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03 // Bidirectional STEM Calculators // FINANCEr_real (%) = (((1 + r_nom / 100) / (1 + i / 100)) - 1) × 100

Fisher Real Inflation-Adjusted Return Calculator

The exact Fisher equation converts between nominal investment return r_nom and inflation rate i to reveal true purchasing-power growth: 1 + r_real = (1 + r_nom) / (1 + i).

r_real (%) = (((1 + r_nom / 100) / (1 + i / 100)) - 1) × 100
Pick which value you want to calculate (or type into any field):Solving for: r_real (%) — Real Inflation-Adjusted Return
Calculated

True purchasing-power annual return in percent

-2050
%

Stated pre-inflation return rate in percent

-1060
%

CPI inflation rate in percent

-530
%
Calculated Result · Real Inflation-Adjusted Return (r_real (%))
5.8252

Step-by-Step Calculation

01Canonical Law: r_real (%) = (((1 + r_nom / 100) / (1 + i / 100)) - 1) × 100
02Given Inputs (Base Units): r_nom (%) = 9, i (%) = 3
03Solve for r_real (%) (Real Inflation-Adjusted Return): r_real (%) = 5.8252

The exact Fisher equation converts between nominal investment return r_nom and inflation rate i to reveal true purchasing-power growth: 1 + r_real = (1 + r_nom) / (1 + i).

Real-World Reference Values

US Equities Long-Run Real Return6.5% – 7.0% / yr

Nominal ~10% less ~3% historical CPI inflation

10-Year TIPS Real Yield1.8% – 2.4% / yr

Treasury Inflation-Protected Securities benchmark

Safe Withdrawal Rate (Trinity)4.0% Real Drawdown

Inflation-indexed retirement spending baseline

20-Row Comparison Table

Real Inflation-Adjusted Return (r_real (%)) · Nominal Investment Return (r_nom (%))

Fisher Real Inflation-Adjusted Return Calculator — Nominal Investment Return → Real Inflation-Adjusted Return
#Nominal Investment Return (r_nom (%))Real Inflation-Adjusted Return (r_real (%))Δ %
011.125 -1.8204 -131.25%
022.0461 -0.926162 -115.90%
032.9671 -0.031937 -100.55%
043.8882 0.862289 -85.20%
054.8092 1.7565 -69.85%
065.7303 2.6507 -54.50%
076.6513 3.545 -39.14%
087.5724 4.4392 -23.79%
098.4934 5.3334 -8.44%
109 Current5.8252 0.00%
1110.3355 7.1219 +22.26%
1211.2566 8.0161 +37.61%
1312.1776 8.9103 +52.96%
1413.0987 9.8045 +68.31%
1514.0197 10.6988 +83.66%
1614.9408 11.593 +99.01%
1715.8618 12.4872 +114.36%
1816.7829 13.3815 +129.71%
1917.7039 14.2757 +145.07%
2018.625 15.1699 +160.42%
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Frequently Asked Questions

Why is r_real slightly lower than simply subtracting r_nom - i?+

Because inflation also erodes the purchasing power of the investment gains earned during the year, dividing by (1 + i/100) is more accurate than simple subtraction.

How do I find the nominal return needed to earn 5% real return during 4% inflation?+

Lock r_nom (%), set r_real = 5 and i = 4. The exact Fisher requirement is 9.20% nominal.

What happens when inflation exceeds the nominal yield on cash?+

Real return r_real turns negative, meaning purchasing power shrinks even as the nominal account balance grows.