CAGR Calculator
Compute the compound annual growth rate from any start/end value pair. Returns CAGR, doubling time, total return, and forward projections at 1, 3, 5, 10, and 20 years.
Results
$10,000 → $50,000 over 10 yearsForward projections (at this CAGR)
| Years from end value | Projected value | Multiple of start |
|---|---|---|
| +1y | $58,731 | 5.9× |
| +3y | $81,033 | 8.1× |
| +5y | $111,803 | 11.2× |
| +10y | $250,000 | 25.0× |
| +20y | $1,250,000 | 125.0× |
The compound annual growth rate of 17.46% means $1 grew to $ 5.00 over 10 years — strong — well above broad market averages. At this rate, the investment doubles every 4.31 years.
Frequently asked questions
Why CAGR matters
When someone tells you a portfolio "averaged 12% returns over 20 years," they almost always mean CAGR — the smoothed compound rate, not the arithmetic average of year-by-year returns. The distinction is fundamental: CAGR is the rate at which compounding actually moved your money, while arithmetic average ignores the math of how returns interact with each other.
The arithmetic-vs-geometric trap
A two-year sequence of +50% then -50% has an arithmetic average of 0%. But $1 going up by 50% and then back down by 50% leaves you with $0.75 — a -25% total return, or about -13.4% CAGR. The arithmetic average says you broke even; the CAGR tells you the actual truth. For any multi-period analysis, only CAGR matters.
The gap between arithmetic mean and CAGR widens with volatility. For a 10% expected return:
- 0% volatility: arithmetic = CAGR = 10%
- 15% volatility: arithmetic 10%, CAGR ~8.9%
- 30% volatility: arithmetic 10%, CAGR ~5.5%
- 50% volatility: arithmetic 10%, CAGR ~-2.5%
This is "volatility drag" — high-vol assets compound much worse than their arithmetic averages suggest. It's why levered ETFs (3x daily) underperform 3x of the underlying index over multi-year periods.
Doubling time and the Rule of 72
At a constant CAGR, the time to double the investment is ln(2) / ln(1 + CAGR). The famous Rule of 72 approximates this as 72 / CAGR_percent — accurate to within a few percent for CAGRs between 4% and 25%. So 7.2 years to double at 10%, 4.8 years at 15%, 3 years at 24%. The calculator returns the exact value.
Limitations honest people acknowledge
- CAGR ignores intermediate volatility. A 10% CAGR over 20 years could come from a smooth ride or from a roller coaster. CAGR doesn't care; your nervous system does.
- CAGR is not predictive. Past CAGR tells you what happened, not what will happen. Forward-looking CAGR for US equities is widely estimated at 6-7% real, not the ~10% historical figure.
- CAGR ignores cash flows. If you contributed money or withdrew during the period, CAGR is misleading. Use IRR (
/v1/tvm/irr) instead, which handles arbitrary cash flow timing. - Survivorship bias amplifies reported CAGRs. The funds and stocks you can look up today are the ones that survived. Failed investments don't appear in datasets, biasing all backward-looking averages upward by 1-3% in equity studies.
Related calculators
For risk-adjusted return analysis, see the Sharpe ratio calculator. For investments with periodic cash flows, the API exposes IRR at /v1/tvm/irr (the QuantOracle API docs). For projecting forward outcomes with realistic uncertainty (instead of constant-CAGR extrapolation), use the Monte Carlo simulation calculator — same starting value, but with volatility baked in to give a distribution of possible outcomes rather than a single line.