Rule of 72 Calculator
The Rule of 72 is a shortcut that estimates how many years it takes money to double at a given annual return. It is not perfect, but it is fast, memorable and surprisingly useful when you want rough intuition before running a full projection.
The exact result uses the compound growth formula rather than the shortcut.
How the Rule of 72 works
At 7%, the shortcut gives about 10.3 years. The exact compound result is about 10.24 years. That small gap is why the rule is useful for intuition but not a replacement for a full calculator.
Why people use it
- It turns abstract percentages into a time estimate you can feel.
- It helps compare return assumptions quickly.
- It is good for rough planning conversations before detailed modelling.
Where it can mislead you
| Situation | Why the shortcut is weaker |
|---|---|
| Very low or very high rates | The shortcut becomes less precise outside the middle range. |
| Monthly contributions | The rule does not account for new deposits being added along the way. |
| Fees, taxes or inflation | Your real doubling time may be longer than the headline estimate. |
Best related pages
When to switch to the main calculator
Use the Rule of 72 for mental math and fast comparisons. Switch to the main compound interest calculator when you want to model a real scenario with starting balance, monthly contributions, contribution timing and a year-by-year breakdown.
How accurate the Rule of 72 is, rate by rate
The Rule of 72 estimates doubling time by dividing 72 by the percentage growth rate. It is an approximation of t = ln(2) / ln(1 + r), and it is accurate over exactly the range investors care about.
| Annual return | Rule of 72 estimate | Exact doubling time | Error |
|---|---|---|---|
| 2% | 36.00 years | 35.00 years | +2.8% |
| 4% | 18.00 years | 17.67 years | +1.9% |
| 6% | 12.00 years | 11.90 years | +0.9% |
| 7% | 10.29 years | 10.24 years | +0.4% |
| 8% | 9.00 years | 9.01 years | -0.1% |
| 10% | 7.20 years | 7.27 years | -1.0% |
| 12% | 6.00 years | 6.12 years | -1.9% |
| 15% | 4.80 years | 4.96 years | -3.2% |
| 20% | 3.60 years | 3.80 years | -5.3% |
Exact figures assume annual compounding.
The rule is essentially exact at 8%, where its error is 0.07%, and stays within about 1% across the 6–10% band that covers most long-run equity assumptions. It drifts high at very low rates and low at very high ones, which is why the Rule of 70 is preferred for inflation and the Rule of 72 for returns.
The mathematically correct numerator for small rates is 100 × ln(2) ≈ 69.3. 72 trades a little accuracy for a great deal of convenience: it divides cleanly by 2, 3, 4, 6, 8, 9 and 12, which is what makes the rule usable in your head. The upward adjustment also happens to cancel the curvature of the logarithm at around 8%, which is why the approximation is best exactly where it is most used.
Using it in reverse, and in series
- Find the rate you need. Divide 72 by the years available. To double in 9 years you need about 8% a year.
- Count doublings. At 7%, roughly a decade per doubling means about three doublings in thirty years — an eightfold increase. Checked against the exact figure, $10,000 at 7% compounded monthly reaches $81,165 over thirty years, or 8.1 times.
- Apply it to costs, not just returns. A 1% annual fee against a 7% return is a rate of 6%, which is 12 years per doubling rather than about 10. Over a career that is a whole doubling lost.
- Apply it to inflation. At 3%, prices double in about 24 years by the Rule of 72 — though the Rule of 70's 23.3 years is closer to the exact 23.45.
The rule's real value is not precision. It is that it converts a percentage into a timespan, and people reason far better about time than about rates. “This fund charges 1%” is abstract; “this fund costs me a doubling” is not.
Questions about the Rule of 72
What is the Rule of 72?
Divide 72 by the annual percentage return to estimate how many years an investment takes to double. At 7% that gives 10.3 years against an exact 10.24.
How accurate is the Rule of 72?
Within about 1% for rates between 6% and 10%, and essentially exact at 8%. It overstates doubling time at low rates and understates it at high ones.
When should I use the Rule of 70 instead?
For low rates — inflation, population growth, low-yield savings. Below roughly 5% the Rule of 70 is the closer approximation.
Does the Rule of 72 work with monthly contributions?
No. It answers how long a fixed amount takes to double through growth alone. With ongoing deposits the balance passes double much sooner, but mostly from your own money.