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((short description|Kinetic energy of a bullet))
((More citations needed|date=December 2009))
[[File:Muzzle velocity.jpg|thumb|[[pellet gun|Pellet]] exiting muzzle, with formula for energy overlaid.]]

'''Muzzle energy''' is the [[kinetic energy]] of a [[bullet]] as it is expelled from the [[muzzle (firearm)|muzzle]] of a firearm. Without consideration of factors such as aerodynamics and gravity for the sake of comparison, muzzle energy is used as a rough indication of the destructive potential of a given firearm or cartridge.  The heavier the bullet and especially the [[Muzzle velocity|faster it moves]], the higher its muzzle energy and the more damage it will do.

==Kinetic energy==

The general formula for the kinetic energy is
<math display=block>E_\mathrm{k} = \frac{1}{2} mv^2,</math>
where ''v'' is the [[velocity]] of the bullet and ''m'' is the [[mass]] of the bullet.

Although both mass and velocity contribute to the muzzle energy, the muzzle energy is proportional to the mass while proportional to the ''square'' of the velocity. The velocity of the bullet is a more important determinant of muzzle energy. For a constant velocity, if the mass is doubled, the energy is doubled; however, for a constant mass, if the velocity is doubled, the muzzle energy increases ''four'' times. In the [[SI system]] the above ''E''<sub>k</sub> will be in unit [[joule]]s if the mass, ''m'', is in [[kilogram]]s, and the speed, ''v'', is in [[metres per second]].<ref>((cite book |last1=Beer |first1=Ferdinand P. |last2=Johnston |first2=E. Russell Jr |last3=Cornwell |first3=Phillip J. |title=Vector Mechanics for Engineers |date=2013 |publisher=McGraw-Hill |location=New York, NY |isbn=978-0-07-740232-7 |page=768 |edition=10th))</ref>

==Typical muzzle energies of common firearms and cartridges==

((mainarticle|Table of handgun and rifle cartridges))

Muzzle energy is dependent upon the factors previously listed, and velocity is highly variable depending upon the length of the barrel a projectile is fired from.<ref>((cite web|url=http://www.ballisticsbytheinch.com/|title=BBTI - Ballistics by the Inch - Home|publisher=ballisticsbytheinch.com))((better source|date=March 2018))</ref> Also the muzzle energy is only an upper limit for how much energy is transmitted to the target, and the effects of a [[ballistic trauma]] depend on several other factors as well. There is wide variation in commercial ammunition.  A ((convert|180|gr|abbr=on)) bullet fired from [[.357 Magnum]] handgun can achieve a muzzle energy of ((convert|580|ftlbf|J|abbr=on)).  A ((convert|110|gr|abbr=on)) bullet fired from the same gun might only achieve ((convert|400|ftlbf|J|abbr=on)) of muzzle energy, depending upon the manufacturer of the cartridge.  Some [[.45 Colt|.45 Colt +P]] ammunition can produce ((convert|1200|ftlbf|J|abbr=on)) of muzzle energy.((cn|date=June 2018))

==Legal requirements on muzzle energy==
((See also|Game law))
Many parts of the world use muzzle energy to classify guns into categories that require different categories of licence. In general guns that have the potential to be more dangerous have tighter controls, while those of minimal energy, such as small air pistols or air rifles, require little more than user registration, or in some countries have no restrictions at all. [[Overview of gun laws by nation]] indicates the various approaches taken. [[Firearms regulation in the United Kingdom]] is a complicated example, but is demarked by muzzle energy as well as barrel length and ammunition diameter.

Some jurisdictions also stipulate ''minimum'' muzzle energies for safe hunting. For example, in [[Denmark]] rifle ammunition used for hunting the largest types of game there such as [[red deer]] must have a kinetic energy ''E''<sub>100</sub> (i.e.: at ((convert|100|m|yd|abbr=on)) range) of at least ((convert|2700|J|ftlbf|abbr=on)) and a bullet mass of at least ((convert|9|g|gr|abbr=on)) or alternatively an ''E''<sub>100</sub> of at least ((convert|2000|J|ftlbf|abbr=on)) and a bullet mass of at least ((convert|10|g|gr|abbr=on)).<ref>((cite web|url= https://www.retsinformation.dk/Forms/R0710.aspx?id=13103 | title=Bekendtgørelse om skydevåben og ammunition, der må anvendes til jagt m.v. |at=Ammunition |work= retsinformation.dk |publisher=[[Miljøministeriet]]|access-date=2015-03-10|date= 2012-12-17|trans-title=Hunting weapons and ammunition act|language=Danish))</ref> [[Namibia]] specifies three levels of minimum muzzle energy for hunting depending on the size of the game, ((convert|1350|J|ftlbf|abbr=on)) for game such as [[springbok]], ((convert|2700|J|ftlbf|abbr=on)) for game such as [[hartebeest]], and ((convert|5400|J|ftlbf|abbr=on)) for [[Big Five game]], together with a minimum caliber of ((convert|7|mm|abbr=on)).<ref>((cite web|url= http://www.napha-namibia.com/legal-information/hunting-laws-rifle-importation/ |website= napha-namibia.com |title= NAPHA - Namibia Professional Hunting Assiation: Hunting Laws& Rifle Importation |access-date= 5 July 2015))</ref>

In [[Germany]], [[airsoft guns]] with a muzzle energy of no more than ((convert|0.5|J|ftlbf|abbr=on)) are exempt from the [[Gun legislation in Germany|gun law]],<ref>((cite web |url= http://www.bmi.bund.de/SharedDocs/FAQs/DE/Themen/Sicherheit/waffenrecht_soft_air_waffen.html |website= www.bmi.bund.de |title= Ab welcher Geschossenergie fallen Soft-Air-Waffen unter das Waffengesetz? |access-date= 2015-09-17 |trans-title= From which muzzle energy does Airsoft guns fall under the gun law? |language= de |archive-url= https://web.archive.org/web/20160304053233/http://www.bmi.bund.de/SharedDocs/FAQs/DE/Themen/Sicherheit/waffenrecht_soft_air_waffen.html |archive-date= 2016-03-04  ))</ref> while [[air guns]] with a muzzle energy of no more than ((convert|7.5|J|ftlbf|abbr=on)) may be acquired without a [[firearms license]].<ref>((cite web|url= http://www.gesetze-im-internet.de/waffg_2002/BJNR397010002.html |website= gesetze-im-internet.de |title= Waffengesetz (WaffG) |access-date= 2015-09-19 |trans-title=gun law |language= de))</ref>

[[Mainland China]] uses a varied concept of "'''muzzle ratio kinetic energy'''" (((lang-zh|枪口比动能))), which is the [[quotient]] ([[ratio]]) of the muzzle energy [[divided]] by the [[gun barrel#Bore|bore]] [[cross sectional area]], to distinguish genuine guns from "imitation" [[replica]]s like [[toy gun]]s.  The [[Ministry of Public Security (China)|Ministry of Public Security]] unilaterally introduced the concept in 2008 leading up to the [[2008 Summer Olympics|Beijing Olympic Games]], dictating that anything over 1.8&nbsp;J/cm<sup>2</sup> to be defined as real firearms. This caused many existing toy gun products on the Chinese market (particularly [[airsoft]]) to [[legal issues in airsoft#China|become illegal]] overnight, as almost all [[airsoft gun]]s shooting a standard ((convert|0.20|g|gr|abbr=on)) [[airsoft pellet|((convert|6|mm|abbr=on)) pellet]] have a [[muzzle velocity]] over ((convert|76|m/s|abbr=on)), which translates to more than ((convert|0.58|J|ftlbf|abbr=on)) of muzzle energy, or 2.0536&nbsp;J/cm<sup>2</sup> of "ratio energy". For comparison a [[Baseball_(ball)|standard baseball]] [[changeup]] thrown at ((convert|34|m/s|abbr=on)) has 1.951&nbsp;J/cm<sup>2</sup> of "ratio energy" which also exceeds the 1.8&nbsp;J/cm<sup>2</sup> of a real firearm while a [[fastball]] can reach over 3.5&nbsp;J/cm<sup>2</sup> or nearly double the level of a real firearm.  The subsequent crackdowns by [[public security bureau (China)|local law enforcement]] led to many seizures, arrests and prosecutions of individual owners for "trafficking and possession of illegal weapons" over the years for weapons that were previously permitted.

==See also==
*[[Free recoil]]
*[[Muzzle velocity]]
*[[Power factor (shooting sports)]]

==Resources==
*Edward F. Obert, ''Thermodynamics'', McGraw-Hill Book Co., 1948.
*Mc Graw-Hill encyclopedia of Science and Technology, volume ebe-eye and ice-lev, 9th Edition, Mc Graw-Hill, 2002.

==References==
((Reflist))

((Firearms))

((DEFAULTSORT:Muzzle Energy))
[[Category:Ammunition]]
[[Category:Ballistics]]

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