{{short description|Unit of electric charge}} {{Infobox unit | bgcolor = | name = ampere-hour | image = Duracell rechargeable batteries.JPG | caption = Rechargeable NiMH 1.2 V batteries{{br}}''Top'': AA battery (2500 mA⋅h){{br}}''Bottom:'' AAA battery (1000 mA⋅h) | standard = Non-SI metric unit | quantity = Electric charge | symbol = A⋅h | symbol2 = A h | extralabel = | extradata = | units1 = SI units | inunits1 = 3600 C }}
An '''ampere-hour''' or '''amp-hour''' (symbol: '''A⋅h''' or '''A h''', often simplified as '''Ah''') is a unit of electric charge, recommended for use in batteries and electrolytic devices.<ref name="IEV"/> It has dimensions of electric current multiplied by time and corresponds to the charge transferred by a steady current of one ampere flowing for one hour (3,600 seconds). Thus 1{{nbsp}}A⋅h equals 3600 A⋅s or 3.6{{nbsp}}kC (kilocoulombs).<ref name="IEV">{{cite web |url=http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=113-02-10 |title=electric charge (Symbol Q). IEV 113-02-10 |date=2020 |website=electropedia.org |publisher=International Electrotechnical Commission (IEC) |access-date=2020-09-20 |quote=Note 7 to entry: The coherent SI unit of electric charge is coulomb, C. The unit ampere-hour is used for electrolytic devices, such as storage batteries: {{nobr|1 A·h {{=}} 3,6 kC.}}}}</ref><ref name="NIST-SI-Guide">{{cite book |first1=Ambler |last1=Thompson |first2=Barry N. |last2=Taylor |title=Guide for the Use of the International System of Units (SI). NIST Special Publication 811 |edition=2nd |url=https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf |publisher=National Institute of Standards and Technology |location=Gaithersburg |date=2008 |page=45 |quote=To convert from ''ampere hour'' (A·h) ... to coulomb (C) ... multiply by {{val|3.6|e=3}}}}</ref>
The commonly seen '''milliampere-hour''' (symbol: '''mA⋅h''' or '''mA h''', often simplified as '''mAh''') is one-thousandth of an ampere-hour (3.6 C).
== Use == The ampere-hour is frequently used in measurements of electrochemical systems such as electroplating and for battery capacity where the commonly known nominal voltage is understood.
A ''milliampere second'' (mA⋅s) is a unit of measurement used in X-ray imaging, diagnostic imaging, and radiation therapy. It is equivalent to a ''millicoulomb''. This quantity is proportional to the total X-ray energy produced by a given X-ray tube operated at a particular voltage.<ref>[http://www.ehss.vt.edu/Programs/RSD/Xray/xray09.htm X-ray Safety Handbook, 9.0 Terms and Definitions, VirginiaTech Environmental, Health and Safety Services] {{webarchive |url=https://web.archive.org/web/20070723051053/http://www.ehss.vt.edu/Programs/RSD/Xray/xray09.htm |date=July 23, 2007 }}</ref> The same total dose can be delivered in different time periods depending on the X-ray tube current.
To help express energy, computation over charge values in ampere-hour requires precise data of voltage: in a battery system, for example, accurate calculation of the energy delivered requires integration of the power delivered (product of instantaneous voltage and instantaneous current) over the discharge interval.<ref>{{cite web | url= http://trollingpowersolution.com/how-to-calculate-amp-hours/ | title= How to Calculate Amp Hours – Learn of Convert Watts to Amps | publisher= Leo Evans | year=2016 | access-date=8 December 2016 | first=Najrul Islam | last=Efty Abir}}</ref> Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power.<ref>{{cite book |author=National Research Council (U.S.) |title=Meeting the energy needs of future warriors |publisher=National Academies Press |year=2004 |isbn=0-309-09261-2 |page=27 }}</ref>
When comparing the energy capacities of battery-based products that might have different internal cell chemistries or cell configurations, a simple ampere-hour rating is often insufficient.
== In other units of electric charge == One ampere-hour is equal to (up to 4 significant figures): * 3600 coulombs * 2.247 × 10<sup>22</sup> elementary charges * 0.03731 faradays * 1.079 × 10<sup>13</sup> statcoulombs <small>(CGS-ESU equivalent)</small> * 360 abcoulombs <small>(CGS-EMU equivalent)</small>
== Examples == * An AA size dry cell has a capacity of about 2000 to 3000 milliampere-hours. * An average smartphone battery usually has between 2500 and 6000 milliampere-hours of rechargeable electric capacity. * Automotive car starter batteries vary in capacity but a large automobile propelled by an internal combustion gasoline engine would have about a 50-ampere-hour 12 V battery capacity. * Battery electric vehicle capacities are usually given in kW⋅h, but in 2013, the BMW i3 60 A⋅h was named after the capacity of one of its 96 cells, for a total of 96 × 3.6 V × 60 A⋅h = {{val|20736|u=W.h}} with about 18 kW⋅h usable energy, to match the number of the entry level Tesla Model S60 which had 60 kW⋅h. Later BMW i3 had 94 A⋅h and 120 A⋅h batteries, each topping Tesla's S85, S90 and S100 designations. * Since one ampere-hour can produce 0.336 grams of aluminium from molten aluminium chloride, producing a kilogram of aluminium required transfer of at least 2980 ampere-hours.<ref>T. L. Brown, H. E. Lemay Jr, "Chemistry the Central Science", Prentice-Hall, 1977 {{ISBN|0-13-128769-9}} page 562</ref> One kilogram of aluminium commonly requires 15.37 kW⋅h, thus electric power represents about 20% to 40% of the cost of producing aluminium.
== See also == * Electrochemical equivalent * Kilowatt-hour (kW⋅h)
== References == {{reflist}}
Category:Units of electrical charge Category:Non-SI metric units