The real rate from a nominal rate that is your real rate plus each inflation rate, exactly and by the shortcut. The gap grows with inflation.
Inflation
Nominal rate (shortcut)
Exact real rate
Shortcut says
Overstated by
2%
5.88%
3.807%
3.883%
7.6 bp
5%
8.88%
3.699%
3.883%
18.5 bp
10%
13.88%
3.530%
3.883%
35.3 bp
20%
23.88%
3.236%
3.883%
64.7 bp
50%
53.88%
2.589%
3.883%
129.4 bp
100%
103.88%
1.942%
3.883%
194.2 bp
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What it calculates: Exact answer, Approximation, Exact minus approximate, Cross term r × π.
Updated 22 September 2026 · Transparent assumptions
7% nominal with 3% inflation is a real rate of 3.883%, not the 4% the shortcut gives
Irving Fisher’s equation links three rates. Money lent at a nominal rate i grows by (1 + i); the goods it can buy grow by (1 + r), the real rate, while prices rise by (1 + π). So (1 + i) = (1 + r)(1 + π). Solving for the real rate: r = 1.07 ÷ 1.03 − 1 = 3.883%.
(1 + i) = (1 + r)(1 + π)
The familiar shortcut r ≈ i − π gives 4%. The difference — 11.7 basis points here — is small at low rates, which is why the shortcut is taught, but it is always there and it is always in the same direction: the shortcut overstates the real rate when inflation is positive.
Worked example
i = 7%, π = 3%
r = 1.07 ÷ 1.03 − 1
r = 3.883%
(shortcut: 7 − 3 = 4%)
A 4% real rate with 3% inflation needs a nominal rate of 7.12%: the extra 0.12 is r × π
Multiply out the exact equation and it becomes i = r + π + r × π. The last term is the real return earned on the inflation compensation itself. With r = 4% and π = 3%, the nominal rate that delivers the real return is 0.04 + 0.03 + 0.0012 = 7.12%, not 7%.
i = r + π + rπ
Lenders who set rates by adding inflation to a target real return leave that cross term on the table; at 3% inflation it is negligible, at 30% it is not.
Solving for i
r = 4%, π = 3%
i = 0.04 + 0.03 + 0.04 × 0.03
i = 7.12%
With 50% inflation, a 60% nominal rate is a real return of 6.7%, not 10%
The shortcut breaks down exactly where it is most needed. At 50% inflation, a 60% nominal rate gives a real return of 1.60 ÷ 1.50 − 1 = 6.67% — the subtraction says 10%, overstating the return by a third. At 100% inflation, a 110% nominal rate is 5% real, not 10%.
In economies with high inflation, such as Argentina and Turkey in recent years, the exact form is the only honest one. The table on this page runs the comparison at several inflation rates for your inputs.
High inflation
i = 60%, π = 50%
r = 1.60 ÷ 1.50 − 1
r = 6.67%
(shortcut: 60 − 50 = 10%)
In the long run nominal rates rise about one-for-one with expected inflation
The Fisher effect is the hypothesis that, with the real rate set by saving and investment, a rise in expected inflation raises nominal interest rates by the same amount. It fits the long sweep of data well — nominal rates rose through the inflation of the 1970s and fell with it after the 1980s.
In the short run the link is loose. Frederic Mishkin found in 1992 that US data support a long-run Fisher effect but not a short-run one: nominal rates and inflation share a common trend without moving together month to month, because central banks, risk and expectations intervene.
On 17 September 2026, 4.94% nominal and 2.61% real ten-year yields implied 2.33% inflation
US Treasury Inflation-Protected Securities pay a real yield, so comparing them with ordinary Treasuries of the same maturity gives the inflation the market is pricing in. On 17 September 2026 the ten-year Treasury yielded 4.94% and the ten-year TIPS 2.61%; the published breakeven inflation rate is the simple difference, 2.33%.
The exact Fisher inversion gives a little less: 1.0494 ÷ 1.0261 − 1 = 2.27%. Breakevens also carry liquidity and inflation-risk premiums, so they are an estimate of expected inflation, not a reading of it.
Breakeven inflation
i = 4.94%, r = 2.61%
π = 1.0494 ÷ 1.0261 − 1
π = 2.27%
(published difference: 2.33%)
Taxed at 30%, a 7% nominal return with 3% inflation leaves a real return of 1.84%
Taxes are charged on nominal interest, including the part that only compensates for inflation. At a 30% tax rate a 7% nominal return is 4.9% after tax, and in real terms (1.049 ÷ 1.03) − 1 = 1.84% — less than half the pre-tax real return. Set the tax rate on this page to see it for your figures.
r_after-tax = (1 + i(1 − τ)) ÷ (1 + π) − 1
To keep the same after-tax real return when inflation rises, nominal rates must rise by more than inflation: by Δπ ÷ (1 − τ). Michael Darby described this adjustment in 1975, and it is why moderate inflation weighs heavily on savers in taxable accounts.
Frequently Asked Questions
What is the Fisher equation?
It links nominal and real interest rates: (1 + i) = (1 + r)(1 + π), where i is the nominal rate, r the real rate and π inflation. The approximation is i ≈ r + π.
When is the approximation i ≈ r + π good enough?
When inflation and interest rates are low, the dropped term r × π is tiny. At high inflation it becomes large, and the exact form should be used.
What is the Fisher effect?
The idea that nominal interest rates move one-for-one with expected inflation, leaving real rates unchanged. Evidence supports it over the long run more than month to month.
How do you find expected inflation from interest rates?
Rearrange the equation: π = (1 + i) ÷ (1 + r) − 1. Using a nominal Treasury yield and a TIPS yield of the same maturity gives market-implied (breakeven) inflation.
Sources & References
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Results are estimates for planning and analysis based on the figures you enter. They are not accounting, tax, or financial advice — verify with your own records and a qualified professional before making decisions.
The Fisher Equation: Nominal Rates, Real Returns and Expected Inflation
The exact Fisher equation, (1 + i) = (1 + r)(1 + π), and when the shortcut i ≈ r + π fails — with market breakeven inflation, the Fisher effect and taxes.
Published the exact Fisher equation (1 + i) = (1 + r)(1 + π), solved for any one of the three rates, with the approximation gap and the after-tax real rate.
Reproduced the ten-year breakeven inflation rate from nominal and inflation-indexed Treasury yields.
Added it to an automated formula suite with golden, independent, property, boundary and structural cases.
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