I was flying the other day and heard tower say to another aircraft, "square the base". What does it mean, and when might a controller say this?
The controller wants the base to have two distinct 90° turns, from downwind to base, and base to final. And not one continuous turn from downwind to final. And no shortcuts to be taken to shorten the downwind.
It means the base will be slightly longer, and the downwind more parallel to the runway.
The controller is buying time (delaying the arrival) to accommodate someone else.
Top image is square-the-base, as opposed to the tight circular pattern—which experienced pilots tend to prefer1. (Images above are a mere representation.)
Note: exact answer will depend on the plane's exact location in the pattern.
It's one of those terms you won't find in a manual, like "hold our code".
It's a shorter time extension than "extend downwind leg":
" Squaring the base" or "squaring the base to final" is a non-standard instruction used by the controller asking the pilot to fly the base leg until the correct point where he can make a proper 90° turn onto final.
This being the correct normal procedure in the pattern, he is simply asking the pilot not to cut the corner. This is usually done for spacing to allow enough time for the traffic ahead to clear the runway.
If the controller needs the pilot to expedite his landing he may give the opposite instruction, something like, "proceed to the numbers" or "straight to the numbers." This indicates that the controller wants them to cut the corner and take the most direct route to the threshold making time for traffic following.
Since these instructions are non-standard the wording may vary between different controllers.
The other two answers correctly describe the situation where an aircraft is in the local pattern already. But there is another situation where controllers might tell an aircraft to "square your base to final:" when the aircraft is inbound to the airport and in a position to make a modified straight-in, and the controller does not want them to. Again, this is a delaying maneuver.