A square division is a designation given to the way military divisions are organized. In a square organization, the division's main body is composed of four regimental elements. Since a regiment could be split into separate battalions for tactical purposes, the natural division within a division would be to have two regiments bound together as a brigade. On an organizational chart and if the entire division were formed up in the field, the two brigades of two regiments would typically form a square, hence the name.
Most European divisions were organized as square divisions prior to World War I. They were generally reorganized as triangular divisions during that war. A triangular division generally had its infantry organized into three regiments, either directly controlled by the division headquarters or under a single brigade command. See, for example, the organizational changes of the Imperial German Army's 1st Division. Triangular divisions were smaller, allowing for more divisions to be formed, and were considered more suited for the positional warfare which characterized World War I. A square division typically advanced with two brigades in line or with the brigades echeloned (one ahead of the other), with one regiment forward and one in reserve ready to engage when the first regiment came into contact with the enemy. In positional warfare, the regiments were formed in line to cover as much of a sector as possible, and typically formed their own reserves, with 1–2 battalions forward and the rest in reserve.
During World War I, the United States Army formed its divisions as square divisions, in contrast to the prevailing European norm. The United States had the manpower to form the divisions, and expected to be engaging in more offensive operations as the stalemate of the trenches was broken late in the war. United States Army divisions remained organized as square divisions after the war and up to World War II. In World War II, the U.S. Army reorganized its divisions as triangular divisions. Since the war, combined arms doctrine has all but eliminated the purpose of the all-arms regiment, and brigades are generally organized as combined arms units. The brigades are themselves typically triangular, with three subordinate battalions. Recent reforms in the United States and several European countries have placed greater emphasis on the brigade as the major tactical formation, with the division now acting more like a corps headquarters, controlling several relatively autonomous brigades and parceling out support units based on the tactical situation.
Imperial Japanese Army divisions were organized as square divisions prior to 1938 when they began to form triangular divisions during the Second Sino-Japanese War.
The Chinese National Revolutionary Army divisions were organized as square divisions prior to mid-1938 during the Second Sino-Japanese War.