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TheCalcUniverse

Average Return Calculator

Calculate the compound annual growth rate (CAGR) and simple average return for any investment. Free, instant, and accurate.

✓ Tested formula & cited sources Formula verified 2026-01-15 Runs in your browser — inputs never sent anywhere

See it worked out

Example — Starting Value 10000, Ending Value 18000, Time Period (Years) 5, Annual Returns (comma-separated %) 12, -5, 8, 15, 3:

Compound Annual Growth Rate (CAGR)

12.47%

CAGR smooths the whole period into one steady annual rate — useful for comparing investments, but it hides the ride. The simple average (16.00%) counts each year equally and can overstate returns when growth is volatile; CAGR is almost always the more honest number.

Simple Average Return (Annual)

16.00%

Total Return Over Period

80.00%

Growth Multiple

1.80x

Starting Value

$10,000.00

Ending Value

$18,000.00

CAGR vs Simple Average

3.53% difference — CAGR is the more accurate metric for investments

The formula

CAGR = (EV/BV)^(1/n) − 1 | Arithmetic Average = (r₁ + r₂ + ... + rₙ) ÷ n

CAGR
Compound Annual Growth Rate
Arithmetic Avg
Simple Average
Volatility Drag
Volatility Drag

Worked example — Starting Value 10000, Ending Value 18000, Time Period (Years) 5, Annual Returns (comma-separated %) 12, -5, 8, 15, 3

Compound Annual Growth Rate (CAGR) = 12.47%

Full explanation ↓

How Average Return Calculator Works

CAGR = (EV/BV)^(1/n) − 1 | Arithmetic Average = (r₁ + r₂ + ... + rₙ) ÷ n

CAGR (Compound Annual Growth Rate) is the year-over-year growth rate that would produce the same final result if returns were constant. The arithmetic average simply sums the annual returns and divides by the number of years. CAGR is always lower than or equal to the arithmetic average in volatile markets — this gap is called "volatility drag." The more volatile the returns, the larger the gap between these two metrics, which is why CAGR is the more honest measure of true investment performance.

CAGR
Compound Annual Growth Rate — The smoothed annualized return that accounts for compounding. If a $10,000 investment grows to $18,000 over 5 years, the CAGR is 12.5% — meaning it grew at 12.5% every year to reach the same endpoint. CAGR is the standard for comparing investment returns across different time periods.
Arithmetic Avg
Simple Average — Sum of annual returns divided by number of years. A portfolio returning +25%, -10%, +15% has an arithmetic average of 10%. But the actual CAGR is lower due to volatility. Financial ads sometimes use the arithmetic average to make returns look better.
Volatility Drag
Volatility Drag — The mathematical gap between arithmetic average and CAGR. A 50% loss requires a 100% gain to break even. The more volatile the returns, the larger the gap between average and CAGR. This is why consistent but moderate returns often outperform volatile high returns over time.
CAGR is always lower than or equal to the arithmetic average in volatile markets -- the gap (volatility drag) reveals the true cost of volatility

How to Use

  1. Choose "Starting & Ending Values" to calculate CAGR from a single investment period — useful for real estate, business investments, or any buy-and-hold asset.
  2. Enter the starting value, ending value, and time period in years.
  3. CAGR is displayed first — the most important metric for investment performance. The simple average is shown for comparison.
  4. Choose "Annual Returns" to enter a list of per-year returns (e.g., 12, -5, 8, 15, 3). This mode also shows best/worst years and volatility statistics.
  5. The calculator shows both CAGR and arithmetic average side-by-side, with the volatility drag clearly visible. The difference between them tells you how volatile your returns were.

Quick Reference

CAGR Formula(Ending Value / Starting Value)^(1/years) − 1
S&P 500 CAGR (1926-2024)~10% nominal, ~7% after inflation
Volatility Drag DefinitionThe gap between arithmetic average and CAGR — wider gap = more volatile returns
Rule of 7272 ÷ CAGR ≈ years to double your money (e.g., 7.2% CAGR doubles in ~10 years)
50% Loss RecoveryA 50% loss requires a 100% gain to return to the starting value — sequence risk is why CAGR matters

Common Uses

  • •Calculate the true compound annual growth rate of an investment portfolio over multiple years including the effect of volatility drag.
  • •Evaluate a fund manager performance claim by comparing the advertised arithmetic average return against the actual CAGR.
  • •Analyze a series of annual investment returns to understand how volatility reduces your effective compounded returns over time.

Understanding the Result

The difference between CAGR and arithmetic average is one of the most misunderstood concepts in investing. If a fund manager says "our average annual return was 12%," check if they mean arithmetic or CAGR. Arithmetic averages are always higher in volatile markets. Example: a portfolio that gains 50% one year and loses 50% the next has an arithmetic average of 0% — but the CAGR is -13.4% because the 50% loss erases more than the 50% gain.

This is why CAGR is the only honest measure of investment performance. For financial planning, always use CAGR when projecting future values. The arithmetic average is useful for comparing fund performance to benchmarks only when you understand it overstates true growth. The "annual returns" mode of this calculator makes the volatility drag visible by showing the gap between CAGR and the arithmetic average for your specific return series.

Worked Examples

Priya in Austin, TX invested $25,000 in a mutual fund 7 years ago and her account is now worth $42,500. She wants to know her true annualized return using the Starting & Ending Values mode.

inputMode = simple · startingValue = 25000 · endingValue = 42500 · years = 7

CAGR = (42,500 / 25,000)^(1/7) − 1 = 7.88%. Her total return over the period was 70.00%, and the growth multiple is 1.70x.

Priya's 7.88% CAGR is the honest measure of her investment's annual performance. While the simple arithmetic average would show 10.00% (70% total return divided by 7 years), CAGR accounts for compounding and is the number she should use when comparing her fund against benchmarks or projecting future growth. The 2.12 percentage point gap between her arithmetic average and CAGR represents volatility drag — the mathematical cost of year-to-year return fluctuations.

Marcus in Chicago tracked his stock portfolio returns over 5 years: +22% in year 1, -8% in year 2, +15% in year 3, +5% in year 4, and -3% in year 5. He enters these as annual returns to see his true performance.

inputMode = annual · returnsInput = 22, -8, 15, 5, -3

CAGR = 5.62% over the 5-year period. Arithmetic average is 6.20%. Best year was +22%, worst year was -8%. 3 of 5 years were positive (60%).

Marcus's arithmetic average of 6.20% makes his portfolio look slightly better than the 5.62% CAGR reveals. The 0.58 percentage point gap is volatility drag — his negative years (-8% and -3%) reduced the base from which his gains compounded. Over decades, a seemingly small annual gap compounds into a meaningful dollar difference. This is why mutual fund advertisements that quote "average annual returns" without specifying whether they mean arithmetic or CAGR can be misleading.

Frequently Asked Questions

Why is CAGR always lower than the arithmetic average?
CAGR accounts for compounding and volatility drag. When returns fluctuate, losses reduce the base from which future gains compound. A 50% gain followed by a 25% loss: arithmetic average is 12.5%, but the CAGR is 6.1%. The gap widens with volatility. This is why consistent but moderate returns often outperform volatile high returns over time. A fund that returns 8% every year beats a fund that returns +30%, -10%, +30%, -10% over the same period, even though the volatile fund has a higher arithmetic average.
Should I use CAGR or arithmetic average for financial planning?
Always use CAGR for projecting future values. The arithmetic average overstates growth because it ignores compounding. For Monte Carlo simulations or retirement planning, use CAGR (or better, a distribution of returns centered on CAGR). The arithmetic average is useful for comparing fund performance to benchmarks only when you are aware it overstates true growth. When a fund says "10-year average return," check whether they mean CAGR or arithmetic — the difference can be 1-3% annually.
What is a "good" CAGR?
Historical S&P 500 CAGR (1926–2024): approximately 10% nominal, 7% after inflation. A 10-year CAGR of 8–12% would be considered solid for equities. Bond CAGRs typically run 2–5%. For any investment, compare its CAGR to an appropriate benchmark (S&P 500 for US equities, Bloomberg Aggregate for bonds). A CAGR below the risk-free rate (Treasury yield) over a long period suggests the investment is not compensating you adequately for the risk taken.
How accurate is this calculator for real-world use?
This calculator uses standard mathematical formulas and provides estimates based on the inputs you enter. For financial decisions, always verify results with a qualified professional and check against official statements or lender-provided figures which may include additional factors not modeled here.

Pro Tips

  • →Always use CAGR, not the arithmetic average, when comparing investment performance or projecting future values. The arithmetic average overstates growth because it ignores compounding math — the gap between them (volatility drag) is the true cost of return fluctuations.
  • →A 50% loss requires a 100% gain just to break even. Before celebrating a big winning year, check your CAGR over the full period — volatile high returns often underperform steady moderate ones over time.
  • →When evaluating a fund manager or financial advisor's performance claim, ask explicitly: "Is that the CAGR or the arithmetic average?" If they cannot tell you the difference, that is a red flag.
  • →For retirement planning projections, use a CAGR of 5-7% (after-inflation) rather than the historical 10% S&P 500 average — volatility drag and sequence-of-returns risk make conservative estimates more realistic for long-term planning.

Limitations to Know

  • •CAGR smooths out year-to-year volatility into a single constant rate. Real investments never grow at a steady rate — sequence-of-returns risk means the order of gains and losses matters enormously, especially when withdrawing money during retirement.
  • •This calculator assumes returns are reinvested and does not account for taxes, management fees, expense ratios, trading costs, or inflation. A stated 8% CAGR might be only 5-6% after fees and taxes in a taxable account.
  • •Past returns do not predict future results. A strong CAGR over the last 5-10 years tells you nothing about the next 5-10 years — reversion to the mean is a powerful force in financial markets.
  • •The CAGR from the simple mode is only valid for lump-sum investments held without additions or withdrawals. If you made contributions or withdrawals during the period, use a money-weighted return (IRR) calculation instead.

Sources

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Cite this calculator

TheCalcUniverse. "Average Return Calculator — CAGR vs. Simple Average (Volatility Drag)." TheCalcUniverse, 2026, https://thecalcuniverse.com/finance/average-return-calculator/. Accessed July 27, 2026.

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