Transparent method
The formula
Worked example
Example inputs
How to interpret the result
The Rule of 72 trades precision for a fast mental estimate of doubling time, and like related shortcuts such as the Rule of 115, it holds up reasonably well at moderate, realistic rates and drifts further from an actual compound-growth calculation as the assumed rate climbs higher.
Before you rely on it
What to check
Cross-check the estimate against a full compound-growth calculation for anything beyond a quick mental gut check, especially at an unusually high assumed rate.
The common error
Where people go wrong with rule of 72 calculator
Treating the rule's output as precise enough to build an actual financial plan around. It was built as a fast approximation, and the gap between it and a real compounding calculation grows at higher rates.
Sensitivity evidence
How annual return or interest rate changes the rule of 72 doubling time
| Annual return or interest rate | Rule of 72 doubling time | Rule of 69.3 estimate |
|---|---|---|
| 4.0% | 18.0 years | 17.3 years |
| 6.0% | 12.0 years | 11.5 years |
| 8.0%worked example | 9.0 years | 8.7 years |
| 10.0% | 7.2 years | 6.9 years |
| 12.0% | 6.0 years | 5.8 years |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Annual return or interest rate | 8.0% |
| Rule of 72 doubling time | 9.0 years |
| Rule of 69.3 estimate | 8.7 years |
Where the inputs come from
Enter the annual return or interest rate as a percentage, such as 8 for 8%. The rule works best for rates between about 6% and 10%; at very low or very high rates the estimate drifts. Use the rate after fees, and for inflation, enter the inflation rate to see how quickly prices double. The tool needs only the rate and returns a time, so it is a quick check rather than a plan.
When the result stops applying
The rule is an approximation of the exact doubling time, which uses logarithms. It is accurate to within a few percent for typical rates but less so above 20%. It assumes a constant rate and no deposits or withdrawals, so it cannot model real investing with contributions. Taxes, fees and inflation reduce the actual doubling speed.
What to compare it with
For the exact figure with contributions use the compound interest calculator, and for tripling try the rule of 115. The future value calculator gives exact numbers for a chosen horizon. The rule is handy when comparing two rates: a 2-point difference at 6% versus 8% is the difference between doubling in 12 years and in nine.
People also ask
Frequently asked questions
Why is it the rule of 72 and not 70?
72 has many divisors, which makes mental division easy, and it is accurate for rates around 8%. Some people use 70 or 69.3 for lower rates or continuous compounding.
Does the rule work for inflation?
Yes. Divide 72 by the inflation rate to find how long prices take to double, or purchasing power takes to halve.
How accurate is it?
At 8% the exact doubling time is 9.01 years against the rule's 9.0. Accuracy falls at very high or very low rates.