A walkthrough, end to end.
- 1
Enter a series of annual percentage returns (positive and negative).
- 2
The calculator returns the arithmetic mean, geometric mean (CAGR), and the variance drag (the gap between them).
- 3
Use geometric mean for honest multi-year compound returns; arithmetic only for single-period expectations.
Arithmetic vs. geometric
Arithmetic mean = sum / n. Geometric mean = (Π(1 + rᵢ))^(1/n) − 1. Geometric is always ≤ arithmetic; the gap (variance drag) grows with volatility. CAGR (compound annual growth rate) is just another name for geometric mean.
What you can do with this.
Stock fund performance
Five years of returns: +20%, −10%, +30%, −15%, +25%. Arithmetic average = +10%/yr. Geometric (CAGR) = +8.7%/yr. The geometric is what you actually earned — arithmetic overstates by 1.3%/yr because of volatility.
S&P 500 long-term
S&P 500 since 1928: ~10% arithmetic, ~9.7% geometric. Modest gap because index volatility is moderate. Individual stocks have much wider gaps — small-cap value can be 3%+ apart.
Volatility drag
A stock that goes +50% then −50% loses 25% (gain to $1.50 → $0.75). Arithmetic average is 0%; geometric is −13.4%. Volatility itself reduces compound returns — a counter-intuitive math reality.
When to use each
Geometric (CAGR): for actual realized returns over time. Arithmetic: for expected return of a single random period. Mixing them up overstates retirement projections by 1–3% per year.
Mutual fund advertised returns
Funds typically advertise time-weighted geometric (CAGR) — properly. Beware of any advertised 'average return' that's actually arithmetic — investing prospectuses sometimes blur the line.
Comparing fund performance
Run the calculator with each fund's annual returns over the same period. Compare on geometric mean for fair head-to-head. Adjust further for fees and tax for true after-cost comparison.
Predicting future performance
Past geometric mean is a starting point but not a forecast. Most equity returns are mean-reverting at long horizons; chase past winners with caution.
Average return calculator 2026 — what's current
S&P 500 has delivered ~10.5% nominal arithmetic / ~9.5% geometric over rolling 30-year periods. Current Vanguard 10-year forward forecast: 4–6% real for US equities — well below historical norms.
Frequently asked.
Mathematical inequality: AM ≥ GM with equality only when all values are identical. Volatility creates the gap — bigger swings = bigger gap. Even the upside of high volatility can't compensate.
CAGR is the GEOMETRIC average — what you actually earned compounded annually. The 'average annual return' phrase is ambiguous; assume CAGR unless explicitly stated otherwise.
Subtract fund expense ratio from each year's return before computing average. A 1% expense ratio reduces 30-year terminal wealth by ~25% — that's why low-cost index funds dominate.
No. Calculations run entirely in your browser.