Calculator
Formula used
The Fisher relationship links nominal returns, real returns, and inflation:
(1 + i) = (1 + r)(1 + π).
- Nominal:
i = (1 + r)(1 + π) − 1 - Real:
r = (1 + i)/(1 + π) − 1 - Inflation:
π = (1 + i)/(1 + r) − 1 - Approximation:
i ≈ r + π(works best for small rates)
How to use this calculator
- Select the value you want to solve for.
- Choose Exact for accuracy at higher rates.
- Enter the other two rates as percentages.
- If using per-period rates, set periods per year.
- Press Calculate to see the result above the form.
- Use CSV or PDF buttons to export the latest result.
Example data
These examples assume annual effective inputs.
| Nominal (i) % | Real (r) % | Inflation (π) % | Solved using |
|---|---|---|---|
| 8.150000 | 3.000000 | 5.000000 | Exact: (1+r)(1+π)−1 |
| 12.000000 | ? | 6.000000 | Exact: (1+i)/(1+π)−1 |
| 9.500000 | 4.000000 | ? | Exact: (1+i)/(1+r)−1 |
FAQs
1) When should I use the exact method?
Use exact Fisher when rates are large or inflation is volatile. The compounding interaction can noticeably change results beyond the simple sum approximation.
2) Is the approximation always wrong?
No. If rates are small, i ≈ r + π is often close. The gap grows as rates rise because the cross-term r·π becomes larger.
3) What does “per-period inputs” mean?
It means each rate you enter applies to one compounding period, like a month. The calculator converts per-period rates into annual effective rates using (1+rate)^n−1.
4) Can inflation be negative?
Yes, deflation is possible. The exact formulas remain valid as long as 1+π stays positive. Extremely negative values can make the equation invalid.
5) Why does my exact nominal exceed r + π?
Because the exact equation multiplies factors. The additional amount is the cross-term created by compounding: effectively r·π.
6) Do these rates represent nominal APR?
This tool treats rates as effective over a horizon. If you have APR, first convert it into effective rate for the same compounding period, then enter it.
7) What should I export in CSV or PDF?
Export when you need a clean record for notes, homework, or reporting. The file includes the solved variable, method, input basis, and formatted rates.