Case 1
- Growth rate per period
- 0.07
9.902103
Open with these valuesDoubling Time Calculator
9.902103periods
Result: 9.902103 periodsDivide ln 2, about 0.693, by the growth rate written as a decimal. At 7 % a year that is 0.693 ÷ 0.07 ≈ 9.9 years. The familiar rule of 70 is the same sum rounded — 70 ÷ 7 = 10 — and it always lands a little high, because 0.7 is a little above ln 2.
Worked examples
Case 2
- Growth rate per period
- 0.05
13.862944
Open with these valuesCase 3
- Growth rate per period
- 0.02
34.657359
Open with these valuesHow it's calculated
t = ln(2) ÷ r
- StepWrite the growth rate as a decimal — 5 % becomes 0.05.
- StepDivide ln 2, about 0.693147, by that number.
- ResultRead the answer in the same periods your rate refers to.
Reference table
| Rate (decimal) | Rule of 70 estimate | Doubling time |
|---|---|---|
| 0.01 | 70 ÷ 1 = 70 | 69.314718 |
| 0.02 | 70 ÷ 2 = 35 | 34.657359 |
| 0.05 | 70 ÷ 5 = 14 | 13.862944 |
| 0.07 | 70 ÷ 7 = 10 | 9.902103 |
| 0.10 | 70 ÷ 10 = 7 | 6.931472 |
Questions
How do I calculate doubling time?
Divide the natural logarithm of 2 by the growth rate per period, written as a decimal: t = ln(2) ÷ r. At 7 % per year, r = 0.07, so the doubling time is about 9.9 years.
What is the rule of 70?
The rule of 70 is the mental shortcut: divide 70 by the growth rate in percent, or 0.7 by the decimal rate. At 7 % growth that gives 10 years against the exact 9.9. It works because ln 2 ≈ 0.693, just under 0.7, so the estimate always runs slightly long.
Should I enter the rate as a percent or a decimal?
As a decimal: 5 % is 0.05, and 12 % is 0.12. Divide a percentage by 100 to get there. The calculator assumes the rate stays constant and compounds continuously over the whole span.
What time unit does the result use?
The same period your rate refers to. A rate per year gives an answer in years, a rate per month gives months. Keep the rate and the period consistent and the unit takes care of itself.
Why does a zero or negative rate give no result?
A quantity that is not growing never doubles, so the doubling time is undefined. The formula divides by the rate, and neither zero nor a negative number yields a meaningful answer.
Where is doubling time used?
Anywhere something grows at a roughly constant rate: populations, investment returns and compound interest, inflation, an epidemic, bacteria in a culture, website traffic. It turns an abstract percentage into a horizon you can picture.
Sources and last check
Information, not professional advice.