How the Average Return Calculator works.
arithmetic average = (r₁ + r₂ + r₃) ÷ 3r₁, r₂, and r₃ are annual percentage returns; compounded return multiplies their growth factors.
Worked example
Returns of 8%, -4%, and 12% have a 5.3333% arithmetic mean.
What the result means
Arithmetic return describes the average annual observation; compounded return describes growth.
Edge cases
A period loss below -100% is impossible; exactly -100% produces a zero growth factor and a -100% compounded annual return.
Arithmetic average versus compounded return
The primary result is the arithmetic mean of exactly three period returns: add the three percentages and divide by 3. The separate compounded annual return converts each percentage to a growth factor, multiplies the three factors, and takes the cube root. Use the arithmetic mean to summarize the three observations; use the compounded figure to describe the constant annual rate that would produce the same ending growth over those three periods.
Worked three-period example
For returns of 8%, −4%, and 12%, the arithmetic mean is (8 − 4 + 12) ÷ 3 = 5.3333%. Compounding uses 1.08 × 0.96 × 1.12 = 1.161216, then takes the cube root and subtracts 1, giving about 5.1085% per period. The compounded rate is lower because gains and losses multiply rather than cancel symmetrically.
From percentages to growth factors
Convert each period return r to 1 + r/100 before multiplying. A 12% gain becomes 1.12, a 4% loss becomes 0.96, and a zero return becomes 1. Do not average account balances, add growth factors, or enter decimal rates such as 0.08 when the field expects 8 for 8%. The three entries should describe equal-length consecutive periods on the same return basis.
Volatility, ordering and interpretation
A gain followed by an equal percentage loss does not restore the starting value: +20% then −20% produces 1.20 × 0.80 = 0.96, a 4% total loss. With no deposits or withdrawals, changing the order of the same three returns does not change their final product or compounded annual return, although it changes the path, interim balance and drawdown. The arithmetic mean alone does not capture that volatility drag.
Loss boundaries and numeric checks
A period return cannot be below −100% because an investment value cannot lose more than its entire starting amount without additional liability. An exact −100% period is accepted: its zero growth factor makes the three-period compounded annual return −100%, even if the other two entered returns are positive. Blank, non-finite and out-of-range numeric inputs are rejected instead of producing an exact-looking result.
Scope, cash flows and decision limits
This calculator assumes three equal periods and no deposits, withdrawals, fees, taxes, currency effects or changing measurement basis between them. It does not calculate money-weighted return, internal rate of return, benchmark-relative performance, risk, inflation-adjusted return or future performance. Use dated portfolio cash flows and official statements when contributions, withdrawals or reporting standards matter, and do not treat either average as an investment recommendation or guarantee.
What this calculator does not include.
Investment results exclude fees, taxes, deposits, withdrawals, and future uncertainty.
Average Return Calculator questions.
What is the difference between arithmetic average and compounded annual return?
The arithmetic average adds the three entered percentage returns and divides by 3. The compounded annual return multiplies their growth factors and finds the constant per-period rate that would produce the same three-period ending growth.
Why is the compounded return often lower than the arithmetic average?
Positive and negative returns multiply against different account values, so volatility creates drag. For 8%, −4%, and 12%, the arithmetic average is 5.3333%, while the equivalent compounded annual return is about 5.1085%.
Should I enter 8 or 0.08 for an 8% return?
Enter 8. Each field expects a percentage value, and the calculator converts it internally to the growth factor 1.08. Entering 0.08 would mean 0.08%, not 8%.
What happens if one period loses exactly 100%?
An exact −100% return is accepted and creates a zero growth factor, so the compounded annual return is −100% regardless of positive returns in the other two periods. A return below −100% is rejected.
Does changing the order of the three returns change the answer?
Not when there are no deposits or withdrawals: the same three growth factors have the same product in any order. The path, interim balances and drawdowns can still differ, so the calculator does not describe sequence risk.
Does this calculator include deposits, fees, taxes or risk?
No. It assumes three equal periods with no cash flows and reports only arithmetic and compounded average returns. It does not calculate money-weighted return, fees, taxes, inflation, benchmark performance, volatility, drawdown or future results.