Rule of 72 calculator

How to calculate it

Years ≈ 72 / annual rate (%) · Annual rate (%) ≈ 72 / years

The Rule of 72 is a mental-math shortcut. The exact doubling time is ln(2) / ln(1 + r), where r is the annual rate as a decimal. For a target time of t years, the exact required rate is 2^(1/t) − 1.

Reference: Investor.gov: compound interest and the Rule of 72.

Worked example

At 8% annual growth, 72 ÷ 8 estimates nine years to double. Exact annual compounding gives 9.0065 years, about 0.0065 years longer. To double in five years, the shortcut estimates 14.4%; the exact rate is 14.87%.

Assumptions and limits

• The rate stays positive and constant, with no deposits or withdrawals. A zero or negative rate does not double an investment through growth.
• The comparison uses annual compounding. The Rule of 72 is an approximation, and its error changes with the rate. Read the exact result when precision matters.
• The calculator does not account for fees, taxes, inflation, or variable investment returns. Fractional doubling times describe the mathematical growth model.

Results use unrounded inputs and normally display two decimal places. Very small or large numbers may use scientific notation. Use consistent currency units; no currency conversion is applied.

Common questions