Ampere-hour

An ampere-hour or amp-hour (symbol: A⋅h or A h; often simplified as Ah) is a unit of electric charge, having dimensions of electric current multiplied by time, equal to the charge transferred by a steady current of one ampere flowing for one hour (3,600 seconds), thus equal to 3600 A⋅s or coulomb.^[1][2]

ampere-hour
Rechargeable NiMH 1.2 V batteries Top: AA battery (2500 mA⋅h) Bottom: AAA battery (1000 mA⋅h)
General information
Unit system	Non-SI metric unit
Unit of	Electric charge
Symbol	A⋅h, A h
Conversions
1 A⋅h in ...	... is equal to ...
SI units	3600 C

The commonly seen milliampere-hour (symbol: mA⋅h, mA h, often simplified as mAh) is one-thousandth of an ampere-hour (3.6 coulombs).

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.^[3] 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.^[4] Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power.^[5]

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 × 10²² elementary charges
• 0.03731 faradays
• 1.079 × 10¹³ statcoulombs (CGS-ESU equivalent)
• 360 abcoulombs (CGS-EMU equivalent)

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 = 20736 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.^[6] 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)