Rule of 72 calculator
Enter a growth rate to see how many years it takes to double (and triple), or enter the years to see the rate you need.
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What is the rule of 72?
Divide 72 by the annual growth rate in percent to estimate how many years it takes money to double. At 6% it is 72 ÷ 6 = 12 years; at 9%, 8 years; at 3%, 24 years. The exact answer is ln 2 ÷ ln(1 + rate), which is 11.9 years at 6%, so the shortcut is within a few percent for the usual range of rates. The calculator gives both, and works the other way round to find the rate needed to double in a given time.
Why we built this calculator
The rule of 72 is the quickest way to feel what a rate means. Seeing that money at 2% takes 36 years to double but at 8% only 9 makes compound growth, and the cost of high-interest debt, concrete. It works for savings, investments, inflation (prices doubling) and debt (what you owe doubling). This tool puts the shortcut next to the exact answer so you can see how good the estimate is, and adds the reverse question, which rate do I need, and other multiples such as tripling.
Everything is worked out in your browser. Nothing you enter is sent anywhere.
Why 72 works
At a yearly rate r, money grows by a factor (1 + r) each year, so it doubles when (1 + r)ⁿ = 2, that is n = ln 2 ÷ ln(1 + r). For small r, ln(1 + r) is close to r, and ln 2 is about 0.693, so n is about 69.3 ÷ (100 r) with r in percent, which is the rule of 69.3 and is exact for continuous compounding. People use 72 instead of 69.3 because 72 has many whole-number divisors (2, 3, 4, 6, 8, 9, 12), which makes mental sums easy, and because it makes up for the error at typical rates of 6% to 10%, where annual compounding is a little slower than continuous. The estimate is best between about 6% and 10% and gets a little worse at very low or very high rates.
A quick table
Doubling time at common rates.
| Annual rate | Rule of 72 | Exact |
|---|---|---|
| 1% | 72.0 | 69.7 |
| 2% | 36.0 | 35.0 |
| 3% | 24.0 | 23.4 |
| 4% | 18.0 | 17.7 |
| 5% | 14.4 | 14.2 |
| 6% | 12.0 | 11.9 |
| 7% | 10.3 | 10.2 |
| 8% | 9.0 | 9.0 |
| 9% | 8.0 | 8.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6.0 | 6.1 |
| 15% | 4.8 | 5.0 |
How to use it
- Choose 'years to double' and enter an annual rate, or choose 'rate needed' and enter a number of years.
- To find tripling or any other multiple, change the goal multiple (2 means doubling).
- Compare the exact answer with the rule of 72 estimate.
- Use the table of 10 and 20 years to see what the rate does over a working lifetime.
- Remember that real investment returns vary from year to year.
Use cases
- Seeing how long savings take to double at a savings or GIC rate
- Understanding the cost of high-interest debt: at 20% what you owe doubles in about 3.6 years
- Estimating how fast prices double at an inflation rate
- Deciding what yearly return a goal needs
- Teaching compound growth
- A quick check on a sales pitch that promises doubling
Problems you may run into
Most trouble is about what the rule assumes.
| What you see | Likely cause | What to do |
|---|---|---|
| The rule of 72 and the exact answer differ | The shortcut is an approximation | Trust the exact figure; the rule is for mental sums |
| Real returns do not double on schedule | Returns vary from year to year | Treat the answer as an average over a long time |
| It ignores fees, tax and inflation | Only the rate you enter is used | Use a net-of-fees rate, and subtract inflation for real growth |
| I want to include monthly deposits | The rule is for a single amount | Use the savings goal or compound interest calculators |
| I want monthly compounding | Annual compounding is assumed | The difference is small; use the compound interest calculator for exact monthly figures |
The formula
How the answer is worked out.
exact years to double = ln 2 ÷ ln(1 + r), where r is the yearly rate as a decimalrule of 72: years ≈ 72 ÷ rate in percent; rule of 69.3 for continuous compoundingyears to grow k times = ln k ÷ ln(1 + r)rate needed to grow k times in n years = k^(1 ÷ n) − 1
The tool assumes yearly compounding and a constant rate. The rule of 72 is accurate to about 1 to 3% of the true time for rates between 4% and 15%. Results are shown to two or three decimal places.
Example: money at 6% a year
How long to double at 6%?
- Rule of 7272 ÷ 6 = 12 years
- Exactln 2 ÷ ln 1.06 = 11.90 years
- Triplingln 3 ÷ ln 1.06 = 18.85 years
About 12 years to double
At 12% it would be 6 years by the rule, 6.1 exactly.
Terms on this page
- Compound growth
- Growth that earns more growth, so it speeds up over time.
- Doubling time
- The time for a quantity growing at a steady rate to double.
Common questions
What is the rule of 72?
A shortcut: 72 divided by the yearly rate in percent is roughly the years it takes money to double.
How accurate is it?
Within a few percent for rates from about 4% to 15%.
Why 72 and not 69?
72 divides evenly by many numbers, and it fits the usual 6% to 10% range better for annual compounding.
Can I use it for debt?
Yes. At 20% interest, a balance that is not paid doubles in about 3.6 years.
Can I use it for inflation?
Yes. At 3% inflation, prices double in about 24 years.
Is anything I enter sent to a server?
No. The calculation happens in your browser and nothing you type leaves your device.
Where these numbers come from
- Wikipedia — Rule of 72 The rule, its derivation and its accuracy.
- Wikipedia — Compound interest How interest compounds.
Last verified 2026-10-25 The method on this page is checked against the sources above at least once a year. Spotted something out of date? Tell us and we will fix it.
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