Lanchester's laws

Part of a series on
War (outline)
History Prehistoric Ancient Post-classical castles Early modern military revolution pike and shot napoleonic warfare Late modern industrial warfare fourth-gen warfare
Military Organization Command and control Defense ministry Army Navy Air force Marines Coast guard Space force Reserves Ranks Specialties: Staff Engineers Intel Recon Medical Police Diving Pilot Land units: Infantry Armor Cavalry Artillery Special forces Signal corps Naval units: Warships Submarines Aircraft carriers Landing craft Auxiliary ships 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 Aerial Airborne Space Land Cold-region Desert Fortification Jungle Mountain Urban Subterranean Tunnel Sea Amphibious Blue Brown Green Surface Underwater Seabed Cyber Information
Weapons Air defence Armor Artillery Barrage Biological Camouflage Cavalry Horses Air cavalry Chemical Combined arms Conventional Cyber Denial Disinformation Drone / Robot Electromagnetic Infantry Loitering Missile Music Nuclear Psychological Radiological Submarine Unconventional
Tactics List of military tactics Aerial Airlift Air assault Airbridge Airdrop Anti-aircraft Anti-sub Anti-tank Battle Cavalry Charge Counterattack Counterinsurgency Convoy Defeat in detail Foxhole Drone Envelopment Formation Guerrilla Naval Rapid dominance Encirclement Investment Siege Swarm Screen Tactical objective Target saturation Trench Withdrawal
Operational Military operation Special Operations research Blitzkrieg Expeditionary Deep operation Maneuver Operational manoeuvre group Raid Covert Stay-behind
Strategy List of military strategies and concepts Military campaign Anti-access Attrition Commerce raiding Counter-offensive Culminating Defence in depth Fabian Empty fort Mosaic Deception Defensive Depth Goal Nuclear Naval Offensive Scorched earth
Grand strategy Asymmetric Blockade Broken-backed Class Cold war Colonial Conquest Containment Divide and conquer 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 Order of battle Principles of war Economy of force Medicine Engineers Intelligence Ranks Technology and equipment
Personnel Recruitment Conscription Mobilization Training Specialism Soldier Morale Volunteer Women Children Transgender Harassment Conscientious objector Counter-recruitment
Logistics History War economy Arms industry Materiel Supply-chain management Military–industrial complex Base MOB FOB Outpost
Science Power projection Loss-of-strength gradient Lanchester's laws Force multiplication
Law Occupation Armistice Ceasefire Court-martial Desertion Geneva Conventions Geneva Protocol Islamic rules Justice Lawful / Unlawful combatant Perfidy Jewish laws on war Rules of engagement Martial law War crime
Theory Air supremacy Appeasement Command of the sea Deterrence theory Full-spectrum dominance Overmatch Unrestricted Warfare Just war theory Principles of war Philosophy of war Security dilemma Tripwire force Wargaming Simulation Exercises
Non-warfare Arms control Counter-insurgency deterrence Disaster response Grey-zone Gunboat diplomacy Humanitarian aid Law enforcement Low-intensity conflict Military engineering Peacekeeping Peacebuilding Peace through strength Show of force
Culture Awards and decorations Battle cry Warrior War film Military science fiction War novel Anti-war movement Foot drill War song Uniform Wargame
Related Women in war War resister War studies Horses in warfare Wartime sexual violence Fifth column Mercenary Privateer Private military company
Lists Battles Military occupations Military terms Operations Sieges War crimes Wars Weapons Writers
v t e

Lanchester's laws are mathematical formulas 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]