Doubling Time Calculator

What this calculator tells you

Here is a question that cuts straight to the heart of compound growth. If something grows at a steady rate, how long until it doubles? Ask it about your savings, your investments, or even prices creeping up with inflation, and the answer reveals just how powerful, or how punishing, a steady rate really is.

This calculator gives you that answer exactly. Enter a growth rate, and it tells you the time it takes to double, no rounding and no rule of thumb.

How to use it

There is just one input: the growth rate, entered as a percentage. That could be the return on an investment, the interest on savings, an inflation rate, or the growth rate of anything that compounds steadily.

One quiet thing to keep in mind. The doubling time comes back in the same unit of time as your rate. Feed it an annual rate and the answer is in years. And it assumes that rate holds steady the whole way, which is worth remembering for anything that jumps around from year to year, like stock returns, where the honest move is to use a long run average.

How the doubling time is worked out

The exact doubling time comes from the compound growth formula, and it looks like this:

Doubling time = ln(2) / ln(1 + r)

Here r is your growth rate written as a decimal, and ln is the natural logarithm. The idea underneath is simple: you are solving for how many periods of multiplying by (1 + r) it takes to reach twice what you started with. This tool runs that exact equation, so what it gives you is the precise answer, not an approximation. That matters, because the famous shortcuts people use for this are, by their nature, only close.

The rules of 72, 70, and 69

You have probably heard the Rule of 72: divide 72 by your rate and you get a rough doubling time. At 8 percent, that is 72 divided by 8, or 9 years. It is a wonderful piece of mental math, and it exists because 72 divides cleanly by so many numbers.

There are cousins. The Rule of 70 is a little sharper at low rates and shows up a lot in economics for things like inflation and population. The Rule of 69, or more precisely 69.3, is the most accurate of all for continuous or very frequent compounding, because it comes straight from the true math: the natural log of 2 is about 0.693.

All three are approximations of the exact formula above. They are brilliant for a quick estimate in your head. But they drift from the truth at very low and very high rates, and that is exactly where this calculator earns its place, by handing you the precise figure while the rules hand you a nearby one.

A few worked examples

A few rates, with the exact doubling time next to the Rule of 72 estimate, so you can see how the shortcut holds up.

At 8 percent, the exact answer is about 9.01 years, and the Rule of 72 says 9. Almost perfect, which is the range the rule was built for.

At 6 percent, the exact answer is about 11.90 years, against the rule's 12. Still very close.

At 2 percent, the exact answer is 35 years. Here the Rule of 72 overshoots to 36, while the Rule of 70 nails it at 35. And push up to a steep 20 percent, and the exact answer is about 3.80 years, while the Rule of 72 undershoots at 3.6. The further you get from the comfortable middle, the more the exact formula is worth using, which is what this tool is for.

It is not just for money

Doubling time is really a fact about steady growth of any kind, so this calculator stretches well beyond a savings balance. Point it at an inflation rate and it tells you how long until prices double, and how long until your money buys half as much. Point it at a country's growth and it tells you how long until an economy, or a population, doubles in size.

It works for a growing business too, whether that is revenue, users, or subscribers ticking up at a steady clip. Anywhere something compounds at a constant rate, this single number turns an abstract percentage into a time you can actually picture.

Questions people ask

What unit is the answer in?

The same unit as your rate. An annual growth rate gives a doubling time in years. A monthly rate would give it in months, and so on.

Is this the same as the Rule of 72?

It is the exact version of what the Rule of 72 estimates. The rule is a quick mental shortcut that gets close. This calculator runs the real formula and gives the precise figure, which matters most at very low or very high rates.

Can I use it for stock returns?

You can, but with care. The formula assumes a constant rate, and stock returns swing year to year. Use a long term average return for a sensible estimate rather than a single good or bad year.

Does it work for inflation?

Yes. Enter an inflation rate and it tells you how long until prices double, which is a striking way to see what even a modest rate does to the cost of living over time.

References

The doubling time formula is standard compound growth mathematics. The rules of thumb and their accuracy are well documented.

1. Investopedia. Rule of 72: definition, usefulness, and how to use it, on the shortcut and its accuracy relative to the exact formula. https://www.investopedia.com/terms/r/ruleof72.asp
2. Broverman, S. A. Mathematics of Investment and Credit (compound growth and the doubling relationship). ACTEX Publications.