Returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.

If this function is not available, and returns the #NAME? error, install and load the Analysis ToolPak add-in.


  1. On the Tools menu, click Add-Ins.
  2. In the Add-Ins available list, select the Analysis ToolPak box, and then click OK.
  3. If necessary, follow the instructions in the setup program.



X     is the value at which to evaluate the function.

N     is the order of the function. If n is not an integer, it is truncated.


  • If x is nonnumeric, BESSELK returns the #VALUE! error value.
  • If n is nonnumeric, BESSELK returns the #VALUE! error value.
  • If n < 0, BESSELK returns the #NUM! error value.
  • The n-th order modified Bessel function of the variable x is:


where Jn and Yn are the J and Y Bessel functions, respectively.


The example may be easier to understand if you copy it to a blank worksheet.

ShowHow to copy an example

  1. Create a blank workbook or worksheet.
  2. Select the example in the Help topic.

 Note   Do not select the row or column headers.

Selecting an example from Help

Selecting an example from Help
  1. Press CTRL+C.
  2. In the worksheet, select cell A1, and press CTRL+V.
  3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
Formula Description (Result)
=BESSELK(1.5, 1) Modified Bessel function at 1.5 with an order of 1 (0.277388)
Applies to:
Excel 2003