Doubling Time Calculator
Calculate exactly how long it takes to double your money at a given interest rate using the precise formula and the Rule of 72 approximation.
How to use this tool
- Enter annual return rate and compounding in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your exact doubling time and the full breakdown beneath it.
The Rule of 72 gives a quick approximation of doubling time. This calculator also shows the mathematically exact result for any compounding frequency.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
Exact Doubling Time (annual compounding, n periods/year):
T = ln(2) ÷ (n × ln(1 + r / n))
For continuous compounding (n = 0): T = ln(2) ÷ r
Rule of 72 estimate: T ≈ 72 ÷ rate%
Rule of 69.3 estimate: T ≈ 69.3 ÷ rate%
How it works
This calculator finds the time required for an investment to double in value using three methods: an exact logarithmic formula derived from the compound interest equation, the Rule of 72 (a widely-used mental-math shortcut), and the Rule of 69.3 (which is mathematically optimal for continuous compounding). The exact formula uses natural logarithms and is accurate for any compounding frequency.
The Rule of 72 is a practical approximation that works best at moderate rates (roughly 2–20% per year); at extreme rates like 100% it diverges noticeably from the exact answer. Results assume a constant rate with no additional contributions.
Worked example
- Annual rate = 100% (r = 1.0); Compounding = 1× per year (annual).
- Exact = ln(2) ÷ (1 × ln(1 + 1.0 / 1)) = 0.6931 ÷ ln(2) = 0.6931 ÷ 0.6931 = 1 year.
- Rule of 72 estimate = 72 ÷ 100 = 0.72 years.
- Rule of 69.3 estimate = 69.3 ÷ 100 = 0.693 years.
Exact doubling time: 1 year; Rule of 72: 0.72 yrs; Rule of 69.3: 0.693 yrs.
Common mistakes to avoid
- Applying the Rule of 72 to very high or very low rates -- below 1% or above 25% the approximation diverges noticeably from the exact formula; use the exact result in those ranges.
- Entering a monthly return rate in a field that expects an annual rate, producing a doubling time measured in years that is actually the doubling time in months.
- Forgetting that taxes on annual gains reduce the effective rate, so the after-tax doubling time is longer than the pre-tax calculation suggests.
Key terms
- Rule of 72
- A mental-math shortcut: divide 72 by the annual interest rate percentage to estimate how many years it takes to double money. Accurate within a few percent at typical rates.
- Rule of 69.3
- A more precise doubling-time approximation based on ln(2) ≈ 0.693, best suited for continuous compounding.
- Natural logarithm (ln)
- The logarithm to the base e (≈ 2.718). Used in the exact doubling-time formula because compound growth is exponential.
- Compounding frequency
- The number of times per year that earned interest is added to the principal and begins earning interest itself.
- Continuous compounding
- The theoretical limit where interest is compounded infinitely often, resulting in growth described by the formula A = Pe^(rt).
Frequently asked questions
- What is the Rule of 72?
- The Rule of 72 is a mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. For example, at 8% it takes about 9 years (72 ÷ 8 = 9).
- What is continuous compounding?
- Continuous compounding assumes interest compounds infinitely often. The doubling time is ln(2) / r, which is the theoretical minimum. In practice, daily compounding is very close to continuous.
- Which rule is more accurate — 72 or 69.3?
- The Rule of 69.3 is more mathematically precise (ln(2) × 100 ≈ 69.3). The Rule of 72 is more popular because 72 has many factors, making mental math easier for common interest rates.