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Average Return Calculator

Find the true average yearly return of an investment, either from a list of yearly returns or from what it was worth at the start and at the end.

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How to use the average return calculator

  1. Choose how you want to calculate: from yearly returns or from a start and end value.
  2. For yearly returns, type each year's return in percent, oldest first, separated by commas or new lines. Use a minus sign for a losing year. Optionally change the starting amount used in the growth table.
  3. For start and end values, enter the starting value, the ending value and the years held. Fractions of a year are fine.

The results show the geometric average (the real compound rate), the arithmetic average, the total return and a year-by-year growth table.

Two kinds of average

Arithmetic mean (r1 + r2 + … + rn) ÷ n Geometric mean ((1 + r1) × (1 + r2) × … × (1 + rn))^(1/n) − 1 Total return (1 + r1) × (1 + r2) × … × (1 + rn) − 1 CAGR (ending value ÷ starting value)^(1/years) − 1

The arithmetic mean is the ordinary average of the yearly numbers. The geometric mean is the single steady rate that would have produced the same end result, which is why it is also called the compound annual growth rate (CAGR). With start and end values you don't need the yearly returns at all: the CAGR formula gives the geometric mean directly.

Worked example

The calculator starts with five yearly returns: 10%, −5%, 15%, 8% and 12%.

  • Arithmetic mean: (10 − 5 + 15 + 8 + 12) ÷ 5 = 40 ÷ 5 = 8.00%.
  • Growth factor: 1.10 × 0.95 × 1.15 × 1.08 × 1.12 = 1.453637, a total return of 45.36%. $10,000 would have grown to $14,536.37.
  • Geometric mean: 1.453637^(1/5) − 1 = 7.77% a year.

Check: $10,000 × 1.0776835 = $14,536.37, the same end value. Growing at a steady 8.00% would have given $10,000 × 1.085 = $14,693.28, more than the investment actually made.

With start and end values instead, $10,000 growing to $18,000 in 5 years is a CAGR of 1.8^(1/5) − 1 = 12.47%. If it took 3.5 years, the CAGR is 1.8^(1/3.5) − 1 = 18.29%.

Why the arithmetic average overstates returns

Losses hurt more than equal gains help. A year of +20% followed by −10% has an arithmetic mean of 5%, but $100 becomes $120 and then $108, a compound rate of just 3.92% a year. The bumpier the returns, the wider the gap: as a rough rule, the geometric mean is about the arithmetic mean minus half the variance of returns.

Yearly returns Arithmetic mean Geometric mean
8%, 8% 8.00% 8.00%
20%, −10% 5.00% 3.92%
50%, −50% 0.00% −13.40%

Use the geometric mean to describe how an investment actually grew or to compare two investments' track records. The arithmetic mean is useful as an estimate of what to expect in a single typical year, which is why some forecasts quote it.

Frequently asked questions

Which average return should I use?

Use the geometric mean (CAGR) for anything about growth over several years, such as comparing funds or projecting a balance. It is the rate that, compounded, reproduces what happened. The arithmetic mean will always be equal or higher, and the gap grows with volatility.

Do the returns need to include dividends?

Yes, for a fair result. Use total returns that include reinvested dividends or interest, not just the change in price. Fund fact sheets usually report total returns; index price levels alone leave out dividends.

How is CAGR different from ROI?

ROI is the total gain over the whole period, regardless of how long it took. CAGR spreads that gain into a yearly rate. A 40% ROI over 3 years is a CAGR of 11.87%; over 10 years it is only 3.42%. The ROI calculator shows both.

What if I added or withdrew money along the way?

Then neither average is exact, because both assume the money stayed put. For an investment with deposits and withdrawals at different times, use the IRR calculator, which works out the money-weighted return from each cash flow.

Related calculators

  • Investment Calculator — Project an investment's end value, or find the contribution, return, starting amount or time a target needs.
  • ROI Calculator — Return on investment as a percentage, the gain or loss, and the annualized ROI from a length or two dates.
  • IRR Calculator — Internal rate of return, NPV and payback period for an investment and a series of yearly or monthly cash flows.
  • Compound Interest Calculator — How a starting balance and monthly contributions grow, with any compounding frequency.

Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.