Compound annual growth rate (CAGR)

Definition (what it is)

CAGR is the constant annualized rate of growth that turns a beginning value into an ending value over a specified multi‑year period, assuming reinvestment and annual compounding. It is a descriptive statistic that “smooths” irregular year‑to‑year changes into a single equivalent annual rate. It applies to any positive-valued quantity (for example, revenue, market size, users, production volume, installed capacity).

Formula

  • CAGR = (Ending value / Beginning value)^(1 / Years) − 1
  • Equivalent growth form: Ending value = Beginning value × (1 + CAGR)^Years
  • Continuous-compounding analogue: r_cont = ln(Ending value / Beginning value) / Years; then CAGR = e^(r_cont) − 1

Purpose and key characteristics

  • Smoothing of variability: Replaces volatile multi-period changes with an equivalent constant annual rate between two endpoints.
  • Time normalization: Annualizes growth, enabling like-for-like comparisons across different time horizons.
  • Scale invariance: Independent of units and magnitudes; applicable to counts, physical output, and monetary measures.
  • Minimal data requirement: Needs only a start value, an end value, and the elapsed time in years (can be fractional).
  • Endpoint sensitivity: Depends only on the beginning and ending values and the period length; ignores intermediate path and volatility.
  • Compounding assumption: Assumes reinvestment and annual compounding; does not depict intra-period fluctuations.

Common uses

  • Performance reporting and benchmarking for companies, products, markets, and portfolios.
  • Market sizing, demand forecasting, and capacity planning.
  • Evaluating adoption rates of technologies, platforms, or customer bases.
  • Communicating long-term trends to stakeholders and comparing alternatives with different durations.

Examples

  • Growth example: A metric rises from 80 to 320 over 4 years. CAGR = (320/80)^(1/4) − 1 = 41.4%.
  • Volatility vs. smoothing: Starting at 100, a series falls 20% in year 1 (to 80) and rises 25% in year 2 (back to 100). AAGR (arithmetic average) = (+2.5%), but CAGR over 2 years = (100/100)^(1/2) − 1 = 0%. CAGR correctly reflects no net growth.

Related terms and distinctions

  • Geometric mean growth rate: Closely related; with equally spaced annual observations, CAGR equals the geometric mean of (1 + annual returns) minus 1.
  • Average annual growth rate (AAGR): The arithmetic mean of period growth rates; ignores compounding and can mislead when volatility is high.
  • Annualized return: Often used interchangeably with CAGR when compounding is assumed annually.
  • Internal rate of return (IRR/XIRR): An annualized rate based on a full series of dated cash flows; unlike CAGR, IRR uses all interim flows rather than just endpoints.

Practical notes

  • Positive values required: CAGR is defined when both beginning and ending values are positive. It is not suitable if values are zero, negative, or cross zero during the period.
  • Declines: Ending values below beginning values yield a negative CAGR (a compounded rate of decline).
  • Partial years and non-annual data: Use exact elapsed time in years. For monthly data, for example, Annualized CAGR = (Ending/Beginning)^(12/Months) − 1.
  • Comparability: State the time horizon explicitly; CAGRs from different durations are not directly comparable without context.
  • Real vs. nominal: For monetary values, specify whether figures are inflation-adjusted. Mixing nominal and real values distorts CAGR.
  • Small-base effects: Very high CAGRs from tiny starting values may not be indicative of sustainable growth.
  • Aggregation: To compare segments, compute overall CAGR from aggregated start and end totals; simple averages of segment CAGRs can mislead.
  • Use with other metrics: Pair with volatility measures, interim growth profiles, or scenario analysis; CAGR alone conceals path and risk.

Rules of thumb

  • Doubling time at a constant CAGR: Years to double ≈ ln(2) / ln(1 + CAGR). (For small rates, 72/CAGR% is a quick approximation.)

Limitations

CAGR is not a forecast model and does not capture variability, seasonality, inflection points, or constraints (such as capacity limits). It summarizes endpoints under an exponential growth assumption; when growth is logistic, cyclical, or highly irregular, complementary analyses are essential.