Counting the number of times a certain character occurs in a certain cell

[OutlawoftheMarsh]

This seems like it should be easy, but I can't find the function for it. Let's say I have a text string in a cell, and I need to know how many times the letter A (don't care about upper/lower case) occurs in that cell. What's the function for that?

For example:
If cell A1 contains "Acronym," the function should return 1 (since there is one A in that word).
If cell A1 contains "Adam," the function should return 2.
If cell A1 contains "adamant," the function should return 3.
Etc.

Thank you!

 

[njimack]

=LEN(A1)-LEN(SUBSTITUTE(A1,"a",""))

 

[Jon von der Heyden]

Try:
=LEN(A1)-LEN(SUBSTITUTE(UPPER(A1),"A",""))

 

[OutlawoftheMarsh]

Thank you both for your brilliant solution!