Calculadora de Tempo de Duplicação
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
t = ln(2) / ln(1 + r) (regra prática: t ≈ 72 / r%)
About this calculator
The Doubling Time Calculator determines how many periods are needed for an initial value to double, given a constant growth rate per period. It uses the exact formula t = ln(2) / ln(1 + r), where r is the growth rate in decimal. For example, with a 5% annual rate, the doubling time is approximately 14.2 years.
This tool is useful for investors estimating the time to double capital in fixed-income investments like CDs or government bonds, or for analyzing population growth or company revenue. The rule of 72 (t ≈ 72 / r%) provides a quick approximation, but the exact formula is more accurate for high rates or fractional periods.
Important considerations: the calculator assumes continuous, constant growth, which rarely occurs in practice. Market fluctuations, taxes, and inflation can significantly alter the result. Use it as an estimate, not a guarantee. For very high rates (above 30%), the rule of 72 loses accuracy, making the logarithmic formula preferable.
Frequently asked questions
What is the difference between the rule of 72 and the exact formula?
The rule of 72 is a quick approximation: divide 72 by the percentage rate. For rates between 5% and 15%, the error is small. The exact formula uses logarithms and is accurate for any rate.
Can I use this calculator for negative rates?
No, the calculator requires a positive rate. If the rate is negative, the value will never double because it is decreasing.
Does the doubling time consider compound interest?
Yes, the formula assumes compound interest, where growth is applied to the accumulated value each period.
How do I interpret the result if the rate is monthly?
The result will be in months. For example, a 2% monthly rate results in approximately 35 months to double.