CAGR Explained: Definition, Formula, and Calculation

Compound Annual Growth Rate (CAGR) is the single, smoothed annual rate that takes you from a beginning value to an ending value over a multi-year span. Think of it as the geometric average return that “turns the crank” once per year to replicate the same total growth you actually experienced. Investors and operators use CAGR to compare products, funds, and business lines with uneven year-to-year results, and to sanity-check long-term plans against realistic compounding. It’s easy to compute with a calculator or spreadsheet, but it’s also easy to misuse if you ignore volatility, cash flows, or timing.

What CAGR measures (and why pros prefer it to simple averages)

CAGR tells you the constant annual rate that would transform a beginning value into an ending value over a specified number of years. Because it’s a geometric mean, it handles ups and downs realistically — unlike an arithmetic average that can overstate long-run growth when returns are volatile. If an investment doubles and then halves, the arithmetic average return looks fine, but the geometric average (and value) say growth is actually zero. That’s why portfolio literature and investor primers emphasize geometric averages (CAGR) for multi-period results.

Another reason practitioners like CAGR: it’s comparable across assets with jagged paths. Two funds can show the same end-to-end growth via very different routes; CAGR strips the path and reports the one rate that gets you there. The trade-off is that you lose information about volatility and sequence of returns — two portfolios with identical CAGR can carry very different risks, especially during withdrawals. Use CAGR for quick comparability, then add risk/context metrics when decisions hinge on path behavior.

Remember that CAGR is not limited to investments. Operators use it for revenues, users, or subscribers, smoothing noisy growth to guide planning and to communicate long-term progress without month-to-month distractions. The interpretation stays the same: “If growth had been steady, it would have been r% per year.”

CAGR formula, step-by-step examples, and spreadsheet shortcuts

The standard formula links beginning value (BV), ending value (EV), and total years (N):

This is just compound interest algebra rearranged to solve for the rate that bridges BV to EV over N periods. Investor education and finance references present the same expression.

Worked example. You invest $10,000 and it grows to $16,000 in five years. CAGR = (16,000 ÷ 10,000)^1/5 − 1 ≈ (1.6)^0.2 − 1 ≈ 9.86% per year. That single number reproduces the same five-year growth without revealing the path.

Excel & Google Sheets. Two simple approaches:

• =RRI(nper, pv, fv) — returns the equivalent annual compound rate (i.e., CAGR).
Example: =RRI(5,10000,16000) → 0.0986 (9.86%).

• =POWER(fv/pv, 1/nper)-1 — the explicit formula using POWER. Both methods are widely documented.

Units and signs. Keep BV and EV in the same currency/units. In spreadsheet financial functions, cash-flow sign conventions matter; with RRI you typically pass positive values for PV and FV to get a positive growth rate.

Partial years. If growth spans 3.5 years, use N = 3.5. If there are dated cash flows in between (deposits/withdrawals), switch to an IRR/XIRR approach because CAGR assumes a simple start-to-finish bridge with no interim cash flows.

When to use CAGR (and when not to): limits, path risk, and alternatives

Use CAGR to compare end-to-end growth across options with similar cash-flow patterns (no interim additions/withdrawals) or to communicate long-horizon progress without path noise. It’s especially handy for revenue/user growth and for funds where you only know start and end values.

Don’t rely on CAGR alone for withdrawal planning, risk assessment, or funds with significant flows. CAGR ignores volatility and the sequence of returns. A retiree experiencing poor returns early can run out of money despite an acceptable long-run CAGR; risk education materials highlight this “sequence risk” and show why path matters during drawdowns.

Prefer IRR/XIRR when timing matters. IRR handles cash-flow timing by solving for the discount rate that sets the present value of dated flows to zero; XIRR uses actual dates. CAGR, by contrast, collapses everything into a single multi-year bridge. Guides comparing CAGR and IRR explain when each is appropriate and why they can differ markedly for the same project.

Arithmetic vs geometric averages. For multi-period returns, the geometric mean (CAGR) better represents the actual growth of money than the arithmetic mean, which can overstate terminal value under volatility. Practitioner notes and CFA literature discuss the distinction and the bias that arises from using arithmetic averages to forecast compounded outcomes.

Context still matters. Two investments can share the same CAGR but have different risk profiles (dispersion, drawdowns). Pair CAGR with variance or standard deviation, and, for withdrawal contexts, with drawdown/sequence risk metrics.

CAGR in practice: quick checks, common errors, and guardrails

Quick checks. If N = 1, CAGR equals the period return. If EV < BV, CAGR is negative; the same formula applies. If EV = 0, CAGR is −100%; if BV = 0, CAGR is undefined — you cannot compute growth from zero capital. Investor primers reinforce that CAGR is just the compounding inverse of the usual future-value formula.

Common errors. Mixing nominal and real values (inflation-adjust first if you want real CAGR). Using arithmetic averages of annual returns in projections (use geometric). Ignoring partial periods (use fractional N or date-based XIRR). Failing to reflect fees or taxes when comparing products (compute on net values where possible).

Implementation guardrails. When demonstrating compounding to stakeholders, link to a simple compound-interest calculator so non-technical readers can sanity-check inputs. Regulators maintain public tools suitable for education and planning; spreadsheets replicate the same math.

Automation. In Excel/Sheets models, wrap RRI or POWER in a helper function and standardize inputs (beginning value, ending value, years). Reference the function documentation if colleagues question the calculation.