Rule of 72 Calculator
Estimate how long money takes to double with the rules of 72, 70 and 69.3, and see how far each is from the exact answer at your rate. Works backwards too: the rate needed to double in a set time.
How to Use
- Choose Doubling time to start from a rate, or Rate to double to start from a number of years.
- Enter the yearly interest rate or growth rate in percent (or the years, in Rate mode).
- Pick how often it compounds: yearly for most investment returns, monthly for loans and savings accounts, continuously for the rule of 69.3.
- Read the exact doubling time and what each rule estimates, with its error in percent.
- Check the table and the error chart to see which rule is closest across the range of rates.
Worked Example
Doubling at 6%. The rule of 72 says 72 ÷ 6 = 12 years. The exact time solves 1.06t = 2, so t = ln 2 ÷ ln 1.06 = 0.693147 ÷ 0.0582689 = 11.8957 years. The rule is 0.104 years (+0.88%) long; the rule of 70 gives 11.667 years (−1.93%).
The rate to double in 10 years. The rule gives 72 ÷ 10 = 7.2%. Exactly, (1 + r)10 = 2, so r = 21/10 − 1 = 7.1773% a year.
The common mistake: using the rule at high rates. At 24% a year, compounded yearly, the rule of 72 says 3 years, but 1.243 is only 1.9066; the exact doubling time is 3.2223 years, 6.9% longer. The error grows with the rate because the rule leans on ln(1 + r) ≈ r, which only holds for small r.
Show Work
Formulas
Pacioli’s Rule
The oldest known statement of the rule of 72 is in Luca Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalita, printed in Venice in 1494 — the same book that first published double-entry bookkeeping. Pacioli gives the rule without proof, as something merchants already used, which suggests it is older still. Logarithms, which explain why it works, were not published until John Napier’s tables of 1614.
The explanation: money doubles when (1 + r)t = 2, so t = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, giving t ≈ 0.693 ÷ r — the rule of 69.3. Because ln(1 + r) is a little less than r, a larger numerator corrects for it at normal rates; 72 is exact at about 7.85% and has many divisors, so it won.
About This Calculator
This calculator puts the three doubling rules next to the exact answer for yearly, quarterly, monthly, daily or continuous compounding, and shows each rule’s error at your rate and across a table of common rates. The exact figures come from logarithms and are checked against the standard time-value functions. For the full growth of an amount over time, with deposits, use the Compound Interest Calculator.
All calculations run in your browser; nothing you enter is sent to a server.
Estimates for planning and education — not financial, tax or legal advice.
Related tools: Compound Interest Calculator, CAGR Calculator, and Inflation Calculator.
Frequently Asked Questions
How accurate is the rule of 72?
Very close for everyday rates with yearly compounding. At 8% it says 9 years; the exact answer is 9.0065. It is exact at about 7.85%, a little long below that (36 years against 35.003 at 2%) and short above it (3 years against 3.2223 at 24%).
Should I use the rule of 70 or the rule of 72?
The rule of 70 is closer at low rates: at 2% it gives 35 years against an exact 35.003, while 72 gives 36. That is why economists quote it for GDP and population growth. The rule of 72 is closer from about 5% up and divides evenly by 2, 3, 4, 6, 8, 9 and 12, which makes it easy to do in your head.
Where does the rule of 69.3 come from?
From ln 2 = 0.693147. With continuous compounding the exact doubling time is ln 2 ÷ r, so 69.3 ÷ rate is almost exact: at 5% compounded continuously it gives 13.86 years against 13.8629. With yearly compounding it is always a little short, because ln(1 + r) is smaller than r.
Does it work for inflation and debt?
Yes — anything that compounds. At 3% inflation prices double, and the value of a dollar halves, in 23.4498 years (the rule of 72 says 24). A credit card balance at 24% APR compounded monthly doubles in 2.9169 years if nothing is paid.
Can I find the rate needed to double my money?
Yes. Divide 72 by the years: doubling in 10 years needs about 7.2% a year; the exact rate is 21/10 − 1 = 7.1773%. For tripling there is a rule of 114 (100 × ln 3 = 109.86, rounded up for yearly compounding): at 8% it says 14.25 years, against an exact 14.2749.
How do I use the Rule of 72 Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Savings goals
Money earning 6% a year doubles in about 12 years by the rule of 72; the exact figure is 11.8957 years.
Long-term investing
$10,000 at 6% for 36 years doubles three times by the rule, to about $80,000; compounded exactly it reaches $81,472.52.
Inflation
At 3% inflation a dollar loses half its buying power in 23.4498 years.
Credit card debt
An unpaid balance at 24% APR, compounded monthly, doubles in 2.9169 years.
Economic growth
An economy growing 2% a year doubles in 35.003 years — the rule of 70 says 35.
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