Two different averages
Suppose an investment goes up 50% one year and down 50% the next. The simple average return is 0%: (50 − 50) ÷ 2. But $100 becomes $150, then $75. You lost 25%. Both numbers are correct; they answer different questions. The simple (arithmetic) average describes a typical year. The compounded (geometric) average describes what actually happened to your money.
Why losses hurt more
A 50% loss needs a 100% gain to get back to even. Percentages apply to whatever balance you have at the time, so a drop shrinks the base the next gain works on. That's why the compounded average is always at or below the simple average, and the gap grows the more returns bounce around.
The formula
Compounded average = (product of (1 + each return))^(1 ÷ number of years) − 1. For +50% and −50%: (1.5 × 0.5)^(1/2) − 1 = −13.4% a year. Multiply your starting amount by (1 + that rate) once per year and you land exactly on the real ending value.
What history looks like
Using S&P 500 total returns (dividends included) from 1928 through 2025, the simple average is about 11.85% a year and the compounded average about 10.02%. After inflation, the compounded figure is about 6.78%. Out of 98 years, 26 were negative. The 2000–2009 preset shows a stretch where the simple average was positive but the money ended lower than it started.
Why this matters for calculators
When someone plugs "the market averages 10%" into a growth calculator, which 10% they mean matters. A steady-rate calculator should use the compounded figure, since that's the rate that reproduces real ending values. Even then, a steady rate hides the order of returns, which matters a lot when money is going in or coming out.
Use your own numbers
Paste any list of yearly returns, separated by commas, and the page shows both averages, the ending value, and how many years were up. Past returns don't predict future returns.
Sources
Last reviewed: Sep 28, 2026