What this calculator does
The regular CAGR calculator works backwards from history: you give it a beginning value, an ending value and a number of years, and it tells you the smooth annual rate that connects them. A reverse CAGR calculator runs the same relationship the other way. You start from an assumed or target compound annual growth rate and solve for whichever of the other three figures you do not already know: how big something grows, what it must have started at, or how long it takes.
This is the more common question when planning rather than reviewing. An investor projecting a portfolio forward already has an assumed growth rate in mind and wants the ending value; someone working towards a savings goal wants to know how many years an assumed rate takes to get there. Both are reverse CAGR problems, and both use the same compounding formula as the forward calculator, just rearranged to solve for a different unknown.
The formula
Pick which figure you want solved: ending value, beginning value, or number of years. Ending value comes from Begin × (1 + CAGR) raised to the power of the years. Beginning value is the same formula rearranged to divide the ending value by that growth factor instead. Number of years takes the natural log of the ratio between ending and beginning value, divided by the natural log of one plus the rate, since the years sit in an exponent and logs are how you pull an exponent back out.
| Term | Meaning |
|---|---|
| CAGR | The assumed compound annual growth rate, entered as a percentage, that value grows at each year. |
| Beginning value | The value at the start of the period, either known or the figure being solved for. |
| Ending value | The value at the end of the period, either known or the figure being solved for. |
| Years | The number of years the compounding runs for, either known or the figure being solved for. |
The inputs explained
| Field | What to enter |
|---|---|
| Solve for | Choose which of the three figures is unknown; the other two fields plus the rate are used to find it. |
| Assumed CAGR (%) | The compound annual growth rate you are assuming or targeting, as a percentage. Must be above -100%. |
| Beginning value ($) | The starting value. Ignored when solving for the beginning value itself. |
| Ending value ($) | The value at the end of the period. Ignored when solving for the ending value itself. |
| Number of years | The number of years the growth runs for. Ignored when solving for the number of years itself. |
When to use it
Projecting a portfolio or savings balance forward
If you are assuming a long-run average return, entering a beginning balance, that assumed rate and a number of years gives a projected ending value, the same way a forward-looking projection is normally built.
Working out how long a goal takes
Given a starting amount, a target amount and an assumed growth rate, solving for years shows how long that target realistically takes to reach at that rate, rather than guessing at a timeline.
Checking what a growth assumption implies backwards
If you know where something ended up and the rate it is assumed to have grown at, solving for the beginning value checks what starting point that combination implies, which is a useful sanity check on a stated growth rate.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the ending value on $50,000 changes with the assumed CAGR
The same $50,000 starting point and 5-year horizon, at a range of assumed compound annual growth rates.
| Assumed CAGR | Ending value | Total growth |
|---|---|---|
| 2% | $55,204.04 | 10.4% |
| 4% | $60,832.65 | 21.7% |
| 6% | $66,911.28 | 33.8% |
| 8% | $73,466.40 | 46.9% |
| 10% | $80,525.50 | 61.1% |
| 12% | $88,117.08 | 76.2% |
How many years it takes $50,000 to reach $100,000 at different rates
A fixed doubling from $50,000 to $100,000, across a range of assumed compound annual growth rates.
Questions
How is this different from the CAGR calculator?
The CAGR calculator solves for the rate itself, given a known beginning value, ending value and number of years, which is the right tool when reviewing what already happened. This reverse CAGR calculator assumes the rate and solves for one of the other three figures instead, which is the right tool for planning forward.
Can I use this to check a growth assumption someone else has given me?
Yes. If you are told a value is projected to reach a certain figure at a certain assumed rate, entering those numbers and solving for years or beginning value checks whether the maths behind that projection actually holds together.
What happens if I enter a CAGR of 0%?
A 0% rate never changes the value at all, so if you solve for years with a beginning and ending value that already match, the answer is that any number of years works. If they do not match, no number of years at 0% can bridge the gap, and the calculator flags that directly.
Why does the calculator reject a CAGR at or below -100%?
A rate of exactly -100% wipes the value out completely in a single year, and anything below that is not a value that can keep compounding, since it would imply a negative balance. The formula needs a growth factor above zero to work, which means the rate itself must stay above -100%.
To find the actual historical rate behind a known beginning and ending value, use the CAGR calculator. To turn a growth projection into a full year-by-year balance rather than a single endpoint, the compound interest style calculators elsewhere on the site build out that detail.