A sigmoid function is a mathematical function that has an “S” shaped curve when plotted.
The most common example of a sigmoid function is the logistic sigmoid function, which is calculated as:
F(x) = 1 / (1 + e-x)
To calculate the value of a sigmoid function for a given x value in Excel, we can use the following formula:
This formula assumes the x value is located in cell A1.
The following example shows how to use this formula in practice.
Example: Calculate Sigmoid Function in Excel
Suppose we have the following list of x values in a column in Excel:
To calculate the value of the sigmoid function for each x value, I can type the following formula into cell B2:
I can then drag this formula down to every remaining cell in column B to calculate the value of the sigmoid function for each x value:
We can then create a line plot to visualize the values of the sigmoid function.
First, highlight every value in column A and B:
Then click the Insert tab along the top ribbon. Then click the Charts group and click the chart titled Scatter with Smooth Lines and Markers:
Once you click this, the following line chart will appear:
The x-axis displays the x values and the y-axis displays the value of the sigmoid function for each x value.
Notice that the plot exhibits the “S” shaped curve that is characteristic of a sigmoid function.
The following tutorials explain how to perform other common operations in Excel: