Compound Growth Calculator (CAGR)
Enter any three of the four variables - initial value, final value, growth rate, and number of periods - and this calculator solves for the missing one. You get the compound annual growth rate (CAGR), total return, doubling time, a period-by-period growth schedule, and a chart of the growth curve. Useful for investments, business revenue, real estate, or any quantity that compounds over time.
Formula
Worked example
An investment grows from $10,000 to $20,000 over 10 years. CAGR = (20,000/10,000)^(1/10) - 1 = 2^0.1 - 1 = 7.18%. The same investment at 8%/year for 10 years gives: 10,000 x 1.08^10 = $21,589. Doubling time at 8%: ln(2)/ln(1.08) = 9.01 years.
What is compound growth?
Compound growth means the increase in each period is calculated on both the original amount and the accumulated gains from prior periods. That reinvestment effect causes exponential rather than linear growth. The compound annual growth rate (CAGR) is the single constant rate that would produce the same total growth over the same number of periods as an investment actually achieved, making it the standard measure for comparing assets with different histories or time horizons.
How the four-variable formula works
The compound growth formula has four variables: initial value (PV), final value (FV), growth rate per period (r), and number of periods (n). The relationship is FV = PV x (1 + r)^n. If you know any three of the four, the fourth can be derived. Solving for FV projects a future balance; solving for r (CAGR) reveals the implied return between two observed values; solving for PV is present-value discounting; and solving for n tells you how many periods a given growth target requires. Use the "Solve for" selector at the top to choose the mode that matches your question.
Doubling time and the Rule of 72
The doubling time is the exact number of periods needed to double the initial value at a given compound rate: t = ln(2) / ln(1 + r). The Rule of 72 is a useful mental shortcut: divide 72 by the percentage rate to get an approximate doubling time. At 8%, the rule gives 72 / 8 = 9 years; the exact formula gives 9.01 years. The approximation is accurate within a few percent for rates between roughly 2% and 25%, and it becomes less reliable at higher or negative rates.
Using CAGR to compare growth across different time periods
If Investment A grew 50% over 3 years and Investment B grew 100% over 7 years, a direct percentage comparison is misleading because the time frames differ. CAGR normalises for time: Investment A has a CAGR of (1.5)^(1/3) - 1 = 14.5%, and Investment B has a CAGR of (2.0)^(1/7) - 1 = 10.4%. Investment A compounded faster per year despite the smaller total return. CAGR is also known as the geometric mean growth rate, and it is more meaningful than the arithmetic average for compounding quantities.
Compound Growth Rate Benchmarks
| Rate Range | Context / Benchmark | Assessment |
|---|---|---|
| < 0% | Depreciation (e.g. vehicles, older equipment) | Negative growth |
| 0% - 2% | Near inflation, low-yield savings accounts | Preservation only |
| 2% - 4% | Broad inflation target, government bonds | Low real return |
| 4% - 7% | Balanced portfolio, 60/40 stocks-bonds blend | Moderate |
| 7% - 10% | Long-run S&P 500 historical nominal average | Strong |
| 10% - 15% | Growth stocks, top-tier venture outcomes | Very strong |
| > 15% | Rare sustained returns, concentrated positions | Exceptional / verify |
Common reference points for compound annual growth rates (CAGR) across asset classes and sectors. Actual returns vary and past performance does not guarantee future results.
Frequently asked questions
What is CAGR and how is it different from average annual return?
CAGR (compound annual growth rate) is the single constant rate that transforms the initial value into the final value over a given number of periods, accounting for compounding. The simple average return, by contrast, averages period-level percentage changes arithmetically. CAGR is almost always lower when returns are volatile, but it reflects the actual investor experience better because it models the reinvestment of gains. For example, a gain of 50% followed by a loss of 33% leaves the investor at break-even, but the simple average return would show a positive 8.5%.
How do I use this calculator to find how long it takes to double my money?
Enter your initial value and growth rate, then look at the "Doubling Time" output below the main result. Alternatively, use the Rule of 72: divide 72 by your annual percentage rate for a quick estimate. At 6%, the doubling time is roughly 12 years; at 9%, roughly 8 years. The exact formula is ln(2) / ln(1 + r), where r is the rate in decimal form.
Can I use this calculator for monthly or quarterly compounding?
Yes. Set "Period unit" to Months or Quarters, then enter the growth rate per period (not per year) in the Growth Rate field. For example, if a savings account pays 5% per year compounded monthly, the monthly rate is approximately 5% / 12 = 0.417%. Enter 0.417 as the growth rate and 60 as the number of periods to project 5 years of monthly growth.
What does a negative growth rate mean?
A negative CAGR means the final value is lower than the initial value - the quantity is declining over time. This is common for depreciating assets such as vehicles, old machinery, or declining business revenue. For example, a car worth $30,000 new that is worth $15,000 after 5 years has a CAGR of (15,000/30,000)^(1/5) - 1 = -12.9% per year.
What is the present value (PV) solve mode used for?
The "Initial Value" solve mode answers the question: how much do I need to invest today to reach a target future value, given a specific growth rate and time horizon? This is the classic present value (discounting) calculation. For example, to have $1,000,000 in 30 years at a 7% annual return, you need $1,000,000 / 1.07^30 = $131,367 today.