How this calculator works
A nominal interest rate is stated in dollars, but the dollars it pays buy fewer goods when prices rise. The Fisher equation separates the two: the nominal rate covers both the real return and the expected loss of purchasing power. With compounding, the exact relationship multiplies the two growth factors rather than adding the rates. The familiar shortcut, real rate approximately equals nominal rate minus inflation, ignores the cross product of the two rates and is close only when both are small. The Fisher effect is the claim that nominal rates rise roughly one for one with expected inflation, leaving the real rate anchored.
Formula
Exact Fisher equation: (1 + i) = (1 + r) × (1 + pi), so r = (1 + i) / (1 + pi) - 1, i = (1 + r) × (1 + pi) - 1 and pi = (1 + i) / (1 + r) - 1. The approximation is r approximately i - pi. i is the nominal rate, r the real rate and pi expected inflation, all as fractions.
Worked example
A nominal rate of 6% with expected inflation of 2.5% gives an exact real rate of 3.4146%. The simple approximation gives 3.5%, an overstatement of 0.0854 percentage points because it ignores the product of the two rates.
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Frequently asked questions
Should I use the exact or the approximate formula?
Use the exact formula whenever rates are sizeable or precision matters. The approximation is handy for back-of-envelope work but drifts as nominal rates and inflation rise.
Is this the same as the Fisher effect?
The Fisher equation is the exact identity. The Fisher effect is the economic proposition that a change in expected inflation is eventually matched by a change in nominal rates, so the real rate stays roughly unchanged.
Which inflation figure belongs here?
The expected inflation rate over the same period as the interest rate, as seen when the rate was set. Using realized inflation after the fact measures purchasing power with hindsight, not the ex ante real rate.