Rule of 72
How fast does money double? Divide 72 by the rate — and because shortcuts deserve honesty, we show the exact answer right next to it.
Anyone with the link can see the numbers included in it.
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Last reviewed: July 20, 2026 · Formulas verified by automated tests before every release.
How does the Rule of 72 work?
Divide 72 by an annual percentage rate to estimate the years needed for a value to double: at 8% growth, 72 ÷ 8 ≈ 9 years. The shortcut stays within about 2% of the exact answer for rates between 3% and 15%, which is why it has survived centuries of mental math.
The shortcut and the exact formula
years ≈ 72 ÷ rate% · exact: years = ln(2) ÷ ln(1 + rate/100)
The rule's magic is divisibility: 72 splits cleanly by 2, 3, 4, 6, 8, 9 and 12, so the answer arrives before a phone unlocks. Our calculator shows the exact figure alongside — at everyday rates the gap is decimal dust, and seeing both builds the right instinct: shortcuts are for conversation, compound math is for decisions. For the full picture with monthly contributions, continue to the compound interest calculator.
The dark twin: inflation
The same arithmetic runs backwards. At 6% inflation, prices double in ~12 years — which means money under a mattress loses half its purchasing power in the same 12. One number, two feelings: 8% growth doubling in 9 years feels slow until you realize 6% inflation halves things almost as fast. That tension is the entire argument for investing.
🎮 60-second challenge: before trusting the formula, test your gut — guess when money doubles and meet the real curve. Most people lose by years.
Sources, assumptions and limitations
- Formula: years ≈ 72 ÷ rate; exact comparison: ln(2) ÷ ln(1 + rate/100)
- Assumptions: Constant annual compounding at the given rate; the approximation is honest within ~2% for rates of 3–15%.
- Not included: Taxes, fees, variable returns — this is a mental-math instrument, not a plan. No external data used.
- Last reviewed: July 23, 2026 by the CalcNotebook team
Frequently asked questions
What is the Rule of 72?
A mental-math shortcut: divide 72 by an annual growth rate to estimate how many years a value takes to double. At 8% a year, 72 ÷ 8 = 9 years. It works for investments, inflation, prices — anything compounding.
How accurate is it?
Remarkably, for a shortcut: within about 2% of the exact answer for rates between 3% and 15% — the range where most real financial questions live. The calculator shows both numbers side by side, so the honesty is built in.
Does it work for inflation too?
Yes, in reverse: at 6% inflation, prices double — meaning cash halves in purchasing power — in about 12 years. It is the fastest way to feel what an inflation number actually does to savings.
Why 72 and not 69.3?
The mathematically pure constant is ln(2) ≈ 69.3, but 72 divides cleanly by 2, 3, 4, 6, 8, 9 and 12 — mental math beats precision for a rule you use in conversation. For exact answers, use the compound interest calculator.