Square of the pawn

A quick test of whether a king can catch a passed pawn, without counting moves.

Draw a square from the pawn to its queening square, with that as one side. If the defending king can step into the square, it catches the pawn. If not, the pawn queens, unless other pieces help.

Two adjustments make it right. If it is the pawn’s side to move, push the pawn one square in your head first. A pawn still on its starting rank can move two squares, so draw the square as if it stood one rank further up.