Exact inflation-adjusted return
Inflation changes the purchasing power of a nominal return. The exact one-period real rate is (1 + nominal) ÷ (1 + inflation) − 1. Subtracting inflation from the nominal rate is a common approximation; this page reports both so the gap is visible. The inflation page changes a dollar amount. Annual return annualizes a total return without inflation. CAGR is a compound growth rate without an inflation adjustment.
Approximation = nominal − inflation
Example
A 7% nominal return with 3% inflation is about 3.8835% real. The approximation 7% − 3% = 4% overstates the exact rate by about 0.12 percentage points. 8% and 3% is about 4.85% real. 23.3% and 3% is about 19.71% real.
What the formula leaves out
Taxes, fees, cash flows, and mismatched measurement periods stay outside this one-period identity. Both inputs must cover the same period. Nominal return and inflation at or below −100% are rejected because their gross growth factors are not positive.