# What’s the real interest rate?

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.

- Page: https://www.acalculator.org/finance/real-interest-rate-calculator
- JSON spec: https://www.acalculator.org/finance/real-interest-rate-calculator.json
- Version: 70164980772d

## Default answer

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%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| nominal | Nominal interest rate | The stated yearly rate, before taking inflation into account. |
| inflation | Inflation rate | The yearly rise in prices, expected or measured. |
| real | Real interest rate | The yearly rate after inflation: how fast buying power grows. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| nominal | Nominal interest rate | (1 + real) × (1 + inflation) − 1, as a percent, to 2 decimals. |
| inflation | Inflation rate | (1 + nominal) ÷ (1 + real) − 1, as a percent, to 2 decimals. |
| real | Real interest rate | (1 + nominal) ÷ (1 + inflation) − 1, as a percent, to 2 decimals. |
| approx | Quick approximation (nominal − inflation) | The nominal rate minus the inflation rate: close to the real rate when both are small. |
| gap | Approximation minus the exact real rate | How many percentage points the quick approximation is above the exact real rate: real × inflation ÷ 100. |

## Method

(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.

## Assumptions

- 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

1. nominal = 15%, inflation = 10% gives real = 4.545455%, approx = 5%, gap = 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.
2. nominal = 9%, inflation = 3% gives real = 5.825243%, approx = 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).
3. nominal = 4%, inflation = 5% gives real = -0.952381%, approx = -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.
4. real = 3%, inflation = 4% gives nominal = 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.
5. nominal = 7.12%, real = 3% gives inflation = 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.

## FAQ

### 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.

## Sources

- Irving Fisher, The Theory of Interest (Macmillan, 1930), Part I, chapter II, "Money Interest and Real Interest", §2 Assuming Foresight (the two rates differ by the rate of divergence between the money and goods standards, strictly true only when reckoned continuously, footnote 19) and §4 (a 15% money rate with prices rising 10% a year is a real rate of about 5%). Library of Economics and Liberty edition. https://www.econlib.org/library/YPDBooks/Fisher/fshToI2.html (retrieved 2026-10-18)
- OpenStax, Principles of Economics 3e, 22.4 The Confusion Over Inflation: a 9% loan made when inflation is 3% has a 6% real interest rate; money earning 4% while inflation is 5% loses value. https://openstax.org/books/principles-economics-3e/pages/22-4-the-confusion-over-inflation (retrieved 2026-10-18)