Calculate arithmetic mean, CAGR, and real inflation-adjusted returns โ see the gap between average and actual compounded growth for any investment.
Enter up to 30 years of annual returns (as percentages) or a starting value, ending value, and number of years. The calculator returns: (1) the arithmetic mean return โ the simple average of annual percentage gains; (2) the geometric mean return (CAGR) โ the single constant annual rate that would produce the same ending balance; and (3) the inflation-adjusted (real) CAGR, adjusting for a long-run inflation assumption. You can also input a lump sum to see what each return figure translates to in terminal dollar value โ making the gap between arithmetic and geometric mean concrete and tangible.
1. Choose input mode: enter annual return percentages year by year, or enter a start value, end value, and number of years.
2. If entering annual returns, type each year's percentage return (e.g., 18, โ12, 25, 6).
3. Optionally enter a starting dollar amount to project terminal value.
4. Set your inflation assumption (default: 3% for long-run historical average).
5. Click "Calculate" to see arithmetic mean, CAGR, real CAGR, and projected terminal values.
6. Use the "Benchmark" toggle to compare your result against the S&P 500's historical ~10% nominal / ~7% real long-run CAGR.
Arithmetic Mean: Sum of all annual returns รท Number of years. Example: returns of +20%, โ10%, +15% โ (20 โ 10 + 15) รท 3 = 8.33%.
CAGR (Geometric Mean): CAGR = (Ending Value รท Beginning Value)^(1/n) โ 1, where n = number of years. For the same returns: $1 ร 1.20 ร 0.90 ร 1.15 = $1.2420 after 3 years โ CAGR = (1.2420)^(1/3) โ 1 = 7.52%. The arithmetic mean overstated the return by 81 basis points. Over long periods, this gap compounds dramatically.
If your CAGR is close to your arithmetic mean, your returns were consistent with low volatility. A wide gap between the two signals high volatility โ you may have had some big up years offset by big down years. The arithmetic mean is useful for estimating the expected return of a single future year; CAGR is the right figure for projecting how a portfolio actually grew or will grow over multiple periods.
This is one of the most consequential and least-explained concepts in personal investing. The mathematics are unforgiving: a 50% gain followed by a 50% loss doesn't leave you flat โ it leaves you 25% down. Your arithmetic mean is 0%, but your actual return is โ25%. The difference โ called the "variance drag" or "volatility drag" โ grows with both the magnitude of swings and the number of periods. For a stock portfolio with annual standard deviation of 15% (typical for a diversified US equity fund), the variance drag is roughly ฯยฒ/2 โ 1.125% per year. That means a 10% arithmetic mean corresponds to only about 8.9% CAGR. Financial advisors who pitch products using arithmetic mean returns are not technically lying โ but they are showing you the more flattering number. Always ask for the CAGR when evaluating an investment's historical performance.
The S&P 500 has returned approximately 10% nominal per year on an arithmetic mean basis and roughly 7% per year in inflation-adjusted (real) CAGR terms over the long run. These numbers are widely used as benchmarks, but three nuances matter enormously:
A "good" average return is one that beats inflation, covers taxes, and helps you reach your goal โ not just one that exceeds the S&P 500 in a single five-year window.
Nominal returns are the headline numbers on your brokerage statement. Real returns subtract the effect of inflation, giving you the gain in actual purchasing power. With 2024 US CPI at approximately 2.9%, a nominal 9% return is a real return of about 5.9% (more precisely: (1.09 รท 1.029) โ 1 โ 5.93%). For long-run planning โ especially retirement projections โ real returns are more relevant because they tell you what your money will actually buy. If you project $1M in nominal terms 25 years from now at 3% inflation, that $1M has the purchasing power of only about $478,000 in today's dollars. The average return calculator lets you toggle between nominal and real return views to avoid this common planning mistake.
Asset allocation: Stocks historically return ~10% nominal long-run; intermediate bonds return ~4โ6%; cash/money market returns 2โ5% in higher-rate environments. A 60/40 portfolio blends these into a long-run expected return of roughly 7โ8% nominal.
Investment costs: Expense ratios, trading commissions, and advisor fees directly reduce your net return. A 0.05% expense ratio index fund delivers nearly all of its gross return to you; a 1.25% actively managed fund must consistently outperform by more than 1.2 percentage points just to match the index on a net basis.
Tax drag: In taxable accounts, dividends and realized gains are taxed annually, reducing the effective compounding rate. Tax-advantaged accounts (401k, Roth IRA) eliminate this drag.
Holding period: CAGR is more meaningful for periods of five years or more. One- or two-year return data is too short to identify skill versus luck in active management.
A Denver financial planner is comparing two funds for a client. Fund A reports five-year arithmetic mean returns: +22%, โ8%, +18%, +14%, โ5% = 8.2% average. Fund B: +10%, +8%, +9%, +7%, +11% = 9.0% average. Fund A's arithmetic mean looks slightly worse, but what about CAGR? Fund A: $1 ร 1.22 ร 0.92 ร 1.18 ร 1.14 ร 0.95 = $1.4744 โ CAGR = (1.4744)^0.20 โ 1 = 8.08%. Fund B: $1 ร 1.10 ร 1.08 ร 1.09 ร 1.07 ร 1.11 = $1.5362 โ CAGR = (1.5362)^0.20 โ 1 = 8.96%. Fund B's smoother ride produces a meaningfully higher CAGR despite a similar arithmetic mean. Volatility drag cost Fund A nearly a full percentage point.
Sofia, 28, wants to know what $15,000 invested today will grow to at 65 using S&P 500's historical 10% nominal CAGR. FV = $15,000 ร (1.10)^37 โ $389,000. At the real 7% CAGR (inflation-adjusted), FV = $15,000 ร (1.07)^37 โ $196,000 in today's purchasing power. The difference highlights why both figures matter: $389,000 is the account balance; $196,000 is what it can actually buy at retirement.
1. Always use CAGR, not arithmetic mean, for multi-year projections. CAGR is what your account statement reflects; arithmetic mean is an overestimate.
2. Input at least 5โ10 years of data. Shorter windows produce highly volatile CAGR estimates that aren't predictive.
3. Adjust for inflation when planning goals. A retirement target set in nominal terms will underwhelm in real purchasing power.
4. Account for fees before entering your returns. If your fund returned 9.5% but charged 0.75% in expenses, enter 8.75%.
5. Benchmark fairly. Compare your diversified equity fund to the S&P 500 total return index, not just price return โ dividends account for about 1.5โ2% of the S&P's historical ~10% return.
A: An average return calculator measures the historical or projected performance of an investment. It computes both the arithmetic mean return (simple average of annual percentages) and the CAGR (the true compounded growth rate), helping investors understand actual portfolio growth versus expected single-year gain.
A: The arithmetic mean adds all annual percentage returns and divides by the number of years โ it is useful for estimating a single future year's expected return. CAGR is the geometric mean: the single constant annual rate that explains actual portfolio growth from start to finish. For volatile returns, CAGR is always lower than the arithmetic mean.
A: The S&P 500 has delivered approximately 10% nominal per year in arithmetic mean terms and approximately 7% per year in real (inflation-adjusted) CAGR terms over the long run. Recent decade returns have run above this average due to low interest rates and technology sector outperformance.
A: A "good" return depends on your risk level and time horizon. For long-term equity investors, beating the S&P 500's ~10% nominal benchmark consistently is difficult โ most active funds underperform over 10+ year periods. For a balanced (60/40) portfolio, a 7โ8% nominal CAGR is reasonable. For inflation-adjusted planning, a 4โ6% real return is solid.
A: Inflation reduces the purchasing power of your returns. If your nominal CAGR is 9% and inflation is 3%, your real return is approximately 5.8%. Over 30 years, this difference is enormous: $100,000 growing at 9% nominal becomes $1.33M, but its real purchasing power is only about $549,000 in today's dollars.
A: Variance drag (also called volatility drag) is the gap between arithmetic mean return and geometric mean (CAGR) caused by the mathematics of percentage gains and losses. For a portfolio with high annual return variability, variance drag can reduce your effective CAGR by 1โ2% per year compared to the arithmetic average.
A: Yes. Enter the property's initial purchase price as the starting value and the current or projected sale price as the ending value, along with the number of years held. The resulting CAGR represents the annualized price appreciation. Add rental income yield separately to estimate total return.
A: At least 5โ10 years of data is recommended for a meaningful average. Fewer than 5 years produces highly variable results that are heavily influenced by market cycle timing. For academic and retirement planning purposes, 20โ30 year periods are most predictive of long-run expected returns.
Brief disclaimer: This calculator provides estimates for educational and planning purposes only. Past performance does not guarantee future results. CAGR, arithmetic mean, and real return figures are mathematical computations based on user-provided data and inflation assumptions. Actual investment returns are affected by fees, taxes, market conditions, and other factors not captured here. Consult a qualified financial professional before making investment decisions.