What is doubling time?
The time needed for an exponentially growing quantity to double.
Doubling Time Calculator
Compute t = ln(2)/k for continuous growth, or Rule of 72 for annual percent rates.
Choose a doubling method
Enter continuous k, or a percent growth rate for Rule of 72.
About this calculator
How to use Doubling Time Calculator, plus the formulas and logic behind the results.
Tool description
Doubling time is how long a quantity takes to become twice as large under exponential growth. Continuous models use ln(2)/k; Rule of 72 is a finance rule of thumb.
How to use
- Select continuous or Rule of 72.
- Enter k > 0 or a positive percent rate.
- Select Calculate to view doubling time.
- Interpret time in the same units as the rate period.
Formulas & reference
t = ln(2) / kRule of 72: t ≈ 72 / r%
Examples
- k = 0.07 → t ≈ 9.9 time units
- 8% → Rule of 72 ≈ 9 years
- Higher rate → shorter doubling time
- Negative rates are not doubling
Calculation logic
Divides ln(2) by k, or 72 by the percent rate, requiring positive rates.
Rule of 72 is approximate. Continuous formula is exact for A₀e^{kt}.
Doubling Time Calculator FAQ
Common questions about this calculator and how to use the results.
When use Rule of 72?
Quick mental estimates for percent compound growth (often annual).
What units does t have?
The same time unit built into k or the percent rate.
Is Rule of 72 exact?
No—it is a convenient approximation.
Can I use percent in continuous mode?
Convert first: 7% → k = 0.07.
What about halving time?
For decay, use ln(2)/|k| with negative growth; this tool focuses on doubling.