Another good topic.
As I recall the Klumpen formation was also used by the French. In all cases it seems to have been a formation born of necessity for men deployed in open order surprised by enemy cavalry before they could fall back on their support or get to covered terrain.
I am not sure how effective this formation was, probably ok against cossacks or a squadron of cavalry, but I would not fancy my chances caught in the open with a regiment of cavalry cantering through.
I think that, for skirmishers, this is fairly well simulated by the failure to over-run on the basis of strength ratio between the cavalry and the skirmishers (is this BG series function retained in the Campaign engine?). If they are over-run, it may not mean that the klumpen type formation was ineffective against the cavalry but, that the skirmishers were unable to form in sufficient time before the cavalry arived.
To form a batallion square requires that the number of companies (and therefore platoons) necessary for the manoeuvre are present. The question then becomes how many men form an effective company.
At the start of the period, all armies formed up in three ranks, (even the British), until their strength dropped below a certain level, at which point the regulations allowed that they adopt a two rank formation. The British preference for a two rank formation was probably forced on them by understrength battalions rather than any tactical foresight.
The minimum strength for the French was 12 files per peloton, (2 pelotons / division; and assume 3 divisions / battalion). The British specified 5 files / section, (minimum of 3 sections / company; and typically 8 companies per battalion, assuming grenadier and light companies detached). This number of files was the basic, minimum number of files for the battalion to be able to manoeuvre effectively in accordance with the regulations. So, when the strength dropped, the battalion would form in two ranks, but the number of files required to conduct the manoeuvres would remain.
This gives minimum strengths of 148 for the French (12 x 2 x 2 3); and 240 for the British (5 x 2 x 3 x

. The size of these squares would be about 50 feet square for the French and 60 feet square for the British. This assumes perfect 2-rank square whereas the regulations allowed for a variety of shapes and even different depths on the faces of the square, or a small reserve in the centre of the square. The point is, that these square formations seem, to me, to be of a reasonable size to resist a cavalry charge.
Below 150 men is the strength of a 'company sized' skirmisher deployment which should take its chances as a Klumpen type formation against cavalry. I would therefore suggest a minimum strength of 150 to 200 men to be able to form an effective square which is consistent with Bill's estimate of 100-240 men. [Right on the money Bill].
As an aside, for a closed square, (masse), formed from a column of 3 divisions, the front division faces forward, the rear division faces about, and three files of the centre division(s) face left and three to the right. Assuming that the battalion had dropped below the minimum number of files specified by the regulations and already been reduced by one rank, this would require only two files to face outward. The theroetical minimum strength of 2 files for each peloton, (4 men for a 2-rank formation) by 6 companies is 24 men. This formation would be about 8-10 feet square and probably fit into your bathroom. Even at 150 men, a 2-rank closed square from a 3 division battalion, would have a frontage of 50 feet and depth of 10-12 feet.
One way to avoid the presence of low strength units on the battlefield is to make them more brittle. Too often, even I suspect in Campaign games, units are fighting to the last man. Routed units are quickly rallied and, in my limited experience, fatigue in the Campaign game is recovered too easily allowing units to return to the fray within a very short time period as though nothing had happened. I recommend a reduction in the rate of fatigue recovery and an increase in fatigue incurred from melee to prevent this. In this way, once routing starts, an army will quickly fall apart, enabling a decisive victory without elevated casualty levels. The game will then become more one of manoeuvre to get to the point where a decisive blow can be made that will start the routing process.
Finally, I would like to see the movement of squares increased. There are several instances of this formation being used to manoeuvre on the battlefield and that the movement was not slower than that of a column. Perhaps a speed of 3 hexes in open terrain would be a reasonable compromise as the formation would be easily disordered by enemy fire at which point its movement would be reduced to the traditional 1 hex.
My thoughts on squares for what they are worth
Regards
Mark