Doubling Time and Rule of 72 Calculator
Enter a growth rate and see exactly how long it takes to double, triple or reach any multiple, next to the quick estimates from the rules of 72, 70 and 69.3 and how far each is out. A second tab works backwards to the rate you need to reach a multiple in a set number of years. A year by year table shows the growth. Everything runs in your browser.
That is about 10 years and 3 months, with the growth added to the total each year (annual compounding).
| Method | Years | Error |
|---|---|---|
| Exact | 10.245 | none |
| Rule of 72 (closest) | 10.286 | +0.40% |
| Rule of 70 | 10.000 | -2.39% |
| Rule of 69.3 | 9.900 | -3.37% |
| Year | Amount | Times the start |
|---|---|---|
| 0 | 1,000.00 | 1.000 |
| 1 | 1,070.00 | 1.070 |
| 2 | 1,144.90 | 1.145 |
| 3 | 1,225.04 | 1.225 |
| 4 | 1,310.80 | 1.311 |
| 5 | 1,402.55 | 1.403 |
| 6 | 1,500.73 | 1.501 |
| 7 | 1,605.78 | 1.606 |
| 8 | 1,718.19 | 1.718 |
| 9 | 1,838.46 | 1.838 |
| 10 | 1,967.15 | 1.967 |
| 11 | 2,104.85 | 2.105 |
The doubling time is how long steady growth takes to double an amount. The exact answer comes from logarithms: the time is ln(2) divided by ln(1 plus the rate). The rule of 72 is a mental shortcut that divides 72 by the rate in percent, and it is close at everyday rates. The rules of 70 and 69.3 are slightly better at lower and at very low rates. A negative rate gives the half-life of a steady decline. This is a pure growth calculation, not investment advice, and real returns are not steady. Everything is worked out in your browser.
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Math & MoneyAbout the Doubling Time and Rule of 72 Calculator
Doubling time is how long steady growth takes to double an amount. With a growth rate r per year, the amount after t years is multiplied by (1 + r) to the power t, so it doubles when that equals 2, which gives t = ln(2) divided by ln(1 + r). At 7 percent a year this is 10.24 years. The rule of 72 estimates the same thing by dividing 72 by the rate in percent, giving 10.29 years at 7 percent, which is close enough for mental arithmetic. At 3 percent the exact time is 23.45 years and the rule gives 24, while the rule of 70 gives 23.33, nearer for low rates. At 10 percent the exact time is 7.27 years and the rule of 72 gives 7.2. With continuous compounding the time is about 69.3 divided by the rate. The same logarithm gives the time to triple, 16.24 years at 7 percent, or to reach any multiple. Working backwards, the rate needed to double in 10 years is 2 to the power one tenth, minus 1, which is 7.177 percent a year. A negative rate gives a half-life: at minus 5 percent a year, an amount halves in 13.51 years. The calculation assumes the rate is steady and that growth is added each year, so it is a guide to compounding and not a forecast of any investment.
How do you calculate doubling time?▾
Divide the natural log of 2 by the natural log of 1 plus the growth rate. At 7 percent, that is 0.6931 divided by 0.0677, which is 10.24 years.
What is the rule of 72?▾
A shortcut that divides 72 by the annual rate in percent to estimate the years to double. At 8 percent, 72 divided by 8 is 9 years. It is accurate for rates of about 6 to 10 percent.
Why 72 and not 70 or 69?▾
72 divides evenly by many common rates, such as 2, 3, 4, 6, 8, 9 and 12, and it fits typical rates well. 69.3 is the more accurate figure for continuous compounding, and 70 is often used for lower rates.
How do you find the rate needed to double in a set time?▾
Raise 2 to the power of 1 divided by the number of years, subtract 1, and multiply by 100. To double in 10 years you need 7.18 percent a year.
Is my data uploaded?▾
No. The calculation runs in your browser and nothing you enter is sent anywhere.