everyone knows it without being told.

That instinct is correct, it is what this calculator does, and it has a distinguished name attached to it.

Real interest rate = Nominal interest rate - Expected inflation rate

Irving Fisher formalised the relationship between those three quantities in the early twentieth century, and it has been called the Fisher equation ever since. His point was that the rate quoted to you is doing two jobs at once. Part of it compensates the lender for inflation eating the money while they wait. What is left over is the genuine price of borrowing, and that leftover is what actually drives whether people save, borrow and invest.

Two boxes, one answer, and the arithmetic is a schoolchild's. Which raises a fair question about why this page continues.

Because Fisher's equation has two forms. This tool uses one of them, and the other is sitting on this same site giving slightly different answers.

What the subtraction quietly drops

Here is the exact version of the same relationship:

1 + nominal = (1 + real) × (1 + inflation)

Rearranged to give you the real rate:

real = [ (1 + nominal) / (1 + inflation) ] - 1

Multiply out the first version and you can see exactly where the two part company. Expanding (1 + real)(1 + inflation) gives you real, plus inflation, plus real multiplied by inflation.

That last term is the one subtraction throws away. It has a name too, the cross term, and it exists for a reason that is easy to state: inflation does not only erode your original money, it also erodes the interest you earned on it. Subtracting one rate from another never accounts for that second erosion.

So the approximation is always slightly generous. It tells you your real return is a little higher than it truly is, and the amount it flatters you by is precisely the cross term.

Worth checking that claim rather than accepting it. At 8 percent nominal and 5 percent inflation, subtraction gives 3.000 percent and the exact formula gives 2.857 percent. The gap is 0.1429. And the real rate multiplied by inflation is 2.857 percent of 5, which is 0.1429.

The same to four decimal places, and it holds at any pair of rates you like.

How wrong is it, in practice

The honest answer is: usually not at all, and occasionally very.

Below about 5 percent inflation the difference lives in the second decimal place and nobody sensible cares. Above 20 percent it exceeds a full percentage point. In the last row the approximation reports a real return half as large again as the truth.

Which gives a rule you can carry: subtract when rates are small, divide when they are not. Ordinary savings account against ordinary inflation, subtraction is fine and is what most textbooks teach. High inflation, an emerging market bond, a hyperinflationary episode, or anywhere the numbers are big, use the exact version.

Our real rate of return calculator runs the exact formula. Same two inputs, so you can put a pair of numbers through both and watch the gap appear. On a page about a difference between two methods it seems only fair that both are available.

Expected inflation, and why the label says expected

Look at the second field. It does not say inflation. It says expected inflation, and the distinction is the difference between two questions that feel identical and are not.

Before the fact. When a bank sets a rate and you accept it, both of you are guessing at future inflation. Whatever real return you think you are getting is a forecast. Economists call this the ex ante real rate, and it is the one that drives behaviour, because it is the only one available when the decision is being made.

After the fact. A year later, actual inflation is known. Now you can work out what you really earned. This is the ex post real rate, and it is the true one.

Those two are the same only if the guess was right, which it rarely is.

And the gap between them is not academic. It decides who won. If you lock in a fixed rate expecting 4 percent inflation and it arrives at 9, your real return collapses and your lender is receiving repayment in money worth much less than they planned. Inflation surprises transfer wealth from lenders to borrowers, and unexpected disinflation does the reverse.

So use the box deliberately. Enter your forecast if you are deciding whether to lend or deposit. Enter the actual figure if you are working out how a past year treated you. The arithmetic is identical and the meaning of the answer is not.

Where do you get a forecast? Central banks publish targets, statistical agencies publish recent actuals, and in markets with inflation indexed government bonds the gap between the ordinary and indexed yields is itself a market estimate of expected inflation, usually called the breakeven rate. That last one is the closest thing to an honest consensus number that exists.

When the answer comes out negative

Inflation above your nominal rate produces a negative real rate, and the first reaction is usually that something has gone wrong. Nothing has. It is a normal condition and it has been the condition in a great many countries for long stretches.

A negative real rate means your money is growing and your purchasing power is shrinking. Both at once, which is why it slips past people. The balance on the statement goes up every month and the trolley of groceries it buys goes down.

Two things follow, and they point in opposite directions.

For a saver it is a slow loss that never appears on any statement. Nothing is deducted, no fee is charged, and yet each year the deposit commands less. Which is why real return, rather than the advertised rate, is the number worth watching on any long term savings product.

For a borrower it is a gift. Repaying a fixed rate loan while inflation runs above that rate means handing back money worth less than the money you were given. This is exactly why fixed rate debt behaves so differently in high inflation than in low, and why our payment calculator figures should be read alongside the inflation rate rather than alone.

One practical note on this tool. Both fields require a value of zero or above, so a period of falling prices cannot be entered as a negative inflation figure. Deflation makes the real rate higher than the nominal one, which is one of the more uncomfortable features of a deflationary economy: the real cost of debt rises even when the central bank cannot cut rates any further.

The same number read from the other side

Nothing in this calculation says whether you are the one lending or the one borrowing, and the answer means something different depending on which chair you are in.

Which is why a high headline rate does not automatically mean expensive credit, and a low one does not mean cheap. A 14 percent loan in a 12 percent inflation environment is cheaper in real terms than a 5 percent loan when prices are flat, and almost nobody thinks about it that way when signing.

Two things this figure deliberately leaves out, both of which sit between it and your actual position.

Tax. Interest is generally taxed on the nominal amount, not the real one, which means you can be taxed on a gain you did not make in purchasing power terms. Our real rate of return calculator works through the order those two adjustments have to be applied in, and the order matters more than people expect.

Whose inflation. Published inflation is an average across a basket that may look nothing like your spending. If most of your money goes on rent, school fees and fuel and those are rising faster than the index, your personal real rate is worse than this calculator says.

Hope that makes the number on your deposit slip a little less comforting, or a little more, depending. If any of this does not square with what your bank is telling you, do let us know, because we would rather find out we are wrong than have you working off a bad figure.

Questions people ask

Why does this give a different answer from your other calculator?

Because there are two forms of the Fisher equation. This one subtracts, which is the standard textbook approximation. The real rate of return calculator divides, which is exact. The gap is the cross term, real multiplied by inflation, and it is small at low rates and large at high ones.

Which one should I use?

Subtraction when inflation is under about 5 percent, where the difference sits in the second decimal place. Division when inflation is high, or when the number is going into anything that matters.

What should I put for expected inflation?

Your forecast, if you are deciding whether to lend or deposit. The actual figure, if you are assessing a period that has already happened. Central bank targets and recent published rates are the usual starting points.

Can the real interest rate be negative?

Yes, whenever inflation exceeds the nominal rate, and it is common. It means the balance grows while the purchasing power falls.

What about deflation?

Falling prices make the real rate higher than the nominal rate. This calculator requires inflation of zero or above, so a deflationary period cannot be entered directly.

What is the difference between ex ante and ex post?

Ex ante uses expected inflation and is what people act on. Ex post uses realised inflation and is what actually happened. They differ whenever the forecast was wrong, which is most of the time.

Does this account for tax?

No. Interest is generally taxed on the nominal amount, so your after tax real return is lower again. The order in which tax and inflation are applied changes the answer, and our real rate of return page works through it.

References

A note on the sources. The relationship on this page is Irving Fisher's, and the distinction between its exact and approximate forms, along with the size of the error the approximation introduces, is standard across monetary economics teaching rather than anyone's house view. The Federal Reserve Bank of St. Louis publishes both the underlying data series and accessible explanations of why real rather than nominal rates drive economic decisions, and its FRED database is where the published real rate series and inflation expectation measures referred to above can be found.

1. Federal Reserve Bank of St. Louis, FRED Economic Data, real interest rate and inflation expectation series, including breakeven inflation rates derived from the spread between nominal Treasury yields and inflation indexed yields. https://fred.stlouisfed.org/
2. Federal Reserve Bank of St. Louis, Page One Economics, economic education series on how price changes affect the value of money and household decisions. https://www.stlouisfed.org/education/page-one-economics-classroom-edition
3. U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Compound Interest, Investor.gov glossary, on interest computed on principal and on accumulated interest, which is the mechanism the cross term describes. https://www.investor.gov/introduction-investing/investing-basics/glossary/compound-interest
4. Fisher, I., The Theory of Interest, Macmillan, 1930, the original statement of the relationship between nominal rates, real rates and expected changes in the price level.