Doubling Time Calculator
Use this page to estimate how long it takes money to double at a given annual rate, or what annual rate you need to double money within a chosen number of years.
The exact result uses compound math. The Rule of 72 is a shortcut that is close in many normal ranges but not perfect.
How to use this page
- Use rate to years when you know the expected annual return and want a quick doubling estimate.
- Use years to rate when you know the doubling deadline and want to see the annual return that would imply.
- Use exact math for planning and the Rule of 72 for a quick sanity check.
Exact doubling time, and what the shortcuts get wrong
Doubling time is the cleanest way to feel a rate. “7% a year” is abstract; “doubles about every decade” is not. The exact answer comes from rearranging the compound interest formula for time, and the familiar mental shortcuts are approximations of it.
| Annual return | Exact doubling time | Rule of 72 says | Rule of 70 says | Rule of 72 error | Rule of 70 error |
|---|---|---|---|---|---|
| 2% | 35.00 years | 36.00 | 35.00 | +2.8% | -0.0% |
| 3% | 23.45 years | 24.00 | 23.33 | +2.3% | -0.5% |
| 4% | 17.67 years | 18.00 | 17.50 | +1.9% | -1.0% |
| 5% | 14.21 years | 14.40 | 14.00 | +1.4% | -1.5% |
| 6% | 11.90 years | 12.00 | 11.67 | +0.9% | -1.9% |
| 7% | 10.24 years | 10.29 | 10.00 | +0.4% | -2.4% |
| 8% | 9.01 years | 9.00 | 8.75 | -0.1% | -2.8% |
| 10% | 7.27 years | 7.20 | 7.00 | -1.0% | -3.7% |
| 12% | 6.12 years | 6.00 | 5.83 | -1.9% | -4.6% |
| 15% | 4.96 years | 4.80 | 4.67 | -3.2% | -5.9% |
| 20% | 3.80 years | 3.60 | 3.50 | -5.3% | -7.9% |
Exact figures use annual compounding: t = ln(2) / ln(1 + r).
The two rules bracket the truth from opposite sides. The Rule of 70 is almost exact at low rates — at 2% its error is 0.01% — and drifts low as rates rise. The Rule of 72 is nearly perfect around 8%, where its error is 0.07%, and drifts high at low rates. If you only remember one, remember 72 for investment returns and 70 for inflation and low-rate savings.
The starting balance cancels out of the equation entirely. $1,000 and $1,000,000 double in exactly the same number of years at the same rate — about 10.2 years at 7%. This is the single most useful property of compound growth to internalise: the rate and the timeline set the multiple, and the balance only sets the size of the result.
Compounding frequency shifts the answer slightly
The table above assumes annual compounding. Compounding more often shortens the doubling time a little, because interest starts earning sooner.
| Compounded | Doubling time at 7% |
|---|---|
| Yearly | 10.50 years |
| Quarterly | 9.88 years |
| Monthly | 9.96 years |
| Daily | 9.90 years |
Monthly compounding brings 7% doubling from 10.24 years down to about 9.96 — roughly three and a half months earlier. Worth knowing, not worth optimising for.
Questions about doubling time
What is the formula for doubling time?
t = ln(2) / ln(1 + r) for annual compounding, where r is the annual rate as a decimal. With n compounding periods per year it becomes t = ln(2) / (n × ln(1 + r/n)).
How long does money take to double at 7%?
About 10.24 years with annual compounding, or 9.96 years compounded monthly. The Rule of 72 estimates 10.3 years, which is close enough for a mental check.
Does doubling time depend on how much I have?
No. The starting amount cancels out of the formula. Only the rate and the compounding frequency matter, which is why doubling time is such a useful way to compare rates.
What about doubling with monthly contributions?
Then the question changes, because part of the increase is your own deposits rather than growth. Use the main calculator and read the interest column, which separates growth from contributions.