Lanchester's laws | Wikipedia Easy Search

War
Part of a series on
History Prehistoric Ancient Post-classical Early modern napoleonic Late modern industrial fourth-gen
Military Organization Command and control Defense ministry Army Navy Air force Marines Coast guard Space force Reserves Regular / Irregular Ranks Specialties: Staff Engineers Intelligence Reconnaissance Medical Military police Land units: Infantry Armor Cavalry Artillery Special forces Signal corps Naval units: Warships Submarines Aircraft carriers Landing craft Auxiliary ship Air units: Fighters Bombers Command Close air support Electronic-warfare Reconnaissance Combat systems: Fire-control system Fire-control radar Director (military) Combat information center Sonar Radar Historical: Ship gun fire-control Gun data computer Torpedo data computer Development: Basic training Military manoeuvrers Combat training
Battlespace Aerospace Air Airborne Space Land Cold-region Desert Jungle Mountain Urban Subterranean Tunnel Sea Amphibious Blue Brown Green Surface Underwater Cyber Information
Weapons Air defence Armor Artillery Barrage Biological Camouflage Cavalry Horses Air cavalry Chemical Combined arms Conventional Cyber Denial Disinformation Drone / Robot Electronic Infantry Loitering Missile Music Nuclear Psychological Radiological Unconventional
Tactics List of military tactics Aerial Airlift Air assault Airbridge Airdrop Battle Cavalry Charge Counterattack Counterinsurgency Defeat in detail Foxhole Drone Envelopment Guerrilla Morale Rapid dominance Siege Swarm Screen Tactical objective Target saturation Trench Withdrawal
Operational Military operation Operations research Blitzkrieg Expeditionary Deep operation Maneuver Operational manoeuvre group Raid
Strategy List of military strategies and concepts Military campaign Attrition Commerce raiding Counter-offensive Culminating Defence in depth Fabian Mosaic Deception Defensive Depth Goal Naval Offensive Scorched earth
Grand strategy Asymmetric Blockade Broken-backed Class Cold war Colonial Conquest Containment Economic Endemic Fleet in being Irregular Liberation Limited Network-centric New generation Perpetual Political Princely Proxy Religious Resource Strategic Succession Technology Theater Total war World war
Administrative Branch Policy Staff Training Service Sociology
Organization Area of responsibility Chain of command Command and control Doctrine Principles of war Economy of force Medicine Engineers Intelligence Ranks Technology and equipment
Personnel Military recruitment Conscription Recruit training Military specialism Women in the military Children in the military Transgender people and military service Sexual harassment in the military Conscientious objector Counter-recruitment
Logistics History Military–industrial complex Arms industry Materiel Supply-chain management Main operating base Forward operating base Outpost
Science Power projection Loss-of-strength gradient
Law Court-martial Geneva Conventions Geneva Protocol Islamic rules Justice Perfidy Jewish laws on war Rules of engagement Martial law War crime
Theory Air supremacy Command of the sea Full-spectrum dominance Overmatch Unrestricted Warfare
Related Outline of war Just war theory Principles of war Philosophy of war War film Military science fiction War game Lanchester's laws Security dilemma Tripwire force Mercenary War novel Women in war War resister War studies Anti-war movement Horses in warfare Wartime sexual violence Fifth column
Lists Battles Military occupations Military terms Operations Sieges War crimes Wars Weapons Writers
v t e

Lanchester's laws are mathematical formulae for calculating the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B.^[1]^[2]

In 1915 and 1916 during World War I, M. Osipov^[3]^{: vii–viii} and Frederick Lanchester independently devised a series of differential equations to demonstrate the power relationships between opposing forces.^[4] Among these are what is known as Lanchester's linear law (for ancient combat) and Lanchester's square law (for modern combat with long-range weapons such as firearms).

As of 2017 modified variations of the Lanchester equations continue to form the basis of analysis in many of the US Army’s combat simulations,^[5] and in 2016 a RAND Corporation report examined by these laws the probable outcome in the event of a Russian invasion into the Baltic nations of Estonia, Latvia, and Lithuania.^[6]

^ Lanchester F.W., Mathematics in Warfare in The World of Mathematics, Vol. 4 (1956) Ed. Newman, J.R., Simon and Schuster, 2138–2157; anthologised from Aircraft in Warfare (1916)
^ Davis, Paul K. (1995). "Lanchester Equations and Scoring Systems". Aggregation, Disaggregation, and the 3:1 Rules in Ground Combat. Rand Corporation. doi:10.7249/MR638.
^ Osipov, M. (1991) [1915]. "The Influence of the Numerical Strength of Engaged Forces on Their Casualties" Влияние Численности Сражающихся Сторонъ На Ихъ Потери (PDF). Tsarist Russian Journal Military Collection Военный Сборник. Translated by Helmbold, Robert; Rehm, Allan. US Army Concepts Analysis Agency. Archived (PDF) from the original on 4 November 2021. Retrieved 23 January 2022.
^ Wrigge, Staffan; Fransen, Ame; Wigg, Lars (September 1995). "The Lanchester Theory of Combat and Some Related Subjects" (PDF). FORSVARETS FORSKNINGSANSTALT.
^ Christian, MAJ Joshua T. (23 May 2019). An Examination of Force Ratios (PDF). Fort Leavenworth, KS: US Army Command and General Staff College. This article incorporates public domain material from websites or documents of the United States Army.
^ David A. Shlapak, and Michael W. Johnson, Reinforcing Deterrence on NATO’s Eastern Flank (Santa Monica, CA: RAND Corporation, 2016)