Euler’s number, denoted as , is a naturally occurring number related to exponential growth and exponential decay. The approximate value of Euler’s number is shown below.

**However**, for the purposes of interpretting formulas and functions, this site consider Euler’s number purely as shorthand for the exponential function. This choice is intentional and hopefully leads to a deeper understanding of the math at play.

The numeric value is still very important and its connection to the exponential function is shown below.

This connection is discussed in-depth on exponential function page.

The value of is formally be defined by the value of the exponential function at . Depending on which definition of the exponential function you are using, the value can either be calculated as a limit or a summation. This is shown below.

The exponential function models exponential growth. The output of the function at any given point is equal to the rate of change at that point. For real number input, the function conceptually returns Euler's number raised to the value of the input.