How to Calculate CAGR: Formula, Examples and Key Limits

What CAGR answers

CAGR turns a beginning value and an ending value into one constant annual growth rate. It answers: what steady yearly rate would connect these endpoints over this duration? It does not tell you what happened in each intervening year.

Use it to describe historical growth or compare like-for-like periods. A result is a mathematical summary, not an expected future return.

Beginning value, ending value and years

The beginning value is the positive amount at the start of the measurement period. The ending value is the amount at its end, measured consistently in the same currency and on the same basis. Duration is the elapsed interval between them, not the number of calendar labels shown on a chart.

For this tool, 12 months equals one year. A fractional year is accepted directly. The calculator does not infer actual dates, leap years or a day-count convention. For annual observations from the end of year one to the end of year six, there are five annual intervals.

When an endpoint growth rate is useful

CAGR can summarize an investment with no external cash flows, or the change in a positive business measure such as revenue. A revenue CAGR describes revenue growth; it is not an investment return or a profitability measure.

Compare the same kind of measure over comparable periods and account for differences in risk. Two investments can have identical endpoint CAGR despite very different drawdowns or volatility. A growth rate alone is insufficient to choose between them.

The CAGR formula

Divide the ending value by the beginning value to obtain the growth multiple. Raise that multiple to the reciprocal of elapsed years, subtract one, then multiply by 100 to report a percentage.

This is the geometric annual equivalent of endpoint growth. The formula follows by rearranging ending = beginning × (1 + annual rate)^years. For zero ending value and positive beginning value, the supported endpoint result is a complete loss of −100%.

CAGR (%) = ((E / B)^(1 / n) − 1) × 100

Worked examples: growth, decline and six months

Consider 10,000 increasing to 16,105.10 over five years without interim cash flows. These hypothetical amounts can be in any one currency; the percentage is unchanged by the currency label.

The total change is 61.051%, while the annual compound equivalent is 10%. Dividing the total percentage by five would give 12.2102%, which does not reproduce the endpoint through compounding.

For a decline from 10,000 to 8,000 over two years, CAGR = (0.8^(1/2) − 1) × 100 ≈ −10.5572809%. For 100 growing to 110 in six months, annualizing gives (1.1^2 − 1) × 100 = 21%, although the observed six-month change is only 10%. Extending that short-term rate into the future is an additional assumption, not an observation.

1. Growth multiple = 16105.10 / 10000 = 1.61051.
2. Annual factor = 1.61051^(1/5) = 1.1.
3. Annualized rate = (1.1 − 1) × 100 = 10%.
4. Check: 10000 × 1.1^5 = 16105.10.

How to use the calculator

Start with consistent endpoint valuations. If contributions or withdrawals occurred, check the cash-flow box: this tool will explain why it cannot report an investment return for that scenario. Do not simply subtract a net contribution and assume its timing does not matter.

1. Select a display market; this only changes formatting.
2. Enter beginning value, ending value and elapsed duration. Choose years or months.
3. Check the cash-flow assumption. If interim flows occurred, stop and choose an appropriate return method.
4. Read CAGR alongside total change and change in value. Inspect warnings and rounding.
5. Use Clear values to remove the scenario; no account or financial-input storage is used.

Read annualized and total change together

The annualized percentage describes the constant equivalent per year. Total change describes the entire interval: (ending / beginning − 1) × 100. Change in value is ending minus beginning, expressed in your chosen display currency.

A negative CAGR represents a shrinking positive endpoint. A zero CAGR means equal endpoints; it does not prove that value was stable between them. A positive CAGR can coexist with large losses during the period. Examine the underlying path and context separately.

Cash flows, reinvestment and valuation assumptions

For investment-return interpretation, the model assumes no external deposits or withdrawals between the valuations. Distributions paid out rather than retained in the measured ending wealth can make a price-only CAGR omit part of the investment outcome. Do not call a price CAGR a total-return figure without accounting consistently for distributions.

The tool does not automatically reinvest income or adjust for fees, taxes, inflation or foreign exchange. If an endpoint already reflects a charge, the rate reflects that valuation basis. State that basis when sharing an interpretation; do not deduct the same cost twice.

Supported values and precision limits

Beginning value must be between 0.000000000001 and 10^30. Ending value may be zero or within that positive range. Duration must be 0.01–1,000 years or 0.12–12,000 months. Inputs use an ungrouped decimal point with at most 12 fractional places. Zero or negative beginning values and negative ending values are outside this model.

The engine uses 50 significant decimal digits with half-even rounding and bounded exponentiation. Extremely high annualized results are rejected. A positive endpoint whose annualized decline is indistinguishable from −100% at supported precision returns an explicit error rather than a false total-loss result. Display rounding is separate: choose two, four or six percentage decimal places. Tiny nonzero rates remain visible; near-total declines are labelled greater than −100%.

Annualizing less than one year can amplify a short-lived change. Months are converted by dividing by 12; exact-date investment returns need a stated date convention and an appropriate model. This calculator neither imports cash-flow files nor solves IRR/XIRR, so convergence and multiple-root analysis are not applicable here.

Common mistakes to avoid

Counting observations instead of intervals, mixing currencies, swapping the endpoints and treating total return divided by years as CAGR all change the meaning or arithmetic. Check these before interpreting a surprising output.

Deposits can increase the ending balance without representing investment performance. For example, 10,000 plus a 5,000 deposit can end at 15,000 even when there is no investment gain. Endpoint CAGR would wrongly suggest growth if described as investment return. Cash-flow amounts and dates matter; use a suitable money-weighted or time-weighted method instead.

CAGR versus arithmetic averages and cash-flow returns

Arithmetic average return adds periodic percentage returns and divides by the number of periods. It need not reproduce compounded wealth. A gain of 20% followed by a loss of 20% has an arithmetic average of 0%, but 100 becomes 96; the two-year CAGR is approximately −2.0204103%.

IRR and XIRR answer different questions by accounting for cash flows and, for XIRR, their dates. They can have no solution or multiple solutions in some cash-flow patterns. This endpoint tool does not attempt to select such a solution. Comparing outputs from different return definitions without checking their assumptions is misleading.

Using the result in the USA, UK, Canada, Australia and India

The same endpoint formula applies to consistently measured values in USD, GBP, CAD, AUD or INR. Choose the display market for familiar currency formatting. Indian grouping, for example ₹1,00,000.00, changes the presentation rather than the calculation. Inputs remain ungrouped decimals, such as 100000.00. Annualized and annualised refer to the same concept here.

Currency selection does not perform FX conversion. Converting both endpoints using different exchange rates can change the measured home-currency return, so choose and state your valuation basis before entering amounts. No live exchange rate is supplied.

There are no country-specific tax assumptions in this model. A pretax endpoint CAGR is not an after-tax return. Account types, tax treatment and inflation vary across markets and circumstances; this guide supplies no current tax rates, allowances or legal conclusions.

Educational scope

These examples illustrate arithmetic and are not investment recommendations. The Capital Intelligence does not assess your circumstances or provide personalized investment advice. Verify valuations, cash flows and the appropriate return definition before relying on an output for a real decision.

Frequently asked questions

Sources and review

Sources reviewed Nov 3, 2026. Consult current local rules before relying on time-sensitive information.

• CFA Institute Research Foundation: SBBI 2021 Summary Edition — geometric return methodology