# Exponential Growth Prediction Calculator

This calculator estimates a future value of something based on past performance. For example, our website's monthly organic traffic (the one from search engines) grew from `43,236`

in July 2016 to `137,018`

2 months later. I want to find out how long it would take to reach 1 million visitors if the growth rate was maintained at this incredible level (I don't think we can grow that fast for a long time, to be honest). So I entered `137018`

in the *initial value* field in the *future* group and `1000000`

in the ( , click to fill in the calculator). It told me we'd reach one million in 3.4 months.

🙋 You can also learn more about future value and more generalized calculations from the future value calculator.

While it's not always true that things follow the exponential growth pattern, sometimes they do. This calculator is meant to help you peek into the future and see how much of something you'll have after some time has passed or the other way around - how much time it will take to reach some goal. Some things grow linearly. Some don't follow any pattern. Sometimes things stop growing. This calculator assumes exponential growth and won't be any help in those other scenarios.

We have built a few other calculators you might find handy:

- Rule of 72 calculator shows how long it takes for some value to double.
- Website ad revenue calculator and CPC/CPM calculator estimate how much money you might be earning with that increased traffic (following the example from the beginning).

## FAQ

### What is exponential growth?

**Exponential growth** means that the **rate** of an increase within a population remains the **same over time**. For instance, if it took one period to go from 100 to 200, it would take one more period to go from 200 to 400. That is, the quantity doubles in each period. If the quantity shrinks similarly (e.g., it halves in each period), then we talk about an **exponential decay**.

### How do I calculate the annual growth rate given monthly growth rate?

To convert the monthly to annual growth rate, you need to:

- Write down the monthly growth rate as a
**decimal**. For instance,`7% = 0.07`

. **Add**`1`

to the monthly growth rate.- Raise the result to the
**power**`12`

. **Subtract**`1`

from the result.- This is it! Your annual growth rate. If you wish to
**convert it to percentages**, multiply the result by 100.

### What is the daily growth rate if the value doubled in 10 days?

The answer is **7.18%**. To arrive at this result:

- Write down the
**ratio of final value to initial value**. In our case, it is**2**. - Write down the reciprocal of the number of periods. Since we have 10 days, we write down
**1 / 10 = 0.1**. - Raise the number from Step 1 to the power from Step 2. That is,
**2**.^{0.1}= 1.0718 - Subtract 1 from the result of Step 3:
**1.07177 - 1 = 0.0718**. - This is our answer! We only need to convert it to a percentage
**0.0718 = 7.18%**.

### What is the formula for daily growth rate in exponential growth?

The formula for ]daily growth rate in exponential growth reads:

**r = (F / I) ^{1/N} - 1**

where:

**r**- the daily growth rate;**F**- the final value;**I**- the initial value; and**N**- the number of periods (days).