Average Return Calculator

Compute arithmetic average, geometric average (compounded per period), and CAGR. Works from a list of period returns or from starting/ending values.

How to Use

  1. Select an input mode: Period Returns (e.g., +5%, −2%) or Start/End Values.
  2. Enter your data. For returns, you can paste a list (one per line).
  3. Pick a frequency if you want annualized figures.
  4. Open Show Work to see formulas and step-by-step calculations.
Inputs

No uploads. Calculations run in your browser. Share links are optional and manual.

Enter returns as percent or decimal values. Mixed formats are not recommended.
Used to annualize the geometric average (optional).
Weights affect arithmetic average only. Geometric average always compounds returns.
Tip: You can paste from Excel/Sheets (one column). Commas are also accepted.
What each metric means
  • Arithmetic average: simple average of period returns (does not compound).
  • Geometric average: compounded per-period average return that matches the same total growth.
  • CAGR: annualized growth rate between a start value and end value over time.
All results are shown as percentages unless noted.
Data tips
  • For returns mode, use total returns per period if possible (price + dividends).
  • Geometric average requires all periods to have 1 + r > 0.
  • Use values mode for a clean CAGR from start/end values.
Show Work (step-by-step)
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Work is shown in decimals (e.g., 0.05 = 5%) for consistency.

Formulas

  • Arithmetic average (simple): r̄ = (1/n) · Σ rᵢ
  • Arithmetic average (weighted): r̄w = (Σ wᵢ rᵢ) / (Σ wᵢ)
  • Geometric average (per period): g = (Π (1 + rᵢ))^(1/n) − 1
  • Annualized geometric average: gₐ = (1 + g)^(p) − 1 where p = periods per year
  • CAGR: CAGR = (End/Start)^(1/Years) − 1
This tool reports the geometric average per period and (if frequency is set) annualized geometric average in Show Work.

FAQ

Which average should I use?

Arithmetic average is common for estimating expected return. Geometric average is better for describing realized compounded performance over time.

Why can arithmetic average be higher than what I actually earned?

Because arithmetic average ignores compounding and volatility drag. Geometric average reflects the actual compounded outcome.

What if a return is −100%?

A −100% period means the value went to zero; geometric average and CAGR become undefined beyond that point.

Tool Info

Last updated:

Updates may include improved parsing, additional frequency options, and edge-case handling.