Rule of 72 and Doubling Time Calculator
How long money takes to double at a given interest rate: the Rule of 72 estimate (72 ÷ rate) next to the exact doubling time from the compound-growth formula, for annual, monthly, daily or continuous compounding. Works for any steady growth rate, from savings to inflation to population.
Last updated: October 2026
Exact doubling time
11.9 years
This calculator gives an estimate for general information only. It is not financial, tax or investment advice. Check the figures with a qualified professional before making decisions, and follow the rules that apply where you live.
Formula below · 1 source (investor.gov) · Updated Oct 2026
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About this calculator
Doubling time is how long a quantity growing at a steady percentage rate takes to become twice as large. Setting the compound-growth equation (1 + i/m)^(m·t) = 2 and solving for t gives the exact doubling time t = ln 2 ÷ (m · ln(1 + i/m)), where i is the annual rate as a decimal and m is the number of compounding periods per year; with annual compounding this is t = ln 2 ÷ ln(1 + i), and with continuous compounding it simplifies to t = ln 2 ÷ i = 0.693 ÷ i. The Rule of 72 is the mental-arithmetic shortcut: years to double ≈ 72 ÷ rate in percent. It works because 100 × ln 2 = 69.3, and 72 is close to that while dividing neatly by 2, 3, 4, 6, 8, 9 and 12; the extra 2.7 also happens to correct for annual (rather than continuous) compounding at rates around 8%. At 6% the rule says 12 years and the exact answer is 11.90; at 8% it says 9 and the exact figure is 9.01. The error grows away from that range: at 2% the rule gives 36 years against an exact 35.0, and at 24% it gives 3 years against 3.22. The Rule of 70 is slightly better for low rates and continuous growth (economists use it for GDP and population), and the Rule of 69.3 is exact for continuous compounding. More frequent compounding shortens the doubling time a little: 6% doubles in 11.90 years compounded annually, 11.58 monthly and 11.55 continuously. The same arithmetic describes any exponential process, so the calculator also answers how long prices take to double at a given inflation rate, a population at a given growth rate, or a debt at a given APR, and the tiles give the tripling and tenfold times (ln 3 and ln 10 in place of ln 2). It assumes the rate is constant and nothing is added or withdrawn; a 0% rate never doubles, which the calculator reports instead of a number.
Doubling time by rate: Rule of 72, Rule of 70, and the exact figure for annual and monthly compounding (years)
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| Rate | Rule of 72 | Rule of 70 | Exact (annual) | Exact (monthly) |
|---|---|---|---|---|
| 1% | 72.00 | 70.00 | 69.66 | 69.34 |
| 2% | 36.00 | 35.00 | 35.00 | 34.69 |
| 3% | 24.00 | 23.33 | 23.45 | 23.13 |
| 4% | 18.00 | 17.50 | 17.67 | 17.36 |
| 5% | 14.40 | 14.00 | 14.21 | 13.89 |
| 6% | 12.00 | 11.67 | 11.90 | 11.58 |
| 7% | 10.29 | 10.00 | 10.24 | 9.93 |
| 8% | 9.00 | 8.75 | 9.01 | 8.69 |
| 9% | 8.00 | 7.78 | 8.04 | 7.73 |
| 10% | 7.20 | 7.00 | 7.27 | 6.96 |
| 12% | 6.00 | 5.83 | 6.12 | 5.81 |
| 15% | 4.80 | 4.67 | 4.96 | 4.65 |
| 18% | 4.00 | 3.89 | 4.19 | 3.88 |
| 24% | 3.00 | 2.92 | 3.22 | 2.92 |
How to use
Example 1 — 6% compounded annually (the defaults). t = ln 2 ÷ ln 1.06 = 0.69315 ÷ 0.058269 = 11.90 years. Rule of 72: 72 ÷ 6 = 12 years, 0.10 years (about five weeks) longer than the exact answer. Rule of 70: 11.67 years. Tripling takes ln 3 ÷ ln 1.06 = 18.85 years and a tenfold increase 39.52 years. Example 2 — 8% compounded monthly. Choose Monthly and enter 8. t = ln 2 ÷ (12 × ln(1 + 0.08/12)) = 0.69315 ÷ (12 × 0.0066445) = 0.69315 ÷ 0.079734 = 8.69 years, against 9.01 years compounded annually and the Rule-of-72 estimate of 9. Monthly crediting of interest speeds the doubling up by about four months. Example 3 — inflation at 3%. Enter 3, annual: prices double in ln 2 ÷ ln 1.03 = 23.45 years (Rule of 72: 24). A retirement plan that starts 24 years out should budget for roughly twice today's prices.
Frequently asked questions
How accurate is the Rule of 72?
For annual compounding at rates between about 4% and 12% it lands within a few weeks of the exact answer: 11.90 vs 12 years at 6%, 9.01 vs 9 at 8%, 7.27 vs 7.2 at 10%. Outside that range it drifts, over-estimating at high rates (3.22 vs 3 years at 24%) and under-estimating slightly at very low rates. For precise planning, or for monthly or daily compounding, use the exact figure this calculator shows.
Where does the number 72 come from?
Solving (1 + i)^t = 2 gives t = ln 2 ÷ ln(1 + i). For small i, ln(1 + i) ≈ i, so t ≈ 0.693 ÷ i = 69.3 ÷ rate%. The approximation ln(1 + i) ≈ i under-states the denominator a little, so the true doubling time is longer than 69.3 ÷ rate; nudging the constant up to 72 corrects for that near 8% and, conveniently, 72 divides evenly by many common rates.
Should I use the Rule of 70 or the Rule of 72?
Use 72 for interest compounded once or a few times a year at ordinary rates (4–12%), where it is the more accurate of the two. Use 70 (or 69.3) for continuously compounding processes such as population growth, GDP growth or inflation measured as a continuous rate, and for low rates under about 3%, where 72 over-estimates. The difference is never more than a few percent of the answer.
Does compounding frequency change the doubling time?
Yes, but only modestly. The nominal rate is split into more frequent, smaller credits, each of which starts earning interest sooner, so the balance reaches double a little faster: at 6% it takes 11.90 years compounded annually, 11.72 quarterly, 11.58 monthly, 11.55 daily and 11.55 continuously. The rate itself matters far more: moving from 6% to 7% saves 1.65 years.
Can I use this for inflation or population growth?
Yes. Any quantity growing at a constant percentage rate follows the same formula. Enter the inflation rate to see how long prices take to double (23.4 years at 3%), a population growth rate to see when a population doubles (35 years at 2%), or a credit card APR to see how fast an unpaid balance doubles (3.5 years at 22% compounded monthly).
What does the calculator return at a 0% or negative rate?
At 0% the balance never changes, so the doubling time is infinite; the calculator says so instead of printing a number. A negative rate (a fee or deflation) shrinks the balance, which never doubles either; to find a halving time, enter the rate as a positive number and read the result as the time to fall by half, since ln(1/2) = −ln 2.
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