Ampere-hour

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

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. 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 A⋅h equals 3600 A⋅s or 3.6 kC (kilocoulombs).

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).

Simple conceptual examples

These examples demonstrate the simple mathematical relationship. In practical usage there are far more factors to consider - see note below.

• 0.5Ah (aka 500 mAh) has an electrical charge with the equivalent* of supplying either:
  • 0.5 Amps for 1 hour
  • 1 Amp for half an hour

• 1Ah (aka 1000 mAh) has an electrical charge with the equivalent* of supplying either:
  • 0.5 Amps for 2 hours
  • 1 Amp for 1 hour
  • 2 Amps for half an hour

• 2Ah (aka 2000 mAh) has an electrical charge with the equivalent* of supplying either:
  • 0.5 Amps for 4 hour
  • 2 Amps for 1 hour
  • 4 Amps for half an hour

*Important note: Amp-hours are a measurement of charge, not a measurement of application. The above examples are a useful reference, but in practice the usable output is not identical, and can vary greatly. For instance:

• Losses: Energy transfer is never 100% efficient, there will always be some loss between energy stored and energy output, how much depends on the circumstances.
• Battery mechanics: Many batteries will have a limitation on how low it can be discharged, for example lead acid leisure batteries usually should not be discharged more than 50% of their rated capacity.
• Current limitations: There are usually limits on the rate at which energy can be transferred. For example a 10Ah battery will usually be capable of delivering approximately 0.5 amps for 20 hours, but it might not be able to transfer 20 amps in half an hour. As the current (amps) increases, you get increasing difficulty with the battery mechanics, cables, receiving device, etc, all being able to handle it; often in the form of heat and fire risk. Also as discharge current increases, capacity decreases (Peukert effect).

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. 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. Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power.

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)

Practical 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. One kilogram of aluminium commonly requires 15.37 kW⋅h, thus electric power represents about 20% to 40% of the cost of producing aluminium.

Confusion with power

Many people buying/comparing batteries are not familiar with electrical concepts, so it's easy for them to mix up amp-hours with watt-hours.

Remember amps only measure current, not power. For power, you need to multiply the current (amps) with the voltage to get Watts.

In other words, a 1Ah (1000mAh) 1.5v battery has much less power than a 1Ah 12v battery.

See also

• Electrochemical equivalent
• Kilowatt-hour (kW⋅h)