How accurate is the rule of 72?

It is very close between roughly 6% and 10%, typically off by a few hundredths of a year. Outside that band the error grows: at 2% it overstates the doubling time by about a year (36.0 versus an exact 35.0), and at 20% it understates it by roughly 0.2 years (3.6 versus an exact 3.80).

How long does it take to double money at 7%?

The rule of 72 gives 72 divided by 7, which is about 10.3 years. The exact logarithmic answer is close, at roughly 10.24 years, so either figure is a reasonable planning estimate at this rate.

Does the rule of 72 work for inflation instead of growth?

Yes, the same math answers how long prices take to double at a given inflation rate. At 3% inflation, prices roughly double in 72 divided by 3, or 24 years; at 6% inflation, they double in about 12 years, which is why sustained high inflation erodes purchasing power far faster than most people expect.

Is the rule of 72 or rule of 70 more accurate?

The rule of 70 is sometimes preferred for lower rates because dividing by 70 tracks the exact continuous-compounding answer slightly more closely below about 5%, while 72 tends to fit discrete annual compounding better in the 6% to 12% range where most investment return assumptions sit. The difference between the two rarely exceeds a few tenths of a year either way.

Can I use the rule of 72 for debt instead of savings?

Yes, in reverse: it estimates how quickly unpaid debt doubles at a given interest rate if no payments are made. A credit card balance charging 24% APR would double in about three years (72 divided by 24) if left completely untouched, which is a useful way to see how fast compounding interest can work against you rather than for you.

Why does the calculator show two different numbers?

The 'rule of 72 estimate' is the quick mental-math shortcut, while the 'exact answer' solves the compounding equation directly using logarithms. They are usually within a few percent of each other, and the gap widens the further the entered rate sits from the 6% to 10% band where the shortcut was designed to work best.

Rule of 72 calculator

The rule of 72 is a mental shortcut for estimating how long a sum of money takes to double at a fixed annual growth rate: divide 72 by the rate. This calculator gives you that quick estimate alongside the exact logarithmic answer, so you can see both how close the shortcut lands and what the real doubling time is once compounding is worked out properly.

How the shortcut compares with the exact figure

The rule of 72 exists because dividing 72 by a percentage is easy to do without a calculator, and 72 has enough small factors (2, 3, 4, 6, 8, 9, 12) that the result is usually a clean number. The exact formula, by contrast, is the natural log of 2 divided by the natural log of one plus the rate, expressed as a decimal.

At an 8% return the shortcut gives 9.0 years, while the exact answer is about 9.01 years, a gap of essentially nothing. The approximation is tightest in the 6% to 10% range and drifts further off at the extremes: at 2% it says 36.0 years against an exact 35.0, and at 20% it says 3.6 years against an exact 3.80, an error of roughly 5%.

As a benchmark, most long-run stock market return assumptions used in retirement planning sit between 6% and 8% nominal, which is exactly the band where the rule of 72 is most trustworthy, so the shortcut and the calculator's exact figure will rarely disagree by more than a couple of months in that range.

Three doubling-time scenarios

A savings account paying 4% compounds to double in about 17.7 years by the exact formula, while the rule of 72 shortcut says 18.0 years; both point to the same conclusion, that a low-yield account is a multi-decade tool for doubling money, not a short-term one.

A diversified portfolio returning 9% a year doubles in about 8.0 years exactly (the shortcut also gives 8.0), triples in about 12.75 years, and reaches four times its starting value in roughly 16.1 years, since each doubling period simply repeats.

A concentrated position or leveraged account targeting 12% a year would double in about 6.1 years and triple in about 9.7 years; at that pace, 25,000 invested today is worth roughly 100,000 in just over 12 years if the 12% rate genuinely holds for that long, which is the part most likely to go wrong.

Where the rule stops working

Every version of this calculation assumes one constant annual rate applied every year with no interruption. Real portfolios do not grow in a straight line: a run of down years followed by a recovery rarely averages out to the same ending balance as a steady rate would produce, because losses require a proportionally larger gain to offset them. A 50% drop needs a 100% gain just to get back to even, so volatile returns generally reach a given multiple slower than a smooth average return of the same arithmetic mean.

The formula also ignores taxes, fees and inflation. A 7% return in a taxable account might behave more like 5.5% to 6% after tax drag each year, which pushes the real doubling time out by several years compared with the pre-tax figure the calculator shows. Inflation does the opposite job in reverse: even if a balance doubles in nominal terms, its purchasing power has only doubled if prices have not also roughly doubled over the same stretch.

At very high or very low rates the linear shortcut simply loses accuracy, because the underlying relationship is logarithmic, not linear. Treat anything below 3% or above 15% as a case where the exact figure, not the 72-divided-by-rate shortcut, is the one worth quoting.

Rate assumptions and account timing

US savings and money-market accounts publish an annual percentage yield (APY) that already reflects compounding frequency, so plugging an APY straight into this calculator gives a doubling time in calendar years without further adjustment. A stated interest rate rather than an APY, common on some CDs and bonds, needs converting first if compounding happens more often than annually, or the doubling time will run slightly long.

In a tax-advantaged account such as a 401(k), IRA, UK ISA or SIPP, the full return compounds untouched and the calculator's figure applies directly. Outside of those wrappers, dividends and realised gains are typically taxed as they occur (in the US) or at disposal (capital gains in the UK), which lowers the effective rate actually compounding year to year.

Rates that reset, such as variable-rate savings accounts or adjustable bond yields, break the single-rate assumption entirely. For those, this calculator is best used as a rough guide at today's rate rather than a forecast, since a rate cut or hike partway through the period changes the real doubling time in ways a single division cannot capture.

Frequently asked questions

How accurate is the rule of 72?: It is very close between roughly 6% and 10%, typically off by a few hundredths of a year. Outside that band the error grows: at 2% it overstates the doubling time by about a year (36.0 versus an exact 35.0), and at 20% it understates it by roughly 0.2 years (3.6 versus an exact 3.80).
How long does it take to double money at 7%?: The rule of 72 gives 72 divided by 7, which is about 10.3 years. The exact logarithmic answer is close, at roughly 10.24 years, so either figure is a reasonable planning estimate at this rate.
Does the rule of 72 work for inflation instead of growth?: Yes, the same math answers how long prices take to double at a given inflation rate. At 3% inflation, prices roughly double in 72 divided by 3, or 24 years; at 6% inflation, they double in about 12 years, which is why sustained high inflation erodes purchasing power far faster than most people expect.
Is the rule of 72 or rule of 70 more accurate?: The rule of 70 is sometimes preferred for lower rates because dividing by 70 tracks the exact continuous-compounding answer slightly more closely below about 5%, while 72 tends to fit discrete annual compounding better in the 6% to 12% range where most investment return assumptions sit. The difference between the two rarely exceeds a few tenths of a year either way.
Can I use the rule of 72 for debt instead of savings?: Yes, in reverse: it estimates how quickly unpaid debt doubles at a given interest rate if no payments are made. A credit card balance charging 24% APR would double in about three years (72 divided by 24) if left completely untouched, which is a useful way to see how fast compounding interest can work against you rather than for you.
Why does the calculator show two different numbers?: The 'rule of 72 estimate' is the quick mental-math shortcut, while the 'exact answer' solves the compounding equation directly using logarithms. They are usually within a few percent of each other, and the gap widens the further the entered rate sits from the 6% to 10% band where the shortcut was designed to work best.

Sources

Federal Reserve Economic Data (FRED), 10-Year Treasury and market return series — Federal Reserve Bank of St. Louis maintains historical interest-rate and return series used to sanity-check the growth-rate assumptions common in long-run doubling-time estimates.
Internal Revenue Service, Topic no. 409: Capital gains and losses — IRS guidance, current as published on irs.gov, on how realised investment gains are taxed in the US, relevant to why after-tax compounding runs slower than a pre-tax rate.
Consumer Financial Protection Bureau, How does compound interest work? — CFPB consumer guidance, last reviewed October 19, 2023, explaining how compound interest and annual percentage yield accumulate over time.