Calculate how long it takes for an investment or population to double at a constant growth rate. Compare exact calculations with the Rule of 72 approximation.
Last updated: March 2026 | By Patchworkr Team
Doubling time is the amount of time it takes for a given quantity to double in size or value at a constant growth rate. It's a fundamental concept in finance (compound interest), biology (population growth), physics (radioactive decay), and economics.
The concept is based on exponential growth. Because the quantity grows faster as it gets larger (since you're earning "interest on interest"), the time it takes to double remains constant as long as the growth rate doesn't change. This is one of the most powerful concepts in understanding compound growth.
For example, if your investment grows at 7% per year, it will take approximately 10.24 years to double, regardless of whether you start with $100 or $100,000.
Important: The output period matches the rate period. If you enter a growth rate in percent per year, the result is in years. If you enter a growth rate in percent per month, the result is in months. Always ensure your rate period and output period expectations are consistent.
How long for an investment to double at 7% annual interest?
It's a mental shortcut that's surprisingly accurate for growth rates between 2% and 20%. It avoids the need for complex logarithms and can be calculated in your head.
For continuous compounding, the formula simplifies to t = ln(2) / r, where r is the continuous rate. In this case, the 'Rule of 69' (69/R) is actually more accurate than 72.
If the rate is negative, the quantity is shrinking. This becomes a 'half-life' calculation - finding how long it takes for a value to reduce by 50%. The same formulas apply with the negative rate.
No! Whether you start with $1 or $1,000,000, the time it takes to double is exactly the same as long as the growth rate is constant. This is the power of exponential growth.
Rule of 69 is more accurate for continuous compounding. Rule of 70 is easier for mental math when dealing with rates that aren't divisible by 72. They're all approximations with slightly different use cases.
Absolutely! Population growth, bacterial growth, viral spread, and any exponential process can use doubling time. Just use the growth rate per time period (year, day, hour, etc.).
Very accurate for rates between 2-20%. At 8%, the error is less than 0.1 years. It becomes less accurate at very low (<2%) or very high (>20%) rates.
Using Rule of 72: 72/10 = 7.2 periods. Using the exact formula: 7.27 periods. So about 7.2 years if it's annual growth.
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