Rule of 72 Calculator
Estimate how long an investment takes to double, then compare the shortcut against the exact compounding answer.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Divide 72 by the annual percentage return and you get the doubling time. It is a mental-maths shortcut, not a formula: the approximation is accurate to within a few tenths of a year for returns between about 5% and 12%, and drifts at the extremes. This page shows both the shortcut and the exact result so you can see the gap.
Worked example
calculated with the default values below
Annual rate of return 7 % · Starting amount 10,000 $ · Years to project 20 years Doubling time (rule of 72) 10.29 years · Doubling time (exact) 10.24 years · Shortcut error 0.04 years · Doublings in the period 1.95 · Value after the period 38,697 $
General background references
Disclaimer
These calculators give estimates for general information only. They are not financial, tax or investment advice and do not take your personal circumstances into account. Before borrowing, investing or filing, confirm the numbers with a qualified adviser in your jurisdiction.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
t72 = 72 ÷ i; t = ln 2 ÷ ln(1 + i ÷ 100); FV = P × 2^(Y ÷ t)
- i
- Annual interest rate (%)
- t72
- 72-rule estimate (years)
- t
- Exact doubling time (years)
- P
- Principal
- Y
- Investment years
Annual compounding; doublings = Y ÷ t; t72 is approximate and the gap to t is reported.
Frequently asked questions
How accurate is the rule of 72?
Reasonably near eight percent, and worse at the extremes. It slightly overstates doubling time at low rates and understates it at high ones. The exact figure comes from dividing the logarithm of two by the logarithm of one plus the rate, and the divergence beyond about fifteen percent is large enough to matter for a long-horizon decision.
Does it work for inflation as well as for growth?
Yes, and that is one of its most useful applications. Divide 72 by the inflation rate to get the years in which money halves in purchasing power. At three percent that is twenty-four years, which is a vivid way to show why cash held for a long period is not a neutral choice.