What’s the real interest rate?
Enter any two of the nominal interest rate, the inflation rate and the real interest rate. The calculator gives the third from the exact Fisher equation, and shows how far the quick rule "nominal minus inflation" is from the exact answer.
- Real interest rate
- 1.94%
A 5% nominal rate with 3% inflation is a real interest rate of 1.94%.
- Quick approximation (nominal − inflation)
- 2%
- Approximation minus the exact real rate
- 0.058%
Real interest rate: 1.94%. A 5% nominal rate with 3% inflation is a real interest rate of 1.94%.
The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use
How to calculate
Computes the real interest rate from the nominal rate and inflation with the exact Fisher equation and the quick approximation, or the nominal rate or inflation from the other two.
Example with the default inputs (Nominal interest rate 5%, Inflation rate 3%): A 5% nominal rate with 3% inflation is a real interest rate of 1.94%.
Formula: (1 + i) = (1 + r) × (1 + π), so r = (1 + i) ÷ (1 + π) − 1, where i is the nominal rate, π the inflation rate and r the real rate; the quick approximation is r ≈ i − π.
- All three rates are for the same period, usually a year, and compound once in that period.
- Use expected inflation for a rate agreed today, or measured inflation to see what a past rate really earned.
- Arithmetic is exact on the typed decimals; rates round once to 2 decimals for display.
Worked examples
Each example is checked against the calculator on every build.
- Nominal interest rate 15%, Inflation rate 10% gives Real interest rate 4.545455%, Quick approximation (nominal − inflation) 5%, Approximation minus the exact real rate 0.454545%.Source: Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html
- Nominal interest rate 9%, Inflation rate 3% gives Real interest rate 5.825243%, Quick approximation (nominal − inflation) 6%.Source: OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation (a 9% loan with 3% inflation is a 6% real rate; 4% interest with 5% inflation loses in real terms). https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation (6% by the quick rule)
- Nominal interest rate 4%, Inflation rate 5% gives Real interest rate -0.952381%, Quick approximation (nominal − inflation) -1%.Source: OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation (a 9% loan with 3% inflation is a 6% real rate; 4% interest with 5% inflation loses in real terms). https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation
- Real interest rate 3%, Inflation rate 4% gives Nominal interest rate 7.12%.Source: Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html
- Nominal interest rate 7.12%, Real interest rate 3% gives Inflation rate 4%.Source: Irving Fisher, The Theory of Interest (1930), chapter II, §2 and §4: the money rate and the real rate differ by the rate of change in prices, exactly only for rates reckoned continuously; a 15% money rate with prices rising 10% a year is a real rate of about 5%. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html
How it works
With the nominal rate i, the inflation rate π and the real rate r, all as decimals for the same period (a percent ÷ 100):
- Fisher equation: (1 + i) = (1 + r) × (1 + π)
- Real rate: r = (1 + i) ÷ (1 + π) − 1 = (i − π) ÷ (1 + π)
- Nominal rate: i = (1 + r) × (1 + π) − 1 = r + π + r × π
- Inflation rate: π = (1 + i) ÷ (1 + r) − 1 = (i − r) ÷ (1 + r)
- Quick approximation: r ≈ i − π
The page also shows the approximation and how far it is above the exact real rate. In percentage points that gap is (i − π) − r = r × π ÷ 100, with r and π in percent.
Why it works: $1 lent at the nominal rate becomes 1 + i dollars, while the goods $1 bought now cost 1 + π dollars. So the loan buys (1 + i) ÷ (1 + π) times as much as before, a real gain of (1 + i) ÷ (1 + π) − 1.
Rules:
- Enter any two of the three rates; the page solves for the third.
- Each rate is more than −100%. The nominal and inflation rates are at most 1,000,000% per period and the real rate at most 1,000%. A solved rate outside those limits gives no answer.
- The arithmetic is exact on the decimals you type. Rates show to 2 decimals and the gap to 3, with halves rounded up (away from 0).
- A solved rate, the quick approximation or the gap that is not 0 but too close to 0 for a 64-bit floating-point number (about 2.5 × 10⁻³²⁴ or less) gives no answer and a message, never a silent 0. The page checks each one from the exact rates (with two rates typed, from the exact third rate; with all three typed, from the typed real rate). For example, real and inflation rates of 10⁻³⁰⁰% give a gap of 10⁻⁶⁰² points, so no answer.
Assumptions
- The three rates are for the same period, usually a year, and compound once per period.
- Taxes are not included.
Worked examples by hand
Fisher's example. A 15% money rate while prices rise 10% a year. Exact: 1.15 ÷ 1.10 − 1 = 0.045455, a real rate of 4.55%. The quick rule gives 15 − 10 = 5%, which is 4.5455 × 10 ÷ 100 = 0.455 points too high. Fisher gives the real rate as about 5%.
OpenStax's loan. A 9% loan when inflation is 3%: 1.09 ÷ 1.03 − 1 = 5.83% (6% by the quick rule).
Losing to inflation. 4% interest with 5% inflation: 1.04 ÷ 1.05 − 1 = −0.95% (−1% by the quick rule).
The nominal rate you need. For a 3% real return with 4% inflation: 1.03 × 1.04 − 1 = 0.0712, a nominal rate of 7.12%. Back again: 1.0712 ÷ 1.03 − 1 = 4% inflation.
Other questions people ask
What is the real interest rate?
The real interest rate is the interest rate after inflation: how fast your buying power grows, not just your dollars. A deposit that pays 5% while prices rise 3% buys about 1.94% more goods after a year, so its real rate is 1.94%.
How do I calculate the real interest rate?
Divide 1 plus the nominal rate by 1 plus the inflation rate, then subtract 1. With a 9% nominal rate and 3% inflation: 1.09 ÷ 1.03 − 1 = 5.83%. The quick rule, 9% − 3% = 6%, is close but a little high.
What is the Fisher equation?
(1 + nominal rate) = (1 + real rate) × (1 + inflation rate). It is named after Irving Fisher, who showed in The Theory of Interest (1930) that the money rate of interest and the real rate differ by the rate at which prices change. The simple difference is exact only for rates compounded continuously; for yearly rates there is a small extra term.
When is "nominal minus inflation" good enough?
When both rates are small. The quick rule overstates the real rate by real rate × inflation rate ÷ 100 percentage points: 0.06 points at 5% and 3%, but 0.45 points at 15% and 10%, and far more when inflation is high.
Can the real interest rate be negative?
Yes, whenever inflation is higher than the nominal rate. Savings that earn 4% while prices rise 5% lose buying power: 1.04 ÷ 1.05 − 1 = −0.95%, about −1% by the quick rule.
Should I use expected or actual inflation?
Use the inflation you expect when you compare a rate before you lend or borrow, because that is what the real rate will be if your forecast is right. Use measured inflation when you look back at what a loan or deposit really earned.