Business / Money
Rule of 72 Calculator
Estimate doubling time from a growth rate or the rate needed to double money, with exact annual compounding and Rules of 70 and 69.3.
Rule of 72 Calculator: Compare four ways to estimate when a balance doubles. Enter an annual growth percentage or a target number of years and use the rate table to see where the shortcuts differ from exact annual compounding. Runs 100% locally in your browser with zero server file uploads.
- Category
- Business & admin tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
- Rule of 72 (years)
- 9.00
- Exact annual compounding (years)
- 9.01
- Rule of 70 (years)
- 8.75
- Rule of 69.3 (years)
- 8.66
| Rate (%) | Rule of 72 | Rule of 70 | Rule of 69.3 | Exact |
|---|---|---|---|---|
| 1 | 72.00 | 70.00 | 69.30 | 69.66 |
| 2 | 36.00 | 35.00 | 34.65 | 35.00 |
| 4 | 18.00 | 17.50 | 17.33 | 17.67 |
| 6 | 12.00 | 11.67 | 11.55 | 11.90 |
| 8 | 9.00 | 8.75 | 8.66 | 9.01 |
| 10 | 7.20 | 7.00 | 6.93 | 7.27 |
| 12 | 6.00 | 5.83 | 5.77 | 6.12 |
| 20 | 3.60 | 3.50 | 3.47 | 3.80 |
For rate r expressed as a decimal, exact years = ln(2) / ln(1 + r). Exact rate = 100 × (2^(1/years) − 1). The shortcuts divide 72, 70 or 69.3 by a percentage rate or by years. They are approximations; 69.3 is close to continuous compounding. Zero or negative growth does not double a positive balance. No contributions, fees or taxes are included.
Rule of 72
Investor.gov: compound interest: https://www.investor.gov/additional-resources/information/youth/teachers-classroom-resources/what-compound-interest introduces the Rule of 72: divide 72 by the annual percentage return to estimate years until an investment doubles. This is a constant-rate illustration, not a return forecast.
Exact calculation and other shortcuts
For annual compounding, years = ln(2) / ln(1 + r), where r is a decimal rate. Inverting gives rate (%) = 100 × (2^(1/years) − 1).
Rules of 70 and 69.3 substitute those constants for 72. The continuous-compounding constant 100 × ln(2) is about 69.3147; 69.3 is a rounded approximation. The exact comparison here always uses annual compounding.
How to use it
- Choose doubling time or the required annual rate.
- Enter a positive growth rate or time in years.
- Compare the exact result and the three shortcuts.
Privacy & limitations
All calculations run in your browser. No financial inputs are uploaded.
Related tools
Frequently asked questions
Why does Rule of 72 differ from the exact result?
It divides 72 by the percentage rate. Exact annual compounding solves (1 + rate)^years = 2, so the shortcut’s accuracy varies with the rate.
What happens at zero or negative growth?
A positive starting balance does not double without contributions at zero or negative growth. Enter a positive rate.
Do the rules include regular savings?
No. They assume one starting balance, a constant growth rate and no additions, withdrawals, fees or taxes.
Free tool · runs in your browser · no account required