Lanchester’s Law of Squares is an empirical law describing how military forces of equal size fight each other in battle. It states that the amount of casualties inflicted by the two opposing sides are proportional to the number of soldiers involved to the power of two. Thus, a force of 10 soldiers could be expected to inflict four times as much casualties to an opposing side as a force of 5 soldiers.
This law was derived from a series of mathematical calculations derived from the analysis of a series of 19th century battles. It was discovered by the British military engineer Frederick William Lanchester, and first published in 1916 in his book “Aerial Warfare”. The law is applicable to any type of battle in which two forces are fighting against one another.
The Law of Squares follows from the fact that in a military engagement, casualties are generally proportional to the ratio of forces. If a larger force fights a smaller force, it stands to reason that the result in terms of casualties will be greater. Using this principle, Lanchester was able to calculate a mathematical expression that describes the casualties and survivor ratios of two forces of equal size.
His calculations showed that casualty and survivor ratios are not simply proportional to the size of the forces involved. In fact, the proportions follow a power law; that is, they increase exponentially with the number of soldiers involved.
In addition to analyzing and formulating the Law of Squares, Lanchester also investigated a number of other basic principles of military combat. He determined that the order of battle is important, as an attack from multiple directions will cause more casualties. He also contended that firepower is more important than numbers, and that military superiority in terms of either weapons, mobility, or tactics always has an advantage.
Little has changed since Lanchester formulated the Law of Squares. It remains a valid and reliable rule of thumb in modern battle. His work continues to provide military theorists with a powerful tool for predicting the number of casualties in any two-sided engagement. It has also been used in business and marketing, as it provides a framework for understanding the importance of both quantitative and qualitative factors influencing the outcome of competition.
Despite the fact that the Law of Squares was formulated over a hundred years ago, it remains an important and relevant concept in modern battle. Lanchester’s work continues to provide military theorists with a powerful tool for predicting and understanding the number of casualties in any battle where two groups of equal size are involved. As such, it remains an incredibly important concept for anyone attempting to study or understand warfare.
