CAGR formula (with a plain-English breakdown)

CAGR stands for Compound Annual Growth Rate. The formula is:

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

• Ending Value ÷ Starting Value gives you the total growth factor (also called the “multiple”).
• ^(1 ÷ Years) converts that total multiple into a per-year compound factor.
• − 1 converts the factor into a rate (then multiply by 100 for a percentage).

• It gives a single “annualized” number you can compare across assets and timeframes.
• It automatically accounts for compounding (unlike simple averages).
• It’s easy to communicate: “This grew at ~X% per year over N years.”

Examples you can copy/paste

Start = $10,000, End = $18,500, Years = 3.5. The growth multiple is 18,500 ÷ 10,000 = 1.85. CAGR = 1.85^(1/3.5) − 1 ≈ 0.191 (≈ 19.1% per year).

Revenue grows from $2M to $3.2M in 4 years. Multiple = 3.2 ÷ 2.0 = 1.6. CAGR = 1.6^(1/4) − 1 ≈ 0.125 (≈ 12.5% per year).

Start = 100, End = 70, Years = 5. Multiple = 0.70. CAGR = 0.70^(1/5) − 1 ≈ −0.069 (≈ −6.9% per year).

How this CAGR calculator works (step-by-step)

The calculator follows the standard CAGR formula and then displays a “human” explanation so you can understand the number quickly (and share it without sounding like a spreadsheet).

• Starting value must be > 0 (CAGR divides by the start value).
• Ending value must be > 0 (CAGR uses a ratio that must be positive).
• Years must be > 0 (time must be positive).

• Multiple = Ending ÷ Starting.
• If multiple > 1, you grew overall. If multiple < 1, you shrank overall.

• Annual Factor = Multiple^(1/Years).
• CAGR = Annual Factor − 1.

• Total growth (%) = (Ending − Starting) ÷ Starting.
• Dollar change = Ending − Starting.
• “Implied yearly path”: what a smooth growth curve would look like (conceptually).

Frequently Asked Questions

• What is CAGR in simple terms?

  CAGR is the steady annual growth rate that would turn your starting value into your ending value over the given number of years. It’s a “smoothed” rate that assumes compounding.

• Is CAGR the same as average annual return?

  Not always. A simple average of yearly returns ignores compounding. CAGR is a geometric rate, so it better represents overall growth across multiple years.

• Can CAGR be negative?

  Yes. If your ending value is lower than your starting value, the ratio is less than 1, and CAGR becomes negative, meaning the value shrank on an annualized basis.

• When should I NOT use CAGR?

  If there are cash flows during the period (monthly contributions, withdrawals, dividends reinvested, capital calls), CAGR can mislead. In those cases, consider IRR/XIRR.

• Does CAGR include dividends, fees, and taxes?

  Only if your ending value already reflects them. This calculator is math-only: it annualizes the change from start to end. If fees/taxes reduced your end value, CAGR will reflect that reduction — but it won’t model them separately.

• How do I calculate CAGR with dates?

  Convert the time between dates into years (for example, 18 months = 1.5 years). For exact-day precision you can use “years = days/365.25” as a good approximation.