BYTETOOLS

Rule of 72 Calculator

See how long it takes an investment to double using the Rule of 72, checked against the exact logarithmic answer so you can see the approximation error.

9.00 yrs
Rule of 72 estimate
9.006 yrs
Exact answer
-0.006 yrs
Approximation error

Which constant fits best at this rate?

RuleYears to doubleError vs exact
Rule of 69.38.662-0.344
Rule of 708.750-0.256
Rule of 718.875-0.131
Rule of 729.000-0.006
Rule of 739.125+0.119
Exact (ln 2 ÷ ln(1 + r))9.006—

At 8% the Rule of 72 is off by 0.07% of the true doubling time. The shortcut is at its most accurate between roughly 6% and 10%, and drifts at very low and very high rates.

Growing 2×

At 8% a year it takes 9.01 years to grow 2× — turning 10,000 into 20,000 before inflation, fees and tax.

The exact result is ln 2 ÷ ln(1 + r) for annual compounding — at 8% that is 9.006 years against the Rule of 72's 9.000. Assumes a constant rate with no withdrawals, fees, tax or inflation. Calculated in your browser; arithmetic, not financial advice.

What is the Rule of 72 Calculator?

The ByteTools Rule of 72 Calculator answers the classic mental-maths question: divide 72 by your annual return and you get roughly how many years it takes for money to double.

  • Rule of 72 alongside the exact ln 2 ÷ ln(1 + r) answer
  • Error shown in both years and percent so the drift is visible
  • Rules of 69.3, 70, 71 and 72 compared in one table
  • Reverse mode: solve for the rate needed to double in N years
  • Extends to tripling, quadrupling or any growth multiple
  • Instant, offline and private — nothing leaves your browser

How to use the Rule of 72 Calculator

  1. 1

    Choose whether to solve for years to double or for the required rate.

  2. 2

    Enter your annual rate of return, or the number of years you have.

  3. 3

    Compare the Rule of 72 answer with the exact logarithmic result.

  4. 4

    Check the error column to see how far the shortcut drifts at your rate.

  5. 5

    Optionally enter a starting amount to see the doubled and tripled values.

About the Rule of 72 Calculator

The ByteTools Rule of 72 Calculator answers the classic mental-maths question: divide 72 by your annual return and you get roughly how many years it takes for money to double. At 8% that is 72 ÷ 8 = 9 years, and the exact logarithmic answer, ln 2 ÷ ln(1.08), is 9.006 years — close enough to do in your head.

What makes this version useful is that it always shows both figures together with the size of the error, so you can see exactly where the shortcut starts to drift. The approximation is excellent between about 6% and 10% and gets progressively worse at very low and very high rates, where the Rules of 69.3, 70 and 71 do better — all of which are shown for comparison.

It also works in reverse: enter how many years you have and it solves for the return you would need to double, and it extends the doubling to any multiple you like. Everything is computed in your browser with nothing uploaded, and it is a maths tool rather than financial advice.

Frequently asked questions

How does the Rule of 72 work?

Divide 72 by the annual percentage return and the answer is roughly the number of years it takes for the money to double. At 6% that is 12 years, at 9% it is 8 years. It works because ln 2 is about 0.693 and, over the usual range of rates, 72 conveniently absorbs the compounding correction.

How accurate is the Rule of 72?

Very accurate between about 6% and 10%, where the error is well under a tenth of a year. At 2% it overstates the doubling time by around a year, and at 25% or more it drifts noticeably the other way. This calculator shows the exact answer next to it so you can always see the gap.

When should I use 69.3 or 70 instead of 72?

The Rule of 69.3 is the mathematically exact constant for continuous compounding, and 70 is a rounded version popular for low rates like inflation or population growth. 72 is preferred for mental arithmetic simply because it divides evenly by so many numbers.

Can the Rule of 72 be used for inflation or debt?

Yes, and it is just as useful in reverse. At 3% inflation, prices double in about 24 years, meaning your purchasing power halves. The same shortcut tells you how quickly a credit card balance doubles if you stop paying it.

What rate do I need to double my money in 10 years?

About 7.2%, from 72 ÷ 10. The exact answer is 7.18%, since 1.0718 raised to the power of 10 is almost exactly 2. Switch this tool to reverse mode and it solves that for any number of years.

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