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Financial Planning

Annualized Return Calculator

Turn a series of yearly returns into the geometric (annualized) average return and compare it with the simple average.

Your inputs

Results

Annualized (geometric) return

6.736%

Simple average of returns
7%
Cumulative return
29.789%
Growth of 1 unit
1.2979

✓Exact calculation — rounded only for display

Inputs are never added to links for financial, salary or health calculators.

What this calculator does

If an investment gains 50 % one year and loses 50 % the next, the simple average is 0 % — but you have actually lost 25 %. The geometric average captures this compounding effect.

Formula and method

Growth = Π (1 + rₖ); Annualized = Growth^(1/n) − 1; Simple average = Σ rₖ ÷ n

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Yearly returns in % (e.g. 10, -5, 15, 8): 10, -5, 15, 8

Results

  • Annualized (geometric) return: 6.736%
  • Simple average of returns: 7%
  • Cumulative return: 29.789%
  • Growth of 1 unit: 1.2979

How to read the results

The annualized return is the constant yearly rate that would have produced the same final result. It is always at or below the simple average when returns vary.

Assumptions and limitations

  • This is a time-weighted measure; it ignores the size and timing of deposits.

Financial results are estimates based on the inputs and assumptions shown. They are not financial advice; confirm figures with your lender, provider or a qualified adviser before making decisions.

Questions

Which average do fund reports use?

Performance figures labelled “annualized” or “average annual return” are geometric averages like this one.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Because this calculator can involve personal financial or health details, your inputs are never added to share links or saved to history. Privacy policy