Calculate CAGR and average investment return with the geometric mean formula. Compare nominal vs real returns against S&P 500 benchmarks | Calculator4U
Calculate the Compound Annual Growth Rate (CAGR).
An average return calculator computes your investment's Compound Annual Growth Rate (CAGR) — the geometric mean that shows your true annualized return after accounting for the compounding effect of gains and losses over time. Unlike a simple arithmetic average, CAGR cannot be inflated by a single great year. It is the standard used by the SEC, CFA Institute, and every major fund company when reporting multi-year performance, and it is the only metric that allows fair comparison between investments held for different time periods.
The formula: CAGR = (Ending Value ÷ Beginning Value)^(1/n) − 1, where n is the number of years. A US investor who put $50,000 into an S&P 500 index fund in January 2015 and held to January 2025 would have seen it grow to approximately $134,000 — a CAGR of roughly 10.4%, nearly matching the 100-year historical average of 10.3%. That same $50,000 earning only an arithmetic average of 10.4% would show a higher paper number due to volatility drag — the CAGR reveals the real compounded result.
The gap between arithmetic and geometric mean grows with volatility. For a portfolio with 20% annual volatility — typical for a 100% US stock portfolio — arithmetic mean overstates actual returns by approximately 1.5–2% per year. Over a 30-year retirement accumulation period, that 2% overstatement translates to projecting $1.15 million when you will actually have $746,000. This is why using arithmetic mean for retirement planning is dangerous: it makes the plan look funded when it is not.
The two numbers every US investor should always calculate side by side: nominal CAGR (raw return) and real CAGR (inflation-adjusted, using the Fisher equation). In a period of 3% average inflation, an 8% nominal CAGR delivers only 4.85% real purchasing power growth. During the 2021–2022 inflation surge when CPI hit 8–9%, a portfolio returning 10% nominal was barely treading water in real terms. Your wealth-building target should be real CAGR of at least 5–6% for long-term financial independence.
To calculate average return on investment, use the CAGR (Compound Annual Growth Rate) formula: CAGR = (Ending Value ÷ Beginning Value)^(1/n) - 1, where n equals the number of years. Step 1: Divide your ending portfolio value by your starting value. Step 2: Raise this ratio to the power of (1 ÷ years invested). Step 3: Subtract 1 and multiply by 100 for percentage. Example calculation: $10,000 invested grows to $19,500 over 5 years. CAGR = ($19,500 ÷ $10,000)^(1/5) - 1 = (1.95)^0.2 - 1 = 1.143 - 1 = 14.3% average annual return. CAGR is the gold standard for investment performance measurement because it accounts for compounding, unlike simple arithmetic averages that overstate actual returns.
Good average return benchmarks by asset class based on historical data (1926-2024): U.S. Large-Cap Stocks (S&P 500): 10-11% nominal CAGR, 7% real (inflation-adjusted). Small-Cap Stocks: 12% nominal, higher volatility. International Developed Stocks: 7-8% CAGR. Emerging Markets: 8-10% CAGR with significant volatility. Investment-Grade Bonds: 5-6% CAGR. Treasury Bonds: 4-5% CAGR. REITs (Real Estate): 9-10% CAGR. 60/40 Portfolio (stocks/bonds): 8-9% CAGR. For retirement accounts (401k/IRA): target 7-8% long-term average after fees. A 'good' return is one that beats inflation (3%) while matching your risk tolerance—conservative investors accept 4-6%, moderate 6-8%, aggressive 10%+.
Geometric mean (CAGR) and arithmetic mean differ significantly for investment returns because of how compounding works. Arithmetic mean simply adds returns and divides by periods—this overstates actual performance. Geometric mean accounts for sequential compounding and shows TRUE annualized growth. Critical example: Year 1 gains 100% ($10,000→$20,000), Year 2 loses 50% ($20,000→$10,000). Arithmetic mean: (100% + -50%) ÷ 2 = 25% 'average.' Geometric mean: ($10,000 ÷ $10,000)^(1/2) - 1 = 0%. You broke even—geometric mean correctly reflects this. The more volatile the investment, the larger the gap. For a portfolio with 20% volatility, arithmetic mean typically overstates returns by 1.5-2% annually. Always use geometric mean (CAGR) when evaluating multi-year investment performance, comparing funds, or projecting retirement growth.
CAGR = (Ending Value ÷ Beginning Value)^(1/n) − 1, where n equals the number of years. Multiply by 100 for percentage. Example: $10,000 growing to $19,500 over 5 years gives CAGR = (1.95)^0.2 − 1 = 14.3% average annual return. This is the geometric mean formula used by the SEC, CFA Institute, and all major fund companies as the industry standard for measuring multi-year investment performance.
Nominal return is your raw investment gain before adjusting for inflation. Real return shows actual purchasing power growth after inflation is stripped out. The Fisher equation: Real Return = (1 + Nominal Return) ÷ (1 + Inflation Rate) − 1. At 3% historical US inflation, an 8% nominal CAGR equals only 4.85% real return. At the 2022 inflation peak of 9%, a 10% nominal return was only 0.9% real — barely positive. Always use real return for retirement planning projections to avoid overestimating future purchasing power.
Investment fees have a dramatic compounding impact on long-term average returns. A 1% annual expense ratio reduces a 10% gross return to 9% net — which sounds small but costs enormously over time. On $100,000 invested for 30 years at 10% gross: the portfolio grows to $1.745 million. At 9% net (after 1% fees): $1.326 million. A single 1% fee costs $419,000 over 30 years on a $100,000 investment. At 1.5% fees (common in actively managed US mutual funds), the gap widens to over $540,000 lost to fees alone. Index funds with 0.03–0.10% expense ratios preserve nearly the full CAGR.
Use 6–7% real (inflation-adjusted) CAGR for conservative long-term 401k projections, or 7–8% nominal if you prefer not to inflation-adjust your future dollar projections separately. The Vanguard Target Retirement series, widely used as a 401k default, has delivered 7.5–8.5% nominal CAGR over 20-year periods. Never use arithmetic mean for retirement projections — always use CAGR (geometric mean) and subtract your fund's expense ratio from the gross benchmark return. A 0.15% index fund costs you $15 per $10,000 per year; a 1.0% active fund costs $100 — that difference compounds to a six-figure gap at retirement.