How to Use ‘e’ in Excel
(Exponential Function)

Even if you don’t clearly remember it now, let me assure you we all have studied about the Euler’s number (the ‘e’) in our school times.

It has various applications and is a mathematical hero. Out from the world of books, if you’re wondering how to use it in Excel and if it can be used in Excel, this tutorial is for you.

Let me explain to you what is ‘e’, how is it derived and how to practically apply and use it in Microsoft Excel. Quickly get your free practice workbook for this guide here before we dive into this article 🤿

Table of Contents

What is ‘e’

‘E’ denotes Euler’s number which is a mathematical constant that equals approximately 2.71828.

It was named after a Swiss mathematician, namely, Leonhard Euler in the 18th century. This number is not an ordinary number – you’ll see is applied widely in mathematics, analysis, and many other fields 👩‍🏫

It is the base of the natural logarithm. It naturally arises in problems where there is exponential growth, decay, or oscillation. Some common examples of such situations include population growth, continuous interest compounding, bacteria growth, radioactive decay, etc.

How to use it in Excel

To use the ‘e’ in Excel, we have the EXP function (also known as the Exponential function).

The EXP function comes from the Math / Trig section of the Functions Library of Excel. It calculates a numeric value which is the exponent (e) raised to any given number. The exponent is 2.71828 which remains constant 🧐

For example, if we raise ‘e’ to the power 1, mathematically it is expressed as:

Any number raised to the power of 1 is equal to itself. Doing the same using the EXP function in Excel, we get:

Raising it to the power 2, this becomes:

Doing the same, we can find the ‘e’ raised to any number in Excel.

Pro Tip!

The value of Euler’s number (e) is a mathematical fundamental constant and an irrational number. It can never be expressed as a complete number or as a fraction.

It is an infinite decimal that never repeats itself:

e=2.7182818284590452353602874713527…

Such a large number!

There is no exact value of ‘e’ since it can never be completely calculated. This decimal number keeps going on forever. Various formulas can be used to calculate the value of ‘e’.

For example, the limit definition 🧾

Where n represents infinity. As this expression continues to grow, the value of this expression grows closer to the complete value of e is 2.71828 (commonly used as 2.71 with two decimal places).

Using the EXP function in Excel

After all the discussion we’ve had about the Euler’s number in Excel, it’s time we see how it is practically applied in Excel.

So here, I have an example where I invest money into a savings account where interest is continuously compounded. This means that you invested $5000 into a savings account that pays compound interest 💲

This means that interest is calculated on $5000 at the annual rate of 5% and added to the principal continuously for 10 years. What will be the future amount of your investment in your account after 10 years?

To calculate this, we need to use the following formula:

Here is when Euler’s number comes into play. As there is no discrete number of times when interest is compounded a year, this means ‘n’ approaches infinity.

The annual interest rate is 5% but, it is being compounded continuously.

To calculate the future value, we will use the ‘e’ as follows:

We didn’t know the value for ‘n’ (the number of times interest is compounded) so we have removed it from the formula replacing it with the Euler’s number as it approaches infinity ♾

Let’s begin working:

Step 1) Writing the Exp function in Excel as follows:

Step 2) Calculate the latter part of the formula by using the EXP function in Excel.

Step 3) Multiply this exponential power to the principal amount.

The Future value comes out as $8,243.6.

This tells that if you invest $5000 today and your banks have a 5% annual interest rate on it for 10 years straight with the interest being compounded continuously, your investment will grow to $8,243 by the end of Year 10 💰

This calculation could not have been done manually since there was no discrete number of times the interest was compounded in these 10 years.

However, using Euler’s number, we can calculate exponential growth where the period approaches infinity. The above example is a practical demonstration of the Euler’s number is practically used.

It is of great significance in many fields including finance.

Pro Tip!

Do you know?

The LN function of Excel is the inverse of the EXP function.

LN function returns the natural logarithm (log function) of a number whereas EXP is the antilogarithm of a number.

For example, EXP (2) = 7.389056099 in Excel.

And LN (7.389056099) = 2 in Excel.

Natural logarithms are based on constant e (i.e. 2.71).

Conclusion

Using the Exp function and the ‘e’ is only one of the many ways how you can calculate growth in Excel. There are endless situations where you’d have to use these growth functions.

My following Excel tutorials with handy Excel tips are recommended to be read by you to find easy, alternative ways to calculate the growth rate and growth in Excel.

• How to Calculate Growth Rate in Excel (Formula)
• How to Easily Calculate CAGR (Using Excel Formulas)