# Doubling Time Calculator

Created by Marcin Manias
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jun 14, 2024

The doubling time calculator, or the doubling period calculator, is a simple tool that lets you calculate how long it will take an amount to double given a constant growth rate. Another name for this concept is the rule of 72, which we covered in the rule of 72 calculator. Since doubling time measures how fast something grows, it is a unit of exponential growth. A unit measuring exponential decay, known as half life, is its opposite. The term half-life tells you how long it takes for something to be reduced to half its initial value and is used to describe radioactive decay.

Read on if you want to find what is the definition of doubling time. We also cover its real-world applications and limitations. Doubling time is more common than you think! On top of that, the article will give you the doubling time formula and teach you how to calculate doubling time with an example.

## What is the definition of doubling time?

As the name implies, doubling time is a term used to describe the time needed for a quantity to double in value. For an amount to double at some point, the quantity must increase by a certain amount each period of time. This increase is called a growth rate. If this increase stays the same over all periods, we can say that the growth rate is constant. There are two reasons why a constant growth rate is important:

• the constant growth rate leads to a constant doubling period. If the growth rate does not change from period to period, the doubling period will not change. It means that no matter the quantity, the time it will take the value to double will be the same. It will take the same amount of time for 1 to grow into 2 as it takes 2 to reach 4, or for 400 to reach 800, as long as the growth rate is constant.
• more importantly, the constant growth rate allows us to calculate the doubling time directly from the growth rate, enabling our doubling time formula calculator to do its magic.

As an interesting side note, doubling time is an application of compound interest, where the percentage increase is also calculated on all other previous increases. In this situation, it's searching for the time it takes to increase by exactly 100%. We write more about this topic in the compound interest calculator.

Doubling time is useful in a number of fields, including: finance (growth of money, compound interest, inflation), medicine (determining the growth of cancer), demography (population), and even mining (natural resources extraction). If you know the constant growth rate, you can use it to find out how long it will take to double the size of a population.

As you've probably noticed by now, the concept of doubling time is straightforward. So why do we need a doubling time calculator? The idea is simple, and the doubling rate equation is very short indeed. However, answering the question How to calculate doubling time by hand? is not that easy. Find out why below!

## Doubling time formula

Now that you know what is the definition of doubling time, it is time to double down on the doubling time equation (pun intended). On the condition that the increase to the quantity is the same from one period to another (it remains constant), the equation is as follows:

$\footnotesize \text{doubling time} = \frac{\log{(2)}}{\log{(1 + \text{increase})}}$

where:

• increase is the constant growth rate expressed as a percentage value,
• doubling time is the time needed for the quantity to double in value for a specified constant growth rate.

You can use logarithms (log in the above formula) with any base in the doubling time formula. It doesn't matter. It works as long as you only care about how to calculate doubling time. Alternatively, you can obtain the same result with the below doubling time equation:

$\footnotesize\text{doubling time} = \frac{1}{\log{}_2(1 + \text{increase})}$

This time a logarithm with a base of two is used. The relation is the one we spoke about in the How to calculate logarithm with an arbitrary base? section of the log calculator.

As you can see, the higher the constant growth rate, the shorter the doubling time. The doubling rate equation enables you to calculate the doubling time from the increase alone, using the logarithm of 2 divided by the logarithm of the exponent of growth: $\log \! {(1+\text{increase})}$.

## Doubling time equation - limitations

The doubling time equation is excellent at working out the time needed for something to double, and it can be applied to many subjects. However, keep in mind that it has its limitations. In practice, it is hard to find constant growth rates. Growth rates tend to fluctuate and change over time, and that is why doubling time can be an unreliable metric.

Be aware that it is even more complex when it comes to money. It is true that doubling time you can show you when $1000 will become$2000, but money changes value over time. That is why your future $2000 will not be worth the same as$2000 right now. To get a great explanation of this concept, and to avoid the headache of calculating it yourself, head over to our time value of money calculator.

## How to calculate doubling time? - an example

Let's see how the doubling time equation works in practice. You have a field of flowers that grows at a constant rate of 15% each year, and you want to find out how long it will take for it to double in size. Let's plug the data into the formula:

\footnotesize \begin{align*} \text{doubling time} &= \frac{\log{(2)}}{\log{(1 + 15/100)}} \\ &= 4.96\ \text{years} \end{align*}

The reverse calculation is also possible. You can use the doubling rate equation to find out at what rate you need to increase your capital by for it to double in 5 years. The answer is about 14.87% a year. Of course, it's better to sit back and let our calculator do the work for you!

You can also explore the exponential growth prediction calculator, which helps estimate future values determined by an exponential function.

## FAQ

### What is the doubling time of a population?

The doubling time of a population is the time needed for such a population to double in size. The doubling time is defined by the formula:
doubling time = log(2) / log(1 + r)
where r is the growth rate.
The growth rate must be constant if you want the formula to give accurate results.

### How do you calculate the doubling time?

To calculate the doubling time of a population:

1. Measure the growth rate of the population. Make sure that it is constant.
2. Find the logarithm of one plus the growth rate.
3. Divide the logarithm of two by the result.
4. That's it: the doubling time doesn't depend on any other parameter.

### How long does it take for a population of E. coli bacteria to double in size?

Around 25 minutes. If we consider the growth rate of E. coli in laboratory conditions, r = 4.3 per hour. We can then apply the doubling time formula:
doubling time = log(2) / log(1 + 4.3) = 0.41 h
That corresponds to 24.6 minutes.

The doubling time depends strongly on the conditions of the environment. While we can measure in minutes in a laboratory, in real-world settings, it can take as long as 15 hours.

### How long does it take for an investment with interest rate 2% per year to double?

35 years. To calculate the time required for an initial investment to double when an interest rate of 2% is applied each year, use the doubling time formula:
doubling time = log(2) / log(1 + 2/100) = 35.00

As you can see, the initial investment or any specified timeframe does not affect the result as long as the interest rate remains constant.

Marcin Manias
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