How does the Rule of 72 work?

Divide 72 by your annual growth rate to estimate the years it takes for money to double. At 8% a year, 72 divided by 8 is about 9 years. To go the other way, divide 72 by your target years to find the rate you would need.

How accurate is the Rule of 72?

It is a close approximation for rates roughly between 6% and 10%, where the error is well under a tenth of a year. For very high or very low rates the exact compounding answer (using logarithms) drifts further from the shortcut — this calculator shows both figures and the gap between them so you can see exactly how far off it is.

Should I use 70, 72 or 73?

72 is the all-rounder because it divides cleanly by many common rates. 70 (or the exact 69.3) is more accurate at very low rates and for continuous compounding, while 73 edges ahead above roughly 12%. The dropdown lets you switch and watch the error column respond.

Can I use it for tripling or tenfold growth, not just doubling?

Yes. The rule scales by the number of doublings: tripling is about 1.585 doublings, so the time is the doubling estimate multiplied by 1.585. This tool does that automatically when you pick triple, quadruple or tenfold as the growth target.

Does it work for inflation as well as investments?

Yes. The same shortcut estimates how long prices take to double at a given inflation rate, or how long until savings lose half their buying power. At 3% inflation, prices roughly double in 24 years.

How do I get the exact doubling time?

The exact figure for annual compounding is ln(2) divided by ln(1 plus the rate). At 8% that is 0.693 divided by 0.0770, about 9.0 years, almost identical to the Rule of 72 estimate. Switch the compounding selector to monthly, daily or continuous to see how the exact answer shifts.

Is anything I enter uploaded?

No — the calculation runs entirely in your browser and nothing you type leaves your device.

Rule of 72 Calculator

The Rule of 72 is the most useful piece of mental arithmetic in personal finance: divide 72 by an annual growth rate to estimate how many years money takes to double. This calculator runs it both ways. Enter a rate to get the doubling time, or enter a target number of years to find the rate you would need to hit it. It is built for sizing up investment returns, inflation, fund fees or any figure that compounds, without opening a spreadsheet — and it goes a step further by showing the exact compound answer right beside the shortcut so you can see how trustworthy the estimate is for your numbers.

How it works

The tool applies two arrangements of the same rule. For doubling time it computes years equal to the rule number divided by the rate. For the rate needed it divides the rule number by your target years. You can swap the rule number between 72 (the classic), 70 and the exact 69.3 (best for low rates and continuous compounding), or 73 (better above about 12%). You can also target triple, quadruple or tenfold growth instead of doubling — the rule scales by the number of doublings involved, so tripling is about 1.585 doublings.

Alongside the estimate, the calculator solves the exact formula using logarithms and lets you choose annual, monthly, daily or continuous compounding for that precise figure. A chart plots the shortcut against the exact curve across a band of rates, and a table lists both numbers side by side with the difference, so the sweet spot — and the edges where the rule starts to drift — are obvious at a glance.

Formula

Years to double ≈ N ÷ rate and rate to double ≈ N ÷ years (with N = 72, 70, 69.3 or 73)

The exact comparison uses t = ln(multiple) ÷ ln(1 + i), where i is the periodic rate and the result is converted back to years for the chosen compounding schedule.

Worked example

At an 8% annual return, money doubles in about 72 ÷ 8 = 9 years — almost exactly the precise answer of 9.01 years, so the error is a rounding artefact. Working backwards, to double in 6 years you would need roughly 72 ÷ 6 = 12% per year, against an exact requirement of 12.25%. Switch the target to tripling and the estimate stretches to about 14.3 years at 8%, because tripling is 1.585 doublings rather than one.

Annual rate	Rule of 72	Exact doubling time
3%	24.0 yr	23.4 yr
6%	12.0 yr	11.9 yr
8%	9.0 yr	9.0 yr
10%	7.2 yr	7.3 yr
12%	6.0 yr	6.1 yr

Everything runs in your browser, so nothing you enter is uploaded or stored.