Understanding your CAGR result
Long-run market averages provide context for a CAGR figure; they describe history, not future performance.
| CAGR (nominal, long-run context) | Historical reference |
|---|---|
| ~10% | Approximate long-run CAGR of US large-cap equities (S&P 500, since 1926) |
| ~5% | Approximate long-run CAGR of US government bonds |
| ~3% | Approximate long-run US inflation (CPI) |
| > 15% sustained | Rare over long periods; typically involves elevated risk or short windows |
- CAGR smooths the path: it says nothing about volatility, drawdowns or the risk taken between the endpoints.
- CAGR assumes no contributions or withdrawals during the period; with intermediate cash flows, a money-weighted return (IRR) is the appropriate measure.
- Nominal CAGR includes inflation; subtracting inflation (or computing CAGR on inflation-adjusted values) gives the real growth rate.
What is CAGR?
Compound annual growth rate (CAGR) is the geometric mean annual growth rate between two values: the single constant rate that, compounded once per year, carries the beginning value to the ending value in the given number of years. It answers the question 'what steady yearly rate is this growth equivalent to?', which makes investments, business revenues and market indices comparable across different holding periods.
CAGR is a smoothed measure by construction. An investment that went from 10,000 to 18,000 over five years has a CAGR of about 12.5% whether it grew steadily or crashed 40% in year two and recovered. Standard investment texts stress this distinction between the geometric mean (which CAGR is) and the arithmetic mean of yearly returns: for any volatile series, the geometric mean is lower, and it is the one that reflects actual wealth accumulation.
CAGR uses only two data points, so it also ignores cash flows in between. If money was added or withdrawn during the period, CAGR over the account balance misstates investment performance; money-weighted measures such as IRR are designed for that case.
How to use this CAGR calculator
- Enter the beginning value — the investment's value or metric at the start of the period.
- Enter the ending value at the end of the period.
- Enter the number of years between the two values (fractional years such as 2.5 are accepted).
- Read the CAGR and the total growth percentage over the whole period.
The CAGR formula
CAGR takes the ratio of ending to beginning value, raises it to the power of one over the number of years, and subtracts one. Total growth is the simple percentage change between the two values.
Worked example: a value growing from $10,000 to $18,000 over 5 years has CAGR = (18,000 ÷ 10,000)^(1/5) − 1 = 1.8^0.2 − 1 ≈ 12.47% per year. Total growth is 80%. Note that 80% ÷ 5 = 16% per year would be wrong — dividing total growth by years ignores compounding and overstates the annual rate.
Common mistakes
- Dividing total growth by the number of years — 80% over 5 years is a 12.47% CAGR, not 16% per year.
- Computing CAGR on an account with deposits or withdrawals during the period, which conflates contributions with performance.
- Comparing a 2-year CAGR with a 20-year CAGR as if equally reliable; short windows are dominated by luck and cycle timing.
- Ignoring inflation when interpreting long-period CAGRs — a 6% nominal CAGR during 3% inflation is about 3% real.
- Averaging yearly returns arithmetically and calling it CAGR; the geometric mean is always lower for volatile series.
الأسئلة الشائعة
How is CAGR calculated?
CAGR equals (ending value ÷ beginning value) raised to the power of 1/years, minus 1. For example, growth from $10,000 to $18,000 over 5 years gives (1.8)^(1/5) − 1 ≈ 12.47% per year. This is the constant annual rate that compounds to the same total growth.
What is the difference between CAGR and average annual return?
The simple (arithmetic) average of yearly returns overstates realized growth whenever returns vary, because losses and gains do not offset symmetrically — a −50% year followed by +50% leaves you at 75% of the start, not 100%. CAGR is the geometric mean, which reflects actual compounded wealth, and it is always at or below the arithmetic average for a volatile series.
What is a good CAGR for an investment?
Context is everything: long-run US equity market CAGR has been roughly 10% nominally (about 6–7% after inflation), and long-run government bonds roughly 5%. A CAGR should be judged against the period's market conditions, the risk taken, and inflation. Sustained CAGRs far above market averages over long periods are rare, and past growth does not indicate future results.
Can CAGR be negative?
Yes. If the ending value is below the beginning value, the CAGR is negative — the constant yearly rate of decline equivalent to the total loss. For example, a fall from $10,000 to $8,000 over 4 years is a CAGR of (0.8)^(1/4) − 1 ≈ −5.4% per year.
Does CAGR work if I added money to the account during the period?
Not as a performance measure. CAGR compares only two snapshots, so deposits inflate the apparent growth and withdrawals deflate it. For accounts with cash flows, money-weighted return (IRR) or time-weighted return — the standard used by fund managers — separate investment performance from the effect of contributions.
المراجع
- Bodie Z, Kane A, Marcus AJ. Investments (12th ed.). McGraw-Hill, 2021 — geometric vs arithmetic average returns.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020 — measures of return.
- CFA Institute. Quantitative methods — measuring returns (time-weighted and money-weighted). cfainstitute.org.
- Federal Reserve Bank of St. Louis. S&P 500 and CPI historical series. FRED Economic Data (fred.stlouisfed.org).
- Dimson E, Marsh P, Staunton M. Triumph of the Optimists: 101 Years of Global Investment Returns. Princeton University Press, 2002.