A compound annual growth rate (CAGR) answers one question: what constant annual rate, compounded, turns the start value into the end value? The exact formula, CAGR = (end ÷ start)^(1/years) − 1, needs a root, and roots don't suit mental math. Two tools make it manageable without a calculator.
How does the Rule of 72 work?
Tool one: the Rule of 72. Something growing at r percent a year roughly doubles in 72 ÷ r years. The rule runs in reverse too. If you know it doubled in n years, the rate is roughly 72 ÷ n. Two lighter-touch cousins do the same job. Using 70 is marginally more accurate at lower rates, and 69.3 is the true continuous-compounding constant, most accurate at very low rates and for a first, very rough pass. All three estimate the same thing, and none needs to be more than approximately right, because doubling time is only ever a sanity anchor. The rule's accuracy isn't uniform. Knowing its sweet spot is what separates a confident user from a lucky one:
| Annual rate | Rule of 72 says (years to double) | Actual years to double |
|---|---|---|
| 6% | 12.0 | 11.9 |
| 8% | 9.0 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 20% | 3.6 | 3.8 |
| 30% | 2.4 | 2.6 |
In the 6–10% band, where most mature-business growth rates fall, the rule is essentially exact. At the extremes it drifts in a known, small direction. At high rates it overstates how fast something doubles, giving fewer years than reality, and at very low rates it understates slightly. For anything from single digits to the low teens, treat the Rule of 72 as exact. Outside that range it's directionally right, off by a matter of months, not years.
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How do you estimate CAGR from total growth?
Tool two: the direction you can always trust. Say a case gives you a start value, an end value and a number of years, and asks for the annualized rate. The fast first move is to take the total percentage change and divide it by the years. That's the naive linear guess, and it's always too high whenever growth is positive. The reason is clean and provable. Compounding a constant rate over several years produces more cumulative growth than multiplying the rate by the number of years. So when you work backward, the true annual rate behind a given cumulative growth has to be a little below the naive guess. The same logic runs in mirror image for a cumulative decline, where dividing by the years understates the true annual rate of decline. For growth spanning more than one year this direction always holds. You can lean on it the way you can't lean on a rule of thumb that sometimes flips.
Worked example: revenue from $180M to $315M
Put the two tools together on a live number. Revenue went from $180M to $315M over five years, a total gain of 75%. The naive linear guess is 75 ÷ 5 = 15% per year. Without touching a calculator you already know two things. The true CAGR is a little below 15%. And the Rule of 72 says 14.4% a year would double the business in five years (72 ÷ 5 = 14.4), but $315M is only 1.75× the start, well short of a full double (2.00×). Put both signals together and a confident, defensible answer is "roughly 12%." The exact figure, computed afterward, is 11.84%. Your mental estimate lands within two-tenths of a point, it took about fifteen seconds, and the room never sat through a silence. Worked Example 2 walks through this case from start to finish.