Finocturne
Macroeconomics

Real Interest Rate & Fisher Calculator

Compare exact inflation-adjusted interest, the Fisher approximation and their percentage-point gap over the same period.

User inputs or hypothetical examples · Consistent units and periods · Local calculation

Inputs

Currently a hypothetical teaching example. Enter 3 in percentage fields for 3%.

Results

Start with your numbers

Review or adjust your inputs, then calculate to see your results and interpretation.

Understand this calculation

The real rate measures purchasing-power growth after adjusting the same-period nominal growth for prices. The approximation minus the exact rate is a percentage-point gap.

See calculation method and assumptions

Formula

Exact real interest rate

Exact real interest rate

Exact multiplicative relation

Fisher approximation

The real rate is the nominal growth factor divided by the same-period price growth factor, minus one. The nominal factor equals the product of the real and price factors; rates in the formulas are decimals.

Variables, rates and periods

i
Same-period nominal interest rate
π
Same-period inflation rate
r
Exact inflation-adjusted real interest rate
Units
Formula rates use decimals: 5% = 0.05. Inputs and displayed rates use percentages; both inputs cover the same period.

Expected and realized inflation answer different questions

  • Both inputs must cover the same period and price measure.
  • Ex ante estimates depend on your inflation assumption;
  • ex post adjustments depend on realized price changes.
  • This tool does not forecast inflation.

Compare exact inflation-adjusted interest, the Fisher approximation and their percentage-point gap over the same period.

Worked example

  1. Enter 5% nominal interest and 3% inflation for the same year.
  2. Divide 1.05 by 1.03, then subtract one.
  3. Compare 1.9417% with 2%; 0.0583 pp is not a relative percentage error.

Frequently asked questions

Can inflation be negative?

Yes. Both nominal interest and inflation must exceed −100% to keep amount and price factors positive.

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