The fastest way to estimate how long money takes to double at a given annual return. Enter a rate — see the rough Rule of 72 alongside the exact compound-growth math for comparison.
| Rule | Purpose | Formula | Years at 7% | Note |
|---|---|---|---|---|
| Rule of 72 | Doubles (2×) | 72 ÷ 7 | 10.3 yrs | Mental-math favourite |
| Rule of 69.3 | Doubles (2×) | 69.3 ÷ 7 | 9.9 yrs | More accurate, less tidy |
| Rule of 114 | Triples (3×) | 114 ÷ 7 | 16.3 yrs | Sibling shortcut for 3× |
| Exact (2×) | Doubles (2×) | ln(2) ÷ ln(1 + r) | 10.2 yrs | Compound-growth truth |
| Exact (3×) | Triples (3×) | ln(3) ÷ ln(1 + r) | 16.2 yrs | Compound-growth truth |
| Exact (10×) | 10× growth | ln(10) ÷ ln(1 + r) | 34.0 yrs | Long-horizon reference |
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Build a compounding portfolio with low-cost index funds and zero-commission trades.
Why we recommend it: Rock-bottom expense ratios let compounding actually compound.
Earn 4–5% on your cash so the Rule of 72 is actually working for you, not against you.
Why we recommend it: At 5%, money doubles every ~14.4 years — not true at 0.01%.
Track your savings rate and free up more capital to put to work compounding.
Why we recommend it: The Rule of 72 only helps if you have dollars doubling in the first place.
The Rule of 72 is a mental-math shortcut to estimate how many years it takes money to double at a given compound annual return. Divide 72 by the annual return percentage. At 7%, money doubles in about 10.3 years. At 10%, in about 7.2 years.
The Rule of 72 is accurate within 1% for interest rates between 5% and 12%. For rates above 15% or below 3%, use the exact formula: years = ln(2) ÷ ln(1 + rate). Our calculator shows both side-by-side.
The exact formula for doubling time is ln(2) ÷ ln(1 + rate) ≈ 0.693 ÷ rate. The number 72 is used instead of 69.3 because it has many integer divisors (2, 3, 4, 6, 8, 9, 12) — making mental math easier.
You need approximately 6.64 doublings to go from $10,000 to $1,000,000. At 7% annual return, each doubling takes ~10.3 years, so roughly 68 years total. At 10%, each doubling takes ~7.2 years — total ~48 years. This is why starting early matters so much.
Yes. Use it in reverse: at 3% inflation, prices double every 72 ÷ 3 = 24 years. At 5% inflation, every 14.4 years. This is why inflation matters enormously over long retirement horizons.
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This calculator is for educational purposes only and does not constitute financial, investment, or tax advice. Investment returns vary year to year; historical averages are not guarantees of future performance. Read our full disclaimer.