Average Return Calculator
Compare arithmetic, geometric, and compound annualized returns for a series of investment periods.
Return series
Arithmetic average return:
Geometric average return:
Compound annual growth rate:
Final value:
Arithmetic mean shows simple average return, geometric average reflects compound performance over the periods.
Arithmetic vs. geometric average — why they differ
The arithmetic average simply adds up each period's return and divides by the number of periods — easy to compute, but it can overstate real performance because it ignores compounding. The geometric average (and the closely related CAGR) instead compounds each period's return together and finds the single steady rate that would produce the same final value — this is the number that actually matches your account's growth.
Frequently asked questions
Why is the geometric average always lower than the arithmetic average (when returns vary)? This is a mathematical consequence of volatility — a loss in one period requires a proportionally larger gain in another just to break even (e.g., a 50% loss needs a 100% gain to recover), which drags the compounded (geometric) result below the simple average of the raw percentages.
Which number should I use to judge my investment performance? Use the geometric average or CAGR — it reflects what actually happened to your money, while the arithmetic average can be misleadingly optimistic for volatile return series.
Is CAGR the same as the geometric average here? For this fixed-period return series, yes — both measure the constant annual rate that compounds to the same final value over the same number of periods.