Fisher Equation Calculator — Real Interest Rate from Nominal & Inflation
Enter the nominal interest rate and the expected inflation rate to find the exact real (inflation-adjusted) rate of return using the Fisher equation. See how nominal and real growth diverge over time.
%
%
years
Inflation-adjusted rate of return — purchasing power gain per year
- 1
Nominal factor
1 + 5.5% ÷ 100 = 1.055 - 2
Inflation factor
1 + 3% ÷ 100 = 1.03 - 3
Real factor
1.055 ÷ 1.03 = 1.024272(1 + nominal) ÷ (1 + inflation) gives the real purchasing-power multiplier. - 4
Real interest rate
(1.024272 − 1) × 100 = 2.4272
How does this calculator work?
Real rate = (1 + nominal) / (1 + inflation) − 1. Approximation: real ≈ nominal − inflation (accurate when both are low). A negative real rate means inflation is eroding purchasing power even as balances grow. Use the exact form at rates above ~5% to avoid meaningful rounding error.
Formula
How this is calculated
The Fisher equation, developed by Irving Fisher in his 1930 work "The Theory of Interest," states that the real interest rate r is related to the nominal rate i and the inflation rate π by the exact formula r = (1 + i)/(1 + π) − 1. This is derived by recognising that $1 lent at nominal rate i grows to (1 + i) in one year in dollar terms, but the purchasing power of that dollar shrinks by a factor of (1 + π) due to inflation — so the real purchasing-power gain is (1 + i)/(1 + π) − 1.
The widely used approximation r ≈ i − π drops the cross-term (i × π)/(1 + π) and is accurate enough when both rates are small. For example, at i = 5% and π = 3%, the approximation gives r ≈ 2% while the exact equation gives r = 1.942% — a difference of 0.058 percentage points. At i = 15% and π = 10% the difference grows to about 0.45 percentage points, making the exact formula increasingly important.
The projection curve shows how $1 grows in real (purchasing-power) terms at the computed real rate, making visible the gap between nominal account balances (which include inflation illusion) and actual purchasing-power gains. A negative real rate — when inflation exceeds the nominal rate — means money held at that rate is losing purchasing power year after year.
Frequently asked questions
A negative real rate means inflation is higher than the nominal rate. A savings account paying 1% nominal when inflation is 4% gives a real rate of about −2.9%, meaning the purchasing power of your savings shrinks by roughly 2.9% per year even though the balance grows in dollar terms. This is common during periods of loose monetary policy or high inflation.
The Fisher equation is the mathematical relationship r = (1 + i)/(1 + π) − 1 that defines the real rate in terms of the nominal rate and inflation. The Fisher Effect is the economic hypothesis built on top of it — that in the long run, a one-percentage-point rise in expected inflation causes nominal rates to rise by one percentage point, leaving real rates unchanged. The equation is the math; the effect is the economic prediction.
Replace the nominal interest rate with the nominal investment return (e.g. an 8% annualised return from equities) and the inflation rate with the prevailing or expected CPI inflation. The result is the real (purchasing-power) return. A portfolio growing at 8% nominal with 3% inflation delivers roughly 4.85% real return — not 5% — due to the exact Fisher equation.
Also known as
TG we-Calculate Editorial Team. (2026). Fisher Equation Calculator — Real Interest Rate from Nominal & Inflation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/fisher-equation-calculator
TG we-Calculate Editorial Team. "Fisher Equation Calculator — Real Interest Rate from Nominal & Inflation." TG we-Calculate. 2026. https://we-calculate.com/calculator/fisher-equation-calculator.
TG we-Calculate Editorial Team, "Fisher Equation Calculator — Real Interest Rate from Nominal & Inflation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/fisher-equation-calculator
@misc{wecalculate_fisher_equation_calculator, title = {Fisher Equation Calculator — Real Interest Rate from Nominal & Inflation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/fisher-equation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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