The formula
How it works
Average a series of investment returns the right way. Enter each period’s percentage return and the calculator gives both the simple average and the geometric average — the compound rate that actually reflects how money grew.
FAQ
Why are there two averages?
The simple (arithmetic) average just adds the returns and divides, which overstates real growth when returns swing up and down. The geometric average compounds them and reflects what you actually ended up with. For volatile returns the geometric figure is always the lower, and more honest, one.
When does the difference matter most?
The more the returns vary, the bigger the gap. A steady 5% every year has equal simple and geometric averages, but a +50% year followed by a −50% year averages 0% arithmetically yet leaves you down 25% — a −13.4% geometric average. For real investments, always compare on the geometric basis.
Is the geometric average the same as CAGR?
Yes — when the periods are equal-length years, the geometric average return is exactly the compound annual growth rate. It answers the same question: what single steady rate would have produced the same total growth.
Can I enter a loss year with a negative return?
Yes, just enter it as a negative percentage like −20. The calculator handles losses correctly in the compounding, though a loss of 100% or more would make the growth factor zero or negative, which is not meaningful.
Why is the geometric average always lower or equal, never higher?
This follows from a mathematical inequality between arithmetic and geometric means — compounding penalizes variability, so any swing away from a constant return can only pull the compounded result down relative to the simple average.
How does volatility relate to the gap between the two averages?
The gap is roughly half the variance of the returns, so a higher standard deviation of returns widens the difference between the arithmetic and geometric averages. This is why comparing volatility alongside the geometric average gives a fuller risk picture.
Do the periods have to be full years?
No — you can enter returns for any consistent period, such as months or quarters, as long as every entry covers the same length of time. The geometric average will then be the average return per period you entered, not automatically an annual figure.
About the average return calculator
This calculator averages a series of periodic investment returns and shows why the method matters. It reports the simple arithmetic average, which most people reach for, alongside the geometric average — the compound annual growth rate that reflects how an amount actually grew across the whole period. Seeing both makes clear how volatility quietly erodes returns, a fact that catches out many investors.
How to use it
Enter each period’s return as a percentage, separated by commas — for example 10, −5, 8, 12, 3. The calculator returns the arithmetic average, the geometric average and the total compounded growth. For that series the simple average is 5.6%, but the geometric average, which is what your money really earned, is a little lower at about 5.4%.
The formula
The geometric average is : each return is turned into a growth factor, all the factors are multiplied together, and the -th root is taken. The arithmetic average is the plain mean, . The two agree only when every return is identical; otherwise the geometric average is always lower.
Where it is used
Investors use it to summarise a fund’s or portfolio’s past performance honestly, since quoting the arithmetic average can flatter a volatile record. Analysts use the geometric mean to compare investments over the same span, and it is the basis of the compound annual growth rate (CAGR) reported in fund fact sheets. Anywhere returns compound over time, the geometric average is the meaningful one.