Average return calculator (arithmetic and geometric)
Enter each period’s return (or the successive values of an investment). The geometric mean tells what you really earned per period; the arithmetic mean overstates it as soon as returns vary.
Result
6.61%Geometric average return per period
- Arithmetic average return per period
- 7%
- Annualized return (compound)
- 6.61%
- Total cumulative return
- 29.16%
- Standard deviation of returns
- 10.61%
- Number of periods
- 4
Inputs
- I am entering
- Returns in %
- List
- 10; -5; 20; 3
- Length of one period
- One year
How it is calculated
Arithmetic = sum of returns ÷ number of periods (plain average, no compounding).
Result
Geometric average return per period
- Arithmetic average return per period
- 7%
- Annualized return (compound)
- 6.61%
- Total cumulative return
- 29.16%
How it is calculated
- Arithmetic = sum of returns ÷ number of periods (plain average, no compounding).
- Geometric = (Π (1 + r))^(1 ÷ n) − 1: the steady return that gives the same end result.
- Annualized = (1 + geometric)^(periods per year) − 1. Total = Π (1 + r) − 1.
- With values, each return = value ÷ previous value − 1.
Example
Yearly returns of 10%, −5%, 20% and 3%: geometric mean 6.61% versus 7.00% arithmetic, 29.16% in total, standard deviation 10.61% over 4 periods.
Good to know
- Time-weighted return: money added or taken out along the way is not counted (this is not a money-weighted return).
- Past performance does not predict future performance.
Frequently asked questions
What is this tool used for?
Enter each period’s return (or the successive values of an investment). The geometric mean tells what you really earned per period; the arithmetic mean overstates it as soon as returns vary.
How is the result calculated?
Arithmetic = sum of returns ÷ number of periods (plain average, no compounding).
What should I check before using the result?
Time-weighted return: money added or taken out along the way is not counted (this is not a money-weighted return).