Do not mix CPI-U with CPI-W, RPI, PCE, or seasonally adjusted and non-seasonally adjusted series. If your investment period is January to January, use January index values for both endpoints.
CPI example: Start CPI 258.906 and end CPI 307.789 means prices rose by 18.88%, so a nominal portfolio gain must exceed that to produce a positive real gain.
From Fisher: \(\displaystyle 1+N=(1+r)(1+\pi)\Rightarrow N=(1+r)(1+\pi)-1\).
Real IRR with Contributions or Withdrawals
Use this advanced mode when money moved in or out during the period. Enter contributions as negative cash flows and withdrawals as positive cash flows.
$
$
yr
Year
Cash flow
CPI/index at cash flow date
Action
Results will appear here.
Cash flows are first converted to start-period dollars using the CPI/index at each cash-flow date, then an annual real IRR is solved from those adjusted flows.
Real Return Basics
Nominal return
Nominal return is the percentage gain before adjusting for inflation. A portfolio that rises from $10,000 to $10,700 has a 7% nominal return.
Real return
Real return estimates the change in purchasing power. It answers whether your investment grew faster than prices.
Inflation and CPI
Inflation is the rate at which prices rise. CPI is one common price index used to deflate nominal returns into start-period dollars.
Real CAGR
Real CAGR is the annualized after-inflation growth rate over a multi-year period. It is useful when start and end values span several years.
Purchasing power
Purchasing power is what money can buy. If your nominal balance rose but prices rose faster, your purchasing power fell.
Fees and taxes
Fees, expense ratios, and tax drag reduce the nominal return available to beat inflation. Enter them only when they apply to your situation.
Worked Examples
1) Real return from nominal return and inflation
Inputs: nominal return 7%, inflation 3%.
Formula:(1.07 / 1.03) - 1 = 0.038835.
Interpretation: the exact real return is 3.8835%, so purchasing power grew by about 3.88%.
2) Real CAGR from portfolio values and CPI
Inputs: $10,000 start, $20,000 end, 8 years, CPI 180 to 260.
Interpretation: the real CAGR is 4.1516%; the $20,000 ending value is worth $13,846.15 in start-period dollars.
3) Required nominal return for a target real return
Inputs: target real return 4%, assumed inflation 2.5%.
Formula:(1.04 * 1.025) - 1 = 0.066.
Interpretation: you need a 6.6000% nominal return to have a 4% real return if inflation is 2.5%.
Assumptions and Sources
This tool uses the exact Fisher formula for annual rate comparisons and CPI/index ratios for period-based real value calculations. Calculations run locally in your browser; the page does not fetch or store your inputs.
Financial-information disclaimer: This calculator is for general education and arithmetic checks. It is not financial, investment, tax, or legal advice.
Real Return Calculator FAQ
What is the difference between real return and nominal return?
Nominal return is the return before adjusting for inflation. Real return removes inflation so the result estimates how much purchasing power changed.
Should I use the exact Fisher formula or nominal minus inflation?
Use the exact Fisher formula when precision matters: real return = (1 + nominal return) / (1 + inflation) - 1. Nominal minus inflation is a quick approximation that is closest when rates are small.
Should CPI be annual or period-based?
Use CPI values that match the start and end of the investment period. For a January 2020 to January 2025 return, use the January 2020 and January 2025 index values from the same CPI series.
How should I handle negative inflation?
Enter negative inflation as a negative percentage, such as -1.5. In deflation, the exact formula can make the real return higher than the nominal return.
Are taxes and fees included?
They are included only if you enter them. The calculator has optional annual fee, expense ratio, and tax drag fields so you can compare real return before and after those costs.
How should dividends be treated?
Include reinvested dividends in the nominal return or ending portfolio value. If dividends were paid out and not reinvested, treat them as cash flows in the advanced mode.
Is this financial advice?
No. This calculator is for general education and arithmetic checks. It does not recommend investments or account for your full tax, risk, or cash-flow situation.
