Editing Circular error probable (section)

{{original-research|date=June 2024}}

{{Short description|Ballistics measure of a weapon system's precision}}
{{Redirect|Circular error|the circular error of a pendulum|pendulum|and|pendulum (mathematics)}}

[[File:Circular error probable - percentage.png|thumb|CEP concept and hit probability. 0.2% outside the outmost circle.]]

'''Circular error probable''' ('''CEP'''),<ref name=tech_paper>Circular Error Probable (CEP), Air Force Operational Test and Evaluation Center Technical Paper 6, Ver 2, July 1987, p. 1</ref> also '''circular error probability'''<ref>{{Cite web | last = Nelson | first = William | year = 1988 | title = Use of Circular Error Probability in Target Detection | url = https://apps.dtic.mil/sti/citations/ADA199190 | archive-url = https://web.archive.org/web/20141028112628/http://www.dtic.mil/dtic/tr/fulltext/u2/a199190.pdf | url-status = live | archive-date = October 28, 2014 | location = Bedford, MA | publisher = The MITRE Corporation; United States Air Force }}</ref> or '''circle of equal probability''',<ref>{{Cite book |author1-link=Robert Ehrlich (physicist) | last = Ehrlich | first = Robert | year = 1985 | title = Waging Nuclear Peace: The Technology and Politics of Nuclear Weapons | location = Albany, NY | publisher = [[State University of New York Press]] | page = [https://books.google.com/books?id=-tEpgCSNV7sC&pg=PA63 63] }}</ref> is a measure of a weapon system's [[Accuracy and precision|precision]] in the [[military science]] of [[ballistics]]. It is defined as the radius of a circle, centered on the aimpoint, that is expected to enclose the landing points of 50% of the [[Round (firearms)|rounds]]; said otherwise, it is the [[median]] error radius, which is a 50% [[confidence interval]].<ref name=tech_paper/><ref>{{Cite book | editor-last = Payne | editor-first = Craig | year = 2006 | title = Principles of Naval Weapon Systems | location = Annapolis, MD | publisher = [[Naval Institute Press]] | page = [https://books.google.com/books?id=F3q59-hcGDoC&pg=PA342&dq=%22precisely+50%22 342] }}</ref> That is, if a given munitions design has a CEP of 100&nbsp;m, when 100 munitions are targeted at the same point, an average of 50 will fall within a circle with a radius of 100&nbsp;m about that point.

There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a form of the [[standard deviation]]. Another is the R95, which is the radius of the circle where 95% of the values would fall, a 95% [[confidence interval]].

The concept of CEP also plays a role when measuring the accuracy of a position obtained by a navigation system, such as [[GPS]] or older systems such as [[LORAN]] and [[Loran-C]].