Rule of 72 Calculator
Quick mental math to estimate investment doubling time using the classic Rule of 72
⚙️Calculator Mode
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1 year15 years30 years
For visualization purposes (doesn't affect Rule of 72)
⏱️Time to Double Your Money
Rule of 72 Estimate:
9.0
years
Exact Calculation:
9.0
years
Accuracy:99.9%
Error Margin:±0.01 years
Multiple Doubling Periods
See how your $10,000 grows over multiple doubling periods at 8%
| Period | Years | Rule of 72 Value | Exact Value | Difference |
|---|---|---|---|---|
| Start | 0.0 | $10,000 | $10,000 | |
| 1x Double | 9.0 | $20,000 | $19,990 | $10 (-0.05%) |
| 2x Double | 18.0 | $40,000 | $39,960 | $40 (-0.10%) |
| 3x Double | 27.0 | $80,000 | $79,881 | $119 (-0.15%) |
| 4x Double | 36.0 | $160,000 | $159,682 | $318 (-0.20%) |
| 5x Double | 45.0 | $320,000 | $319,204 | $796 (-0.25%) |
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Key Insight
The Rule of 72 becomes slightly less accurate over multiple doubling periods, but remains a remarkably useful approximation for quick mental calculations.
📐 The Math Behind It
Rule of 72 Formula:
Years to Double = 72 ÷ Interest Rate
Example: 72 ÷ 8% = 9 years
Exact Formula (using natural logarithm):
Years to Double = ln(2) ÷ ln(1 + r)
Where r is the interest rate as a decimal
Why 72? Because 72 has many factors (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72), making mental division easier for common interest rates. It also happens to be remarkably accurate for rates between 6-10%.