Fisher Effect Calculator
From nominal and real rates, or inflation, compute the Fisher effect — how inflation and nominal rates relate to the real rate.
Input Data
Results
At a glance:The Fisher Effect describes how nominal rate, real rate and inflation relate: (1 + nominal) = (1 + real)(1 + inflation). Real ≈ nominal − inflation. Enter any two to derive the third. It reveals the real return after inflation and the break-even inflation for nominal bonds. Beware using nominal returns alone — inflation can erase most of the real gain.
Formula
Exact: (1 + nominal) = (1 + real) × (1 + inflation).
Nominal = (1 + real)(1 + inflation) − 1.
Real = (1 + nominal) ÷ (1 + inflation) − 1.
Inflation = (1 + nominal) ÷ (1 + real) − 1.
Approx: real ≈ nominal − inflation.
$$$(1+i) = (1+r)(1+\\pi)$$$$$$i = (1+r)(1+\\pi) - 1$$$$$$(1.03)(1.02) - 1 = 5.06\\%$ $r+\\pi=5\\%$$$How to Use
- Enter any two of nominal rate, real rate and inflation.
- Pick which to compute; view the result.
- Compare exact vs approximate to see the compounding gap at large rates.
Real rate by nominal and inflation (exact Fisher)
| Nominal rate | Inflation | Real (exact) | Approx (nom−infl) |
|---|---|---|---|
| 3.00% | 2.00% | 0.98% | 1.00% |
| 5.00% | 2.00% | 2.94% | 3.00% |
| 15.00% | 10.00% | 4.55% | 5.00% |
| 3.00% | 5.00% | −1.90% | −2.00% |
At low rates the exact and approx nearly match; as rates rise the gap (the real×inflation cross term) grows. Inflation above the nominal rate means a negative real return despite positive nominal — purchasing power falls.
Case Studies
Case 1: From nominal and inflation to real rate
A Hong Kong time deposit: nominal 5%, inflation 2%.
Exact real = (1 + 5%) ÷ (1 + 2%) − 1 = 1.05/1.02 − 1 ≈ 2.94%; the simple 5% − 2% = 3% is close but slightly over.
Interpretation: after inflation the true purchasing-power gain is about 2.94%, not the 5% on the rate card. The Fisher effect reminds you to look past the nominal number to the real return.
Case 2: Inflation outruns the nominal rate
A bond yields 3% nominal, but that year inflation is 5%.
Real = (1.03/1.05) − 1 ≈ −1.90% — even though the nominal is positive, purchasing power falls about 1.9%.
Interpretation: a positive nominal return can still be a real loss under high inflation. Savers should prefer inflation-linked or higher real-return assets; borrowers gain as real debt shrinks. Always strip inflation via the Fisher effect to see true return.
FAQ
Why not just subtract inflation?
Nominal minus inflation is only an approximation valid for small rates. The exact Fisher relation includes compounding; at high rates the gap is noticeable, so use the exact form for accuracy.
What is the real rate?
The real rate is the return after inflation — the true gain in purchasing power. A nominal 5% with 2% inflation yields a real ~2.94%; if inflation is 6%, the real return is negative despite positive nominal.
How is break-even inflation used?
For a nominal bond, the break-even inflation is the inflation that makes its nominal return equal the real return of an inflation-linked bond; it is the inflation rate the market prices in. Higher actual inflation than break-even hurts nominal-bond holders.
Why does high inflation erode nominal returns?
Because the nominal return you see is not the real purchasing-power gain — inflation quietly eats it. Example: a nominal deposit at 3% when inflation is 5% gives a real return of about 3% ÷ (1+5%) − 1 ≈ −1.9%, i.e. you lose purchasing power despite a positive nominal number. That is why judging 'how much you really earned' must use the real rate, not the nominal. The Fisher effect is exactly the tool: it links the three. Intuition: your money grows at the nominal rate, but goods prices grow at inflation; the residual growth of 'how many goods you can buy' is the real rate. So investing/borrowing must mind real rates: a high nominal deposit with high inflation may be negative real; a borrower sees the real debt shrink when inflation exceeds the nominal rate. Always strip inflation to see true return.
The exact formula vs the approximation — how big is the gap, and why use exact at high rates?
The exact Fisher relation is (1+nominal)=(1+real)(1+inflation), i.e. nominal=(1+real)(1+inflation)−1; the common 'real ≈ nominal − inflation' is only the first-order approximation ignoring the cross term. The gap = real×inflation (the interaction). At low rates (e.g. 3% nominal, 2% inflation) exact real = (1.03/1.02)−1 ≈ 0.98%, approx = 1%, gap ~0.02% — negligible, so the shortcut suffices. At high rates (e.g. nominal 15%, inflation 10%) exact real = (1.15/1.10)−1 ≈ 4.55%, approx = 5%, gap ~0.45% — meaningful; in hyperinflation (nominal 100%, inflation 80%) exact = (2.0/1.8)−1 ≈ 11.1%, approx = 20%, gap ~9%, hugely distorted. So: low rates → approximation fine; high rates/hyperinflation → must use the exact form, and the approximation overstates the real rate, misleading. This calculator shows both so you see the compounding gap at large rates. Note the approximation understates when rates are negative/very low too — use exact throughout.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.