How to calculate CAGR: the formula, step by step

The CAGR formula

CAGR = (Ending value ÷ Starting value)^(1 ÷ Years) − 1

CAGR — compound annual growth rate — is the single constant yearly rate that turns the starting value into the ending value over the period, with each year’s growth building on the last. It needs only three inputs: where you started, where you ended, and how long it took.

Three steps, with a worked example

An investment grows from $10,000 to $25,000 in 5 years.

1. Find the growth multiple. 25,000 ÷ 10,000 = 2.5. The money grew 2.5 times.
2. Take the n-th root. Raise 2.5 to the power 1 ÷ 5 = 0.2: 2.5^0.2 = 1.2011.
3. Subtract 1. 1.2011 − 1 = 0.2011, or 20.11% a year.

Check it by compounding forward: 10,000 × 1.2011⁵ = 25,000. If the check doesn’t land on your ending value, a step went wrong.

Calculating CAGR with logarithms

If your calculator has ln and eˣ keys but no fractional power, use logarithms — the result is identical:

CAGR = e^( ln(End ÷ Start) ÷ Years ) − 1

1. ln(2.5) = 0.9163
2. 0.9163 ÷ 5 = 0.1833
3. e^0.1833 = 1.2011, so CAGR = 20.11%

No scientific keys at all? The CAGR FAQ shows a square-root trick that works on a basic four-function calculator, accurate to about two decimal places.

Partial years and exact dates

Years don’t have to be whole numbers, and rounding them is the most common source of error. Suppose $50,000 grew to $80,000 between 15 March 2021 and 30 September 2025. That is 1,660 days, or 1,660 ÷ 365.2425 = 4.54 years.

A six-month rounding error moves the answer by more than a percentage point either way. The CAGR calculator has an exact-dates mode that counts the days for you.

Monthly data and short periods

For 18 months of data, use 1.5 years: 1,000 → 1,300 gives (1.3)^(1/1.5) − 1 = 19.11% a year. The compounded monthly rate is (1.3)^(1/18) − 1 = 1.47%.

Be careful annualising very short periods. A 5% gain in two months becomes 1.05⁶ − 1 = 34.01% annualised — a number that assumes the lucky streak continues all year. For periods under a year, the absolute return is usually the more honest figure.

Negative CAGR

When the ending value is lower, the multiple is below 1 and CAGR is negative. $10,000 falling to $7,000 over 3 years: 0.7^(1/3) − 1 = −11.21% a year. CAGR breaks down only when the starting value is zero or negative (for example, a company that moved from a loss to a profit), because there is no meaningful growth multiple to take the root of.

Revenue CAGR for a company

The same formula measures business growth. Revenue of $1.2 million in FY2021 and $3.4 million in FY2025 spans 4 fiscal years (not 5 — count the gaps between reports, not the reports): (3.4 ÷ 1.2)^(1/4) − 1 = 29.74% revenue CAGR. Compare it with profit CAGR over the same years; revenue growing faster than profit means margins are shrinking.

Common mistakes

• Counting data points instead of intervals. Six yearly values span five years.
• Dividing total return by years. 150% ÷ 5 = 30% is a simple average, not CAGR. The real figure is 20.11% — see CAGR vs average annual return.
• Using CAGR when money was added or withdrawn. Monthly SIPs or top-ups need IRR or XIRR.
• Missing brackets in a spreadsheet. =B2/B1^(1/B3)-1 raises only B1 to the power. Write =(B2/B1)^(1/B3)-1, or use RRI — see CAGR in Excel.
• Ignoring dividends. For stocks, a price-only CAGR understates total return — the stock CAGR calculator has a dividends field.

Working backwards

Rearranging the formula answers the reverse questions: future value = Start × (1 + CAGR)^Years, and years = ln(End ÷ Start) ÷ ln(1 + CAGR). Thereverse CAGR calculator solves for any missing input, and the Rule of 72 gives a mental shortcut for doubling time.

Sources and further reading

• Wikipedia: Compound annual growth rate — definition and formula
• Microsoft Support: RRI function — Excel’s built-in CAGR equivalent
• Investor.gov (U.S. SEC): Compound interest calculator — how compounding works

Educational information only — not investment advice. Past performance does not guarantee future results.