Fisher Equation Calculator

Convert a nominal interest rate into a real, inflation-adjusted rate using the Fisher equation, and see how a lump sum's purchasing power changes over time.

Quick Facts

Formula
1 + i = (1 + r)(1 + π)
i is the nominal rate, r the real rate, and π the expected inflation rate, all expressed as decimals.
Common shortcut
r ≈ i − π
A simple approximation that is close for small rates but understates the exact real rate as rates rise.

Your Results

Calculated
Real interest rate (exact)
-
(1 + i) / (1 + π) − 1
Real interest rate (approx.)
-
Simple shortcut: i − π
Purchasing-power value
-
Amount's real value after the time horizon
Approximation gap
-
Exact rate minus approximate rate

Ready

Enter the nominal rate, expected inflation, amount, and time horizon, then press Calculate.

How the Fisher Equation Calculator works

The Fisher equation converts a nominal interest rate — the rate printed on a savings account, bond, or loan — into a real, inflation-adjusted rate that shows whether your money is actually gaining purchasing power. It is the standard tool economists and financial planners use to answer "am I really getting ahead, or just keeping up with prices?"

The formula

The exact Fisher equation states that 1 + i = (1 + r)(1 + π), where i is the nominal interest rate, r is the real interest rate, and π (pi) is the expected inflation rate, all expressed as decimals over the same period. Solving for the real rate gives:

r = (1 + i) / (1 + π) − 1

A widely used shortcut, the Fisher approximation, drops the cross term between the two rates and simplifies to r ≈ i − π. It is easy to compute in your head and close enough when both rates are small, but it systematically understates the exact real rate as either rate grows.

Worked example

With an 8% nominal rate and 3% expected inflation, the exact real rate is (1.08 / 1.03) − 1 ≈ 4.854%, while the approximation gives a flatter 8% − 3% = 5.000% — a gap of about 0.146 percentage points. Compounded over 5 years, $10,000 growing at the exact real rate is worth roughly $12,674.55 in current purchasing power, meaning it buys about as much then as $12,674.55 buys today, even though the account balance in nominal dollars will be higher still.

What moves the real rate most

  • Expected inflation: a higher inflation assumption lowers the real rate for any fixed nominal rate — this relationship is the entire reason the Fisher equation exists.
  • Nominal rate: a higher nominal rate raises the real rate, roughly one-for-one at low rates, though the exact formula scales it by dividing through (1 + π).
  • Time horizon: the horizon does not change the real rate itself, but it compounds it — the gap between nominal growth and real purchasing-power growth widens every additional year.

Exact versus approximate — when the shortcut breaks down

At low single-digit rates the approximation is usually fine for a quick estimate. At higher rates the gap grows fast: with a 20% nominal rate and 15% inflation, the exact real rate is (1.20 / 1.15) − 1 ≈ 4.348%, while the approximation says 5.000% — a gap of about 0.65 percentage points, more than four times larger than the low-rate example above. For any comparison involving double-digit rates or high-inflation currencies, use the exact formula rather than the shortcut.

Frequently Asked Questions

What is the Fisher equation?
The Fisher equation links the nominal interest rate, the real interest rate, and expected inflation: 1 + i = (1 + r)(1 + π), where i is the nominal rate, r is the real rate, and π is the expected inflation rate. Solving for r gives the exact real, inflation-adjusted rate: r = (1 + i) / (1 + π) − 1.
What is the difference between the exact and approximate real rate?
The exact Fisher equation gives r = (1 + i) / (1 + π) − 1. A common shortcut, the Fisher approximation, is r ≈ i − π. The shortcut is close when rates are small, but it increasingly diverges from the exact value as nominal rates or inflation rise, because it drops the i × π cross term that the exact formula includes.
Why can the real interest rate be negative?
The real rate is negative whenever inflation outpaces the nominal rate. For example, a savings account paying 2% nominal interest during 5% inflation actually loses purchasing power each year, even though the account balance itself keeps growing in dollar terms.
How is the purchasing-power value calculated?
The calculator compounds the exact real rate over the chosen time horizon: purchasing-power value = amount × (1 + exact real rate)^years. That equals the future nominal amount, amount × (1 + nominal rate)^years, expressed in current purchasing power after dividing out inflation over the same period.

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