Using e (Euler’s Number) in ExcelStep-by-step Guide on How to use the EXP function

Patrick Louie

Microsoft Excel is such a wonderful piece of software.

With it, you can perform a plethora of functions.

You can use it to perform mathematical equations for you.

It even knows lots of the mathematical constants such as pi or π.

Just include the syntax PI() in your formula and you’re good to go.

Here’s an example:

It should return us with the numerical value of pi which is 3.1416….

Pretty amazing, right?

But enough about pi.

Let’s talk about another mathematical constant which is e or Euler’s number.

And just like π, Excel also recognizes Euler’s number.

This is great as we can use Excel to perform calculations that involve such a very useful mathematical constant.

Euler’s number has an approximate numerical value of 2.71828(…).

It’s also an irrational number which is why we cannot show it as a simple fraction.

A complicated number, but it is often used in many mathematical and scientific calculations.

It’s especially useful in the areas of finance and statistics.

That’s why it’s very helpful that we can use Excel to perform calculations that use Euler’s number.

In this article, we will be learning how we can use e or Euler’s number in Microsoft Excel.

We will also learn what e or Euler’s number is and its significance in mathematics and mathematical equations.

By the end of the article, we should have a better grasp of what Euler’s number is and how to use it in Excel.

What is e (Euler’s Number)?

e or Euler’s number is a mathematical constant that has an approximate numerical value of 2.7182(…).

It’s an irrational number, which means that it can’t be written as a simple decimal or fraction.

It is the result of the following equation (which is an infinite series):

It is particularly useful in equations that involve compound or continuous growth.

An example of this would be compounding interests.

Another example would be the calculation of the ever growing human population.

Any logarithm that uses e as its base is considered a Natural logarithm.

It is especially useful in the areas of finance and statistics where there are a lot of factors that have a compounding or continuous growth.

Most mathematical equations that use e also use a combination of a rate of growth or decay and a time period (e.g. 1 year, 5 hours, etc.).

Oftentimes, these other variables are used as exponents of e.

Using e in Excel (with the EXP function)

Seeing how e is very useful, it’s no wonder why there is an Excel function for it.

We can use e in excel by using the EXP function.

With it, we no longer have to memorize the numerical value of e as well as input it every time we need to use it.

The syntax for the EXP function is as follows:

=EXP(n)

Where n is a numerical value.

It could be 0, 1, 13, or even an equation as long as it results in a number.

The EXP function also sets n as the exponent of e.

If we were to set n as 0, then it would result in 1 (which is always the result if you set the exponent of any number to 0).

If we were to set n as 1, it should give us the numerical value of e.

Remember that n is an exponent of e.

It’s not a multiple of e.

So if you want to know the value of 2e, =EXP(2) is not the right formula.

Rather, it should be =2*EXP(1).

Example of Using e in complex calculations

We can also the EXP functions for complex calculations.

For example, let’s say that a city has a population of 330,000.

It is expected to grow annually at a rate of 2.5% for the next 5 years. Using e, we can approximate what the city’s population will be after five years.

To do so, we will need to use the following formula:

A = P*(e^rt)

Where:

A = The approximate population after a set time

P = The initial population

r = the rate of growth

t = the amount of time

If we were to translate this formula into Excel terms, it should look like this:

=P*EXP(rt)

And if we replace the variable with our data above, the formula should look like this:

=330,000*EXP(2.5%*5)

Using the EXP function, we find out that the approximate population of the city after 5 years is 373,939.

Step-by-step Guide on How to use the EXP function

Here’s an easy-to-follow guide on how to use the EXP function in Excel:

  • Select the cell where we want to input the result of the EXP function. As an illustration, we will be selecting cell C3. A green border should appear on cell C3, which indicates that we’re selecting it.

  • On the formula bar, input =EXP(. Then choose a value. It could be a number, an equation, or a cell that has a numerical value in it. For illustration purposes, we will be choosing 1 as the value. Then after choosing the value, we will be closing the formula by typing a close parenthesis ). The formula should look like this:

  • After we’re done inputting the formula, all we need to do is press the “Enter” key. The result of the EXP function should show on the selected cell, which is cell C3 in our illustration.

Reminders on using the EXP function

To use the EXP function properly, you have to keep the following in mind:

  • The value that is enclosed in the parentheses should be a numerical value. If it is an equation or refers to a cell, it should result in a numerical value. Using non-numerical values as the value for EXP will result in the cell showing this:

  • Also, the value enclosed in the parentheses will become the exponent of e. If it is set to 0, then the EXP function will return a value of 1. If it is set to 1, then the EXP function will return a value of 2.718282(…) which is the approximate value of e. Setting it to 2 will result in the square of e.
  • To know the value of multiples of e, you will have to make a multiplication formula. Setting values enclosed in the parentheses to the value of multiples will not work. For example, if you want to know the value of 5e, rather than inputting =EXP(5), what you need to input is =5*EXP(1)

And that’s the end of the article.

I hope that the illustrations and steps above taught you how to use e in Excel.