# Doubling Time (Rule of 70)

## Did you know?

Doubling time (also known as the rule of 70) is the amount of time that it takes for a quantity of something to duplicate in size. Simply put, how long will it take for a certain thing to double? To calculate this, you would use the rule of 70. This rule calculates the doubling time by dividing 70 by the growth rate.

You might notice this is quite similar to the rule of 72, which has you divide the number 72 by the annual rate of return. Both formulas derive from far more complicated logarithms that are difficult to do by hand and on the fly. These rules simplify them fairly accurately. So what is the biggest difference? Obviously, the rule of 70 uses the number 70 in its calculation, while the rule of 72 uses the number 72. This might seem straightforward, but these rules are typically used for different calculations.

The rule of 70 is used more to focus on growth, especially population growth. For example, how long will it take for the current population of llamas to double in size? In contrast, the rule of 72 is used more in finance to determine how long it will take an investment to double with a fixed interest rate. For this definition of doubling time, we will be focusing on the rule of 70.

## Doubling Time Formula

$Years\: to\: Double = \dfrac{70}{Interest\: Rate}$

In this formula, the growth/interest rate should be written as a whole number, not as a decimal. For example, if a population has a growth rate of 15%, you would use the whole number of 15 for the variable R instead of 0.15.

The frequency of time in which you want to see the doubling time is relative to the frequency of your growth rate. As a result, you should make sure your rate matches that time frame appropriately. To demonstrate, if you are wanting to know how many years it will take for a group to double, you should be using an annual growth rate. But, if you are wanting to see the growth in months, use a monthly growth rate.

You should be applying the doubling time formula to populations or quantities that are experiencing exponential growth. In this situation, “Exponential growth” is when the rate of growth is rapidly increasing at a constant rate compared to the current quantity. For instance, if a population was only experiencing minimal or sporadic growth rates, you probably wouldn’t use the doubling time formula.

As the growth rate, or variable R, increases, the doubling time will be faster. Essentially, if there is faster growth, it will take less time to reach that doubled quantity. If you increase the number of seeds you plant in the spring, you are going to see a lot more vegetables in the summer.

## Doubling Time Example

A local state college has been working hard to increase its online student population. Last year, they had 71,946 students. If they increase the number of their admitted students by 6% each year, how long will it take for them to double their annual count of online students?

Let’s break it down to identify the meaning and value of the different variables in this problem.

• Growth Rate: 6%

We can apply the values to our variables and calculate the doubling time:

$Years\: to\: Double = \dfrac{70}{6} = 11.67\: years$

In this case, the state college would double their online students in 11.67 years.

While the school has a good estimate, they can now consider other factors. Do they have the capability to handle that many students in that period of time? They might also wonder if growth that fast might affect the quality of the education they offer. There are many things to evaluate, but knowing the doubling time can help you make more informed choices looking forward.

## Doubling Time Analysis

Doubling time is an analytic tool used to project how long in the future before you reach the goal of doubling.

You might be wondering why it is that the doubling time, or rule of 70. is not typically used for finance. Why is the rule of 72 better for investment calculations? If you were to break down both rules to show each step of the calculation, the Rule of 72 uses more whole numbers, making it much easier to explain to clients who are wanting to understand how you are making their money double.

If you are examining populations specifically, you will see their growth rate vary greatly. For organic populations, larger organisms will have a slower growth rate than smaller ones. This is because they are made differently and are more prone to outside influences. Larger organisms typically have more cells and, therefore, take longer to develop. Giraffes, for example, take a lot longer to grow and mature than rabbits. Therefore, the growth rate of rabbits is significantly higher than that of giraffes.

Additionally, populations with larger organisms are more likely to hit their carrying capacity sooner. The “carrying capacity” is the maximum quantity that a population can preserve, based on the available supplies of food, water, etc. Because of this, no population can endlessly double, despite the current growth rate. They are still susceptible to other factors like lack of resources, disease, and changes to their habitat.

When a group or population reaches the carrying capacity, you will likely start to see a decline in the population. This is known as logistic growth. While the Doubling Time won’t account for factors like this, you should still be including them in the big picture of your estimation.

## Doubling Time Conclusion

• The doubling time is the amount of time that it takes for a quantity of something to double in size.
• Doubling time is more commonly known as the rule of 70.
• This formula is most helpful for populations or quantities that are experiencing exponential growth.
• The doubling rime formula requires only one variable: the interest/growth rate.
• The growth rate should be written as a whole number, not as a decimal.
• As the growth rate increases, so will the doubling time.

## Doubling Time Calculator

You can use the doubling time calculator below to quickly estimate how long it will take to double a quantity by entering the required numbers.