● Mental math for compounding

Rule of 72 Calculator

Divide 72 by your annual return rate to see how many years it takes to double your money. Works for investments, debts, and inflation.

The Rule of 72: at 6% annual return, money doubles in 72÷6 = 12 years. At 9%, it doubles in 8 years. At 2% inflation, purchasing power halves in 36 years. This simple rule is one of the most useful mental shortcuts in personal finance.

⏳

Enter rate → see doubling time instantly

⚙️

Your inputs

Annual rate

Starting amount (optional)

📊

Results

Years to double (Rule of 72)

—

Exact years (ln formula)

—

Rule of 72 accuracy

—

$10,000 becomes after doubling

—

Years to triple (Rule of 114)

—

Years to 10× (Rule of 240)

—

Doubling time by rate

Rate (%/yr)	Rule of 72 (years)	Exact (years)	What $10,000 becomes

How it's calculated

The Rule of 72: mental math for compounding

The Rule of 72 is a quick way to estimate how many years it takes for an investment to double: simply divide 72 by the annual percentage rate. At an 8% return, money doubles in roughly 72 ÷ 8 = 9 years; at 6% it takes about 12 years. No calculator, no logarithms — just one division you can do in your head.

It works because compound growth follows an exponential curve, and 72 is a handy stand-in for the exact mathematical constant (ln(2) × 100 ≈ 69.3) that governs doubling. The approximation is most accurate for everyday rates between roughly 6% and 10%, staying within about 1–2% of the precise answer for the whole 3%–25% range. At very high rates it drifts, so for those you should fall back on the exact logarithmic formula.

The rule also runs in reverse: divide 72 by the number of years you have to find the annual rate you'd need. If you want to double your money in 9 years, you need about 72 ÷ 9 = 8% per year. The same logic applies to anything that grows or shrinks at a steady rate, including inflation eroding your purchasing power.

The rule approximates the logarithmic formula for doubling time by using 72 as a convenient divisible constant close to ln(2) × 100 ≈ 69.3.

Rule of 72: Doubling years ≈ 72 ÷ rate(%) Exact formula: Doubling years = ln(2) ÷ ln(1 + rate) = 0.6931 ÷ ln(1 + rate) For tripling: 114.3 ÷ rate For 10×: 230.3 ÷ rate (ln(10) × 100)

1
Annual rate
—
2
Years to double (72 ÷ rate)
—
3
Years to triple (114 ÷ rate)
—

Rule of 72: Mental shortcut: 72 ÷ annual rate = years to double. Accurate within 1-2% for rates 3%–25%.
Compounding: Earning returns on previous returns. The "72" captures this exponential growth pattern.
Doubling time: The number of periods needed for an investment to grow to twice its initial value at a constant growth rate.
Annual rate: The yearly percentage growth applied to your balance, such as an investment return or an interest rate. It is the number you divide 72 by.
Rule of 70 / 69: Variants of the same idea using 70 or 69.3 instead of 72. They are slightly more precise (69.3 ≈ ln(2) × 100) but 72 is preferred because it divides evenly by more numbers.

🔢 Worked example

At 8% a year, money doubles in about 72 ÷ 8 = 9 years. The exact formula gives ln(2) ÷ ln(1.08) ≈ 9.01 years — the Rule of 72 is remarkably close.

Disclaimer: the Rule of 72 is an approximation for educational purposes. Actual investment returns vary and are not guaranteed. Always confirm with an official source before deciding.

Frequently asked questions

What does the Rule of 72 mean for retirement planning?

It turns an abstract rate into a countable number of doublings between today and your retirement date, which is the only thing that really matters over a long horizon. Measured on this page: at 8% a year money doubles every 9.00 years (exact figure 9.0065), at 6% every 12.00 years, and at 4% every 18.00 years. So a saver 27 years from retirement earning 8% gets three full doublings out of the same money — it ends up eight times larger — while at 4% the same 27 years buy only one and a half doublings. That gap, not the difference between 4 and 8 as numbers, is what a percentage point of fee or of return actually costs over a career. The same panel puts it another way: at 8% it takes 30.00 years to multiply by ten, and at 6% it takes 40.00. Two cautions before you plan on it. The rule assumes a single constant rate and nothing added or withdrawn, so it describes a lump sum left alone, not a plan you keep contributing to; and it says nothing about inflation, so if you want the answer in purchasing power, feed it your return minus expected inflation instead of the headline return.

What is the Rule of 72?

The Rule of 72 is a mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 6%, money doubles in 12 years. At 9%, in 8 years. It works well for rates between 3% and 25%.

Why 72 specifically?

72 is a good approximation of ln(2) × 100 ≈ 69.3, and it has the advantage of being highly divisible (by 2, 3, 4, 6, 8, 9, 12) — making mental math easy. Using 70 is slightly less accurate but even easier to divide. 69.3 is most mathematically precise.

Can the Rule of 72 apply to inflation?

Yes — divide 72 by the inflation rate to find when purchasing power halves. At 4% inflation: 72÷4 = 18 years. This is why keeping cash under a mattress is harmful during inflation — your savings lose half its value in less than 20 years at modest inflation.

Is the Rule of 72 accurate?

Very accurate for rates 3%–25%. At 8%, Rule of 72 gives 9 years vs the exact 9.006 years — less than 0.1% error. At extreme rates (50%, 100%), the error grows — use the exact logarithm formula instead.

Why 72 and not another number?

72 gives a good approximation of ln(2) ÷ r because it's highly divisible (by 2, 3, 4, 6, 8, 9, 12) making mental math easy. For precise calculations use ln(2)/ln(1+r). 70 and 69.3 (≈ln(2)×100) are also used for quick estimates.

What is the Rule of 114 and Rule of 144?

Rule of 114: divide 114 by the rate to find years to triple your money. Rule of 144: divide 144 by the rate to find years to quadruple your money. Example at 8%: double in 9yr (72/8), triple in ~14yr (114/8), quadruple in 18yr (144/8).

Are my results saved? Do I need an account?

No account or sign-up needed. Every calculation is saved automatically in your own browser, and you can also pin a result with the save button. Nothing is sent to any server: the data stays on your device and can be erased at any time with the clear button.

How do I track my progress over time?

From the fourth entry onward a “View comparison chart” button appears, opening a line chart with every entry in time order plus an indicator panel: total change, average per entry, lowest and highest value and the period covered. You can also export the history as CSV.

About this calculator

This Rule of 72 calculator estimates how long it takes to double your money at a given rate of return, using one of the most useful mental shortcuts in personal finance: divide 72 by the annual percentage rate. At 6% a year, money doubles in about 12 years; at 9%, in roughly 8.

The same shortcut runs in reverse for inflation: at 2% inflation, purchasing power halves in about 36 years. Treat the result as a quick, close approximation rather than an exact figure — it is meant for fast comparisons and building intuition about how powerfully compounding and inflation work over time.

By Vinicius Fonseca · Reviewed against official sources · Updated Jul 2026 · How we calculate →