Constant Growth Rate Calculator
One equation runs every growth question: a value today, a value later, a rate, and a time. Most calculators only solve it in one direction, so finding how long a target takes, or what a balance becomes, means starting over somewhere else. This calculator solves the constant growth equation in all three directions from one screen.
Choose whether you want the rate, the time, or the future value. The tool hides the field you are solving for, shows the exact formula it used with your numbers substituted in, and adds the doubling time with a Rule of 72 cross-check.
Assumes a constant rate every period. Real investments vary; treat projections as scenarios, not promises.
Quick Answer
Key takeaways
- One equation, three questions: FV = PV x (1 + g)^n. Solve it for g, for n, or for FV depending on what you already know.
- The rate this tool finds for a lump sum is the same number CAGR reports. The difference is framing and scope, explained in the boundary section below.
- Doubling time is built in: ln(2) / ln(1 + g), shown next to the Rule of 72 estimate so you can sanity check either figure.
- Periods are unit free. Match the rate to the period count (annual rate with years, monthly rate with months) and the math is identical.
- Quick Answer
- How to use the constant growth rate calculator
- One formula, three directions
- Worked example: watching $10,000 compound at 10%
- Constant growth rate or CAGR: the boundary between the two pages
- Doubling time and the Rule of 72
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the constant growth rate calculator
Start with the mode selector, because it decides which field disappears. In rate mode you enter the present value, future value, and periods, and the rate field hides itself. In time mode the periods field hides and the rate field appears. In future value mode the future value field hides. The calculator is pre-filled in rate mode with $10,000, $16,105.10, and 5 periods, so pressing Calculate immediately returns the 10.00% in the Quick Answer.
Read the formula line under every result. It substitutes your actual numbers into the equation, so a result can be checked on paper in seconds, and the copy button captures both the answer and that working. If your question is narrowly about the annual percentage growth of an investment series, the dedicated compound annual growth calculator frames the same rate calculation in CAGR terms; the boundary section below explains exactly where the two pages divide the work.
One formula, three directions
Each mode is the same relationship rearranged, which is why the three answers in the Quick Answer agree with each other. Rate mode takes the nth root of the total growth factor: $16,105.10 / $10,000 = 1.61051, and the fifth root of 1.61051 is 1.10, a 10.00% rate. Time mode uses logarithms because the unknown sits in the exponent. Future value mode is the original equation with nothing rearranged at all. If you need the starting value instead, solving the same equation for PV is what the backward compound interest calculator is built around.
| Mode | You enter | It solves | Example result |
|---|---|---|---|
| Growth rate | PV, FV, periods | g | 10.00% per period |
| Time needed | PV, FV target, rate | n | 7.27 periods to double |
| Future value | PV, rate, periods | FV | $16,105.10 |
Worked example: watching $10,000 compound at 10%
Constant growth means each period grows the new, larger balance, not the original deposit. The year by year path behind the headline numbers looks like this:
| Period | Value at period end | Growth that period |
|---|---|---|
| 0 | $10,000.00 | Start |
| 1 | $11,000.00 | $1,000.00 |
| 2 | $12,100.00 | $1,100.00 |
| 3 | $13,310.00 | $1,210.00 |
| 4 | $14,641.00 | $1,331.00 |
| 5 | $16,105.10 | $1,464.10 |
Total growth of 61.05% over 5 periods is not 5 times 10% added up (that would be 50%); the extra comes from growth on growth. That gap is the entire reason the rate is found with a root rather than a simple division, and it widens fast: at 10% for 20 periods the same $10,000 reaches $67,275.00, not the $30,000 a linear guess suggests. For a performance figure that strips a series down to this same smoothed rate, the CAGR return calculator reports it in investment return terms.
Constant growth rate or CAGR: the boundary between the two pages
Honesty about scope matters here, because the two tools overlap. For one lump sum growing over whole periods, the constant growth rate and CAGR are mathematically identical, and both pages will give you the same 10.00% for the worked example above. Neither page pretends otherwise.
The division of labor is this. Use this page when your unknown is not the rate: when you need the time to reach a target, a projected future value, a doubling time, or a rate over periods that are not years, such as months or quarters. Use the compound annual growth page when your question is specifically the annualized percentage performance of a value series, framed the way fund reports and business coverage frame it. If a future merge of the two pages ever makes sense, the math above is the reason it would be a merge of framing, not of formulas.
Doubling time and the Rule of 72
At a constant rate g, a value doubles in ln(2) / ln(1 + g) periods. The Rule of 72 replaces that with 72 / rate, a shortcut old enough to appear in Renaissance arithmetic texts and accurate within a few percent for rates between roughly 2% and 20%. This tool prints the exact figure and the Rule of 72 estimate together in rate and time modes: at 10% they are 7.27 and 7.2, close enough that either can catch a typo in the other. At very high rates the shortcut drifts (at 50% it says 1.44 periods against an exact 1.71), which is exactly when the exact figure earns its place.
What competing calculators miss
CAGR tools dominate this search term, and they are good at the one thing they do. Reviewed against this page, three gaps repeat.
Miss 1: rate only. The standard CAGR calculator cannot tell you how long a target takes or what a balance becomes, because it never rearranges the equation. This tool solves all three directions, which is the entire reason it exists alongside a CAGR page.
Miss 2: years only. Most rivals hard-code annual periods. Here a period is any unit, so a monthly growth rate over 36 months and an annual rate over 3 years both work without conversion gymnastics.
Miss 3: no doubling cross-check. Competitors that mention the Rule of 72 rarely show it next to the exact logarithmic doubling time. Printing both turns a memorized shortcut into a verification step.
Frequently Asked Questions
Use g = (future value / present value) raised to the power of 1 / periods, minus 1. For $10,000 growing to $16,105.10 in 5 periods: (16,105.10 / 10,000) to the power of 0.2, minus 1, equals 10.00% per period.
For a single lump sum they are the same number: CAGR is the constant annual rate connecting a start and end value. The difference is scope. This calculator is a general solver that also finds the time to a target and projects a future value for any period length, while the dedicated CAGR page frames the same rate math around a value series in annual percentage terms.
Exactly 7.27 periods: doubling time = ln(2) / ln(1.10). The Rule of 72 estimates 72 / 10 = 7.2, which is why this calculator shows both figures side by side in rate and time modes.
Divide 72 by the growth rate in percent to estimate the doubling time in periods. It is a mental math shortcut that stays within a few percent of the exact logarithmic answer for typical single digit and low double digit rates.
Yes. In rate mode, if the future value is below the present value, the tool returns a negative rate: the constant rate of decline that connects the two values. A $10,000 value falling to $9,000 in one period gives a rate of -10.00%.
Switch to the future value mode and use FV = present value x (1 + g) to the power of n. At 10% for 5 periods, $10,000 becomes $10,000 x 1.61051 = $16,105.10.
Yes. Periods are generic. Enter a monthly rate and count periods in months, or an annual rate and count in years. Just keep the rate and the period count in the same unit, because the formula cannot tell them apart.
The Gordon growth model values a stock whose dividends grow at a constant rate forever: price = next dividend / (required return minus g). This calculator does not use it. It solves lump sum growth, FV = PV x (1 + g)^n, which is a different formula for a different problem.
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References
- Investopedia reference material on compound annual growth rate and the constant growth formula FV = PV x (1 + g)^n, the standard textbook statement of the equation solved here. Investopedia: Compound Annual Growth Rate. Accessed October 2026.
- Corporate Finance Institute training material on CAGR and future value projections, including solving the growth equation for rate, time, and ending value. Corporate Finance Institute: CAGR. Accessed October 2026.
- US Securities and Exchange Commission investor education resources on compound growth and the effect of a constant return assumption on long term balances. SEC Investor.gov: Introduction to Investing. Accessed October 2026.