Auto-populate cells / repeat formula

I have a list of ca 700k words. Now I want to sort them by lenght. (Later sort them by number of vowels, number of specific letters etc.) Is there an easy way to repeat the formula =LEN(A1) for the entire 700k column? (=LEN(B1) etc.)

Assuming your words are in the range A2:A700001.
Go to cell B2, type =LEN(A2:700001) and press Ctrl+Shift+Enter then. This will evaluate the formula in array-mode and output all the 700000 results in one go without needing to copy any formulas.
Subseqently you can copy the complete range of results and Paste Special... (Shift+Ctrl+V) first elsewhere ‘numbers only’, and then also over the original range. Everything is ready now for sorting.

=== Edit1 ===
The original question sould also be answered:
Enter the formula into the first cell where you want it. Go to the NameBox then and enter the range where you want the formula to be filled in. Then use Ctrl+D for filling down or go Sheet>Fill Cells> and select the needed direction.
Relative addressing will adapt during the fill process. Absolute parts of reference addresses remain unchanged.

In the special case of filling down a doubleclick on the drag handle of the first cell should be sufficient, if the column to fill is adjacent to a contiguously filled column.

Thank you!