Geometric Return Calculator

Compute the compounded average return across several periods, the only average that reconciles values.

About Geometric Return Calculator

Only the geometric mean reconciles the start and end values of a volatile series. The gap to the arithmetic mean grows roughly with half the variance, which is why volatile assets compound more slowly than their average return suggests. A fund advertising a 12% average annual return may have compounded at 9%, and it is the lower figure that determines what your account is worth.

Formula

Geometric Return

Geometric return = (∏(1 + rᵢ))^(1/n) − 1

geometric return: The constant rate that would produce the same final value
volatility drag: Amount by which the arithmetic average overstates compounded growth

Worked example

With the default values below, Geometric Return Calculator returns Geometric Average Return of 7.444%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Year 1 returnaccepts -100–300 %: 15 %
Year 2 returnaccepts -100–300 %: -10 %
Year 3 returnaccepts -100–300 %: 22 %
Year 4 returnaccepts -100–300 %: 8 %
Year 5 returnaccepts -100–300 %: 5 %

Results

Geometric Average Return: 7.444%
Arithmetic Average Return: 8.000%
Cumulative Return: 43.19%
Drag From Volatility: 0.556%
Growth Multiple: 1.4319

Step by step

1Values used
2Geometric Return
3Geometric Average Return= 7.444
4Arithmetic Average Return= 8.000
5Cumulative Return= 43.19
6Drag From Volatility= 0.556
7Growth Multiple= 1.4319

Assumptions and limits

The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Geometric Return calculated?

Geometric return = (∏(1 + rᵢ))^(1/n) − 1 Only the geometric mean reconciles the start and end values of a volatile series. The gap to the arithmetic mean grows roughly with half the variance, which is why volatile assets compound more slowly than their average return suggests.

Why does Geometric Return matter?

A fund advertising a 12% average annual return may have compounded at 9%, and it is the lower figure that determines what your account is worth.

What values do I need to enter?

This calculator takes 5 inputs: Year 1 return, Year 2 return, Year 3 return, Year 4 return, Year 5 return. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.