How long until it doubles,to the period.
The Rule of 72 is the back-of-the-napkin trick: divide 72 by your growth rate and you get the doubling time in your head. This runs it both ways — the 72 shortcut and the exact logarithm — so you see the answer, the error in the shortcut, and what compounding actually does over ten periods.
Your numbers
The steady rate something grows each period — revenue, a list, a follower count, an investment.
The verdict
Doubling time (months)
9.0
Exact: ln(2) ÷ ln(1 + rate).
Rule of 72 (months)
9
The mental shortcut: 72 ÷ rate.
Tripling time (months)
14
To reach 3×: ln(3) ÷ ln(1 + rate).
Growth after 10 periods
2.16×
(1 + rate)¹⁰ — where you land.
Shortcut vs. exact
0.1%
Rule of 72 error
-0.1
Shortcut understates the time.
Shortcut vs. exact, in months
At 8.0% per month, the Rule of 72 lands 0.1% low versus the exact 9.01 months. Close enough to do in your head.
Sensitivity · the rate is everything
Doubling time across growth rates
| Rate per month | Double (months) | Triple (months) | After 10 |
|---|---|---|---|
| 2% | 35.0 | 55.5 | 1.22× |
| 5% | 14.2 | 22.5 | 1.63× |
| 10% | 7.3 | 11.5 | 2.59× |
| 20% | 3.8 | 6.0 | 6.19× |
Halving your doubling time doesn't take twice the rate — going from 5% to 10% per month cuts the wait from 14.2 to 7.3 months. Doubling time is inversely proportional to the rate, so the early percentage points are the cheapest you'll ever buy.
Reference · rule-of-thumb bands
Where common rates land
| Rate per month | Double (months) | Triple (months) |
|---|---|---|
| 2% | 35.0 | 55.5 |
| 5% | 14.2 | 22.5 |
| 8% | 9.0 | 14.3 |
| 10% | 7.3 | 11.5 |
| 15% | 5.0 | 7.9 |
| 20% | 3.8 | 6.0 |
| 40% | 2.1 | 3.3 |
A labeled rule-of-thumb reference, computed with the exact formula ln(2) ÷ ln(1 + rate). The period is whatever you picked above — the math is identical whether it's years, months, or weeks.
Your move
Knowing the clock is easy. Holding the rate is the work.
At 8.0% per month, it doubles in 9.0 months (Rule of 72 says 9.0).
Doubling time is just arithmetic — the hard part is keeping that growth rate steady long enough for the math to pay off. That's a marketing and retention problem, and it's the one I solve. Bring me the channel that's supposed to be doubling and I'll tell you, free, why the rate keeps slipping and what I'd fix first.
Plain English
Doubling time turns a growth rate into a clock.
A growth rate is abstract. "We're up 8% a month" doesn't land until you translate it into time: at 8% a month, you double in roughly nine months. That's doubling time — the number of periods a quantity needs to grow to twice its size at a constant rate. It's how you reason about compounding without a spreadsheet.
The famous shortcut is the Rule of 72: divide 72 by the growth rate (as a whole number) and you get the doubling time. 8% → 72 ÷ 8 = 9 periods. It's a mental-math hack, not magic — 72 just happens to be close to the real constant (100 × ln 2 ≈ 69.3) and has lots of clean divisors. The exact answer comes from the logarithm: ln 2 ÷ ln(1 + rate).
This calculator shows you both, side by side, plus how far apart they are. For typical rates (6–10%) the Rule of 72 is within a rounding error. At very low or very high rates the gap widens, and you'll want the exact figure. We also give you tripling time and where ten periods of this growth actually lands you.
The formula
Doubling time = ln(2) ÷ ln(1 + rate) · Rule of 72 ≈ 72 ÷ rate%
At 8% per period: the Rule of 72 says 72 ÷ 8 = 9.0 periods. The exact formula says ln(2) ÷ ln(1.08) = 9.01 periods — a 0.1% difference. At 1% the shortcut says 72; the exact answer is 69.7, so the rule overshoots. At 40% the shortcut says 1.8; exact is 2.06. The hack is best in the 6–10% band.
You've got a doubling time. Now read it.
Rate under ~3% per period.
Doubling takes 24+ periods and the Rule of 72 starts overshooting. Use the exact figure, and ask whether this is really compounding or just drifting. Small rates need either patience or a structural change to the rate itself.
Rate between 6% and 10%.
This is the sweet spot where the Rule of 72 is dead accurate (within ~1%). Do the math in your head, trust it, and focus on whether you can hold the rate, not on refining the estimate.
Rate above ~25% per period.
The Rule of 72 overstates the time — use the exact log formula. Also sanity-check the rate: very high per-period growth rarely holds for long, so model the deceleration, not a straight line.
Doubling time looks great but the base is tiny.
Doubling $100 to $200 is the same rate as $1M to $2M, but only one moves the business. Pair doubling time with the absolute size, or you'll celebrate a percentage that doesn't pay rent.
How to actually pull doubling time forward
01Compound more often
Same nominal rate, shorter periods. Monthly compounding beats annual; weekly beats monthly. Tightening the loop is free speed.
02Protect the rate, not the total
A constant rate is what doubles you. Anything that nicks the rate — churn, dilution, leakage — pushes the doubling date out further than it feels.
03Stack a second growth lever
Two 4% sources compound to ~8.16% combined, not 8%. Layered, independent growth engines beat one big push.
04Kill the drag first
Net growth is gross growth minus losses. Cutting a 3% monthly churn does more for doubling time than chasing 3 points of new growth.
05Measure in the right period
A 'good' weekly rate and a 'good' annual rate are worlds apart. Always state the period — doubling time is meaningless without it.
06Reinvest the doublings
The second double is bigger than the first. Pour the gains from each doubling back in instead of harvesting, and the curve steepens.
07Watch for the S-curve
Exponential growth is local. Every real rate eventually bends. Use doubling time to plan the next phase, not to extrapolate forever.
08Benchmark against the clock
If a competitor doubles in 6 months and you take 12, they lap you twice a year. Doubling time is the most honest way to compare growth engines.
The vocabulary
- Doubling time
- The number of periods a quantity needs to grow to twice its size at a constant rate. Exactly ln(2) ÷ ln(1 + rate).
- Rule of 72
- A mental shortcut: 72 ÷ growth-rate-percent ≈ doubling time. Accurate near 8%; drifts at very low or very high rates.
- Tripling time
- Periods to grow to 3× the size: ln(3) ÷ ln(1 + rate). The 'Rule of 72' cousin for tripling is the Rule of 114.
- Compound growth
- Growth that builds on the prior period's total, not the original base. The reason doubling time stays constant as the number gets bigger.
- Growth rate per period
- The fraction a quantity increases each period (8% a month, 2% a week). Doubling time is meaningless until you fix the period.
- ln (natural log)
- The logarithm base e. It's what converts a multiplicative growth factor into the additive time it takes to get there.
Doubling time questions, straight answers
Doubling time = ln(2) ÷ ln(1 + rate), where rate is the per-period growth as a decimal. At 8% (0.08) that's ln(2) ÷ ln(1.08) ≈ 9.01 periods. The quick mental version is the Rule of 72: divide 72 by the growth-rate percentage (72 ÷ 8 = 9). Both give the same answer near 8%.
Keep going
A calculator tells you what. A call tells you what to do about it.
Send me the account behind these numbers. I'll tell you straight where the money's leaking and what I'd fix first — free, and you keep it whether you hire me or not.