Doubling Time From Rate Calculator
Convert a constant per-period growth rate into the exact doubling time, and compare it against the Rule of 72 estimate.
How it works
Doubling time = ln(2) / ln(1 + r) · Rule-of-72 shortcut ≈ 72 / (rate as a percent)
Any quantity growing at a fixed rate doubles after a fixed amount of time, no matter where it starts. The exact figure comes from solving (1 + r)^t = 2 for t, giving ln(2)/ln(1 + r). The famous Rule of 72 is a mental-math shortcut that is remarkably close for rates in the single digits, drifting apart only at larger rates where the logarithm bends away from the linear approximation.
Worked example
At 7% per period, the exact doubling time is ln(2)/ln(1.07) ≈ 10.24 periods. The Rule of 72 gives 72/7 ≈ 10.29 — within about half a percent, which is why the shortcut is so widely used.
Sources: Doubling time — Wikipedia
Frequently asked questions
Why is it called the Rule of 72?
72 is chosen because it divides cleanly by many common rates (2, 3, 4, 6, 8, 9, 12) and its estimate is closest to the true logarithmic value for rates around 6–10%. The Rule of 70 is slightly more accurate for continuous or very small rates.
Does the starting amount affect doubling time?
No. Under a constant growth rate the time to double is independent of the starting value — 100 to 200 takes exactly as long as 5,000 to 10,000 at the same rate.
When does the Rule of 72 break down?
It stays within a percent or so for single-digit rates but grows less accurate at high rates. At 25% per period, for example, 72/25 = 2.88 versus the exact 3.11 — off by roughly 7%.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.