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**, when interpreting formulas and functions, this site considers Euler’s number 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 the exponential function page.

The value of is formally 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.