Doubling Time Calculator

Written by:
PK

How long until your money doubles? This doubling time calculator tells you how many periods it takes for a quantity to double given a constant growth rate.

Doubling Time Calculator

Using the doubling time calculator

Enter your expected Rate per period as a percentage. The calculator instantly shows how many periods it takes to double.

The period can be whatever timeframe matches your rate: if you enter an annual return, you get years; monthly return, months.

The doubling time formula

The formula for doubling time is:

\text{doubling time} = \frac{\ln(2)}{\ln(1 + r)}

Where r is the rate per period as a decimal (e.g., 7% = 0.07).

Example: doubling at 7%

How long to double an investment growing at 7% per year?

t = \frac{\ln(2)}{\ln(1.07)} = \frac{0.693}{0.068} \approx 10.24 \text{ years}

The Rule of 72

The Rule of 72 is a mental math shortcut for doubling time:

\text{Doubling time} \approx \frac{72}{\text{rate \%}}

At 8%, money doubles in roughly 72 / 8 = 9 years. At 6%, about 72 / 6 = 12 years. It's surprisingly accurate for rates between 5-15%.

Why 72? It's close to ln(2) × 100 ≈ 69.3, but 72 is easier to divide mentally (it has factors 2, 3, 4, 6, 8, 9, 12...).

Negative rates

If you enter a negative rate, the calculator tells you how many periods ago the amount was twice as high, assuming constant decline. A -5% rate shows -13.51 periods – meaning 13.51 periods in the past.

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PK

PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.

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