The number of possible moves in Chess

Question

Question is related to chess computing about number of possible moves in chess.

I'm not talking about the number of possible positions but about the number of ways a piece can go from one square to any other.

Example 1:

A piece can be on any one of the 64 squares and (approximately) it can go to any other. Thus, the number of possible moves are 64*64 = 4,096. This is clearly an overestimate. In other words, what's the actual number of "from square" and "to square" combinations?

Example 2:

For the square a1, there are 23 possible from - to combinations. Because a knight can go to two squares and a queen can go to twenty one squares (the other pieces don't add any).

Answer 1

Unless I misunderstand your question wouldn't that just be (for every from square) the number of (to) squares that a knight can go to plus the number of squares that the queen can go to. As in the following diagrams which show to how many squares the respective piece can go.

You'd just need to add the two numbers from the diagrams for every square.

Depending on what you need all this for you might have to consider separately the special moves of castling, en passant and pawn promotion.