# Ampere-hour

An **ampere-hour** (symbol A·h, often written Ah) is a non-SI unit of electric charge, equal to the charge transferred by a steady current of one ampere flowing for one hour. It is the customary unit for stating the capacity of batteries, from lead-acid storage batteries rated in ampere-hours to phone and power-bank batteries rated in milliampere-hours (mAh, one thousandth of an ampere-hour).<sup>[1](https://energyeducation.ca/encyclopedia/Ampere_hour)</sup>

| Key fact | Detail |
|---|---|
| Quantity measured | Electric charge; the ampere-hour is a non-SI unit accepted for use alongside SI units<sup>[1](https://energyeducation.ca/encyclopedia/Ampere_hour)</sup> |
| SI equivalent | 1 A·h = 3.6 × 10³ coulombs (exactly), since the coulomb is the SI unit of charge and equals one ampere-second<sup>[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8)</sup><sup> • </sup><sup>[3](https://www.nist.gov/pml/special-publication-330/sp-330-section-2)</sup> |
| Charge in particles | One coulomb corresponds to about 6.241509 × 10¹⁸ elementary charges, so 1 A·h corresponds to about 2.2 × 10²² electrons<sup>[4](https://www.nist.gov/si-redefinition/ampere/ampere-future)</sup> |
| Relation to energy | Watt-hours = ampere-hours × nominal voltage; a 100 Ah battery at 12 V stores about 1,200 Wh<sup>[5](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)</sup> |
| Rated capacity | The charge a manufacturer declares a cell can deliver during an n-hour period at constant current 1/n of the reference current, under specified conditions<sup>[6](https://www.sciencedirect.com/science/article/pii/S2352152X16301797)</sup> |
| Rate dependence | Deliverable capacity falls as discharge rate rises; the relation is described by Peukert's law, and lead-acid chemistry is more affected than lithium<sup>[7](https://www.victronenergy.com/media/pg/BMV-700H/en/battery-capacity-and-peukert-exponent.html)</sup> |

## Definition and SI status

The ampere-hour combines the [SI base unit](https://www.edgepedia.org/si-base-unit) of current, the ampere, with the hour. Because the coulomb, the SI derived unit of electric charge, is defined as one ampere-second (C = A·s), the conversion is exact: one hour contains 3,600 seconds, so 1 A·h = 3,600 C.<sup>[3](https://www.nist.gov/pml/special-publication-330/sp-330-section-2)</sup><sup> • </sup><sup>[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8)</sup> NIST's conversion tables list the ampere-hour to coulomb factor as 3.6 × 10³, and older Bureau of Standards circulars state the same relation in reverse, 1 international coulomb = 1/3600 ampere-hour.<sup>[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8)</sup><sup> • </sup><sup>[8](https://nvlpubs.nist.gov/nistpubs/Legacy/circ/nbscircular60e2.pdf)</sup> An early Bureau of Standards definition describes the ampere-hour as the quantity of electricity flowing in one hour when the current is one ampere, alongside the ampere-second (coulomb) for one second.<sup>[9](https://nvlpubs.nist.gov/nistpubs/bulletin/01/nbsbulletinv1n1p39_A2b.pdf)</sup>

In particle terms, the 2019 SI definition fixes the elementary charge at exactly 1.602176634 × 10⁻¹⁹ coulombs, and one coulomb corresponds to about 6.241509 × 10¹⁸ electrons; an ampere-hour is therefore on the order of 10²² elementary charges.<sup>[4](https://www.nist.gov/si-redefinition/ampere/ampere-future)</sup>

## Use in battery ratings

Battery capacity in ampere-hours is the product of the current in amperes and the time in hours that the battery can supply it.<sup>[10](https://media.defense.gov/2014/Jun/20/2002655900/-1/-1/1/140620-N-ZZ182-6548.pdf)</sup> Manufacturers declare a rated capacity under specified conditions. In the power-systems literature, the rated capacity is the quantity of electricity in ampere-hours that a cell or battery can deliver during an n-hour period when charged, stored, and discharged with constant current 1/n of a reference current.<sup>[6](https://www.sciencedirect.com/science/article/pii/S2352152X16301797)</sup> A lead-acid example from the Department of Energy handbook: a battery rated 200 Ah at the 10-hour rate delivers 20 amperes for 10 hours at the standard temperature of 25 °C (77 °F).<sup>[11](https://archives.standards.doxcelerate.com/documents/doe-hdbk-1084-95-primer-on-lead-acid-storage-batteries)</sup>

The rating is nominal, not a fixed property. Actual deliverable capacity depends on discharge rate, temperature, state of health, and the cutoff voltage used, and capacity testing reports are expected to specify all of these.<sup>[12](https://www.maccor.com/battery-testing-knowledge-center/fundamentals/battery-capacity-testing-methods.html)</sup> The physical reason is that the chemical reactions inside a battery are limited by how much active material can be consumed and how quickly, so a capacity test should use a low current relative to the battery's peak current capability.<sup>[1](https://energyeducation.ca/encyclopedia/Ampere_hour)</sup>

**Discharge rate and Peukert's law.** The faster a battery is discharged, the less capacity is available. The relation between slow and fast discharge is calculated by Peukert's law and expressed as a Peukert exponent; lead-acid batteries suffer more from this effect than lithium batteries.<sup>[7](https://www.victronenergy.com/media/pg/BMV-700H/en/battery-capacity-and-peukert-exponent.html)</sup> The same handbook rule appears in early ordnance guidance: to discharge a storage battery to its normal discharged condition in 8 hours, divide its ampere-hour rating by 8, and a discharge faster than the normal 8-hour rate yields much less than the rated ampere-hours while a slower discharge can deliver considerably more.<sup>[13](https://www.govinfo.gov/content/pkg/GOVPUB-W-18972922f0429c9ad06058a0009b4150/pdf/GOVPUB-W-18972922f0429c9ad06058a0009b4150.pdf)</sup> Discharge rates are also expressed as C-rates: 1C is the current that discharges the entire battery in one hour, so a 100 Ah battery at 1C draws 100 A, and a C5 rate is 20 A for 5 hours.<sup>[7](https://www.victronenergy.com/media/pg/BMV-700H/en/battery-capacity-and-peukert-exponent.html)</sup>

## Ampere-hours versus watt-hours

An ampere-hour measures charge, not energy. Two batteries with the same ampere-hour rating at different voltages store different amounts of energy, because energy is charge multiplied by voltage. The conversion is Wh = Ah × nominal voltage; a 200 Ah battery at 12 V stores about 2,400 Wh, the same energy as a 100 Ah battery at 24 V.<sup>[5](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)</sup> Conversions should use the nominal voltage, not the fully charged voltage; a "12 V" LiFePO4 battery has a nominal voltage of 12.8 V.<sup>[5](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)</sup>

This is why watt-hours are preferred when comparing batteries of different voltages or different products, while ampere-hours remain the standard specification within a single fixed-voltage system, such as a 12 V installation, where they directly indicate relative capacity.<sup>[5](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)</sup> Small consumer products illustrate the convention: power banks are typically rated in mAh at a cell voltage of about 3.7 V, so a 10,000 mAh (10 Ah) pack corresponds to about 37 Wh, and most also carry a watt-hour rating that allows comparison with laptops and other devices.<sup>[14](https://www.techradar.com/best/best-power-banks-australia)</sup> Electric-vehicle packs, by contrast, are usually quoted in kilowatt-hours because the energy content, not the charge alone, determines range.<sup>[5](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)</sup>

## Measurement practice

Capacity is the most common battery test across a product's lifecycle, from characterizing new chemistries in the laboratory to tracking capacity fade in the field to predict end of life. The primary output is ampere-hours, the integral of current over discharge time; watt-hours add the voltage dimension to capture actual energy delivery. Rated capacity is typically measured at a low C-rate under favorable temperature conditions, and a reference performance test at a fixed low C-rate every 50 to 100 cycles is recommended to separate aging trends from rate-dependent effects.<sup>[12](https://www.maccor.com/battery-testing-knowledge-center/fundamentals/battery-capacity-testing-methods.html)</sup> Standardized procedures exist as well: IEC 61960-4:2024 specifies performance tests, markings, and reporting for coin secondary lithium cells, defining a minimum required performance level and a standardized test methodology.<sup>[15](https://webstore.iec.ch/en/publication/76834)</sup>

## References

1. [Ampere hour, Energy Education encyclopedia](https://energyeducation.ca/encyclopedia/Ampere_hour)
2. [NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8)
3. [NIST Special Publication 330, Section 2: Definition of the SI](https://www.nist.gov/pml/special-publication-330/sp-330-section-2)
4. [Ampere: The Future, NIST](https://www.nist.gov/si-redefinition/ampere/ampere-future)
5. [Battery Capacity: Amp-Hours vs Watt-Hours Explained, OffGrid Benchmark](https://www.offgridbenchmark.com/learn/battery-capacity-ah-vs-wh/)
6. [Definitions and reference values for battery systems in electrical power grids, ScienceDirect](https://www.sciencedirect.com/science/article/pii/S2352152X16301797)
7. [Battery capacity and Peukert exponent, Victron Energy BMV-700 manual](https://www.victronenergy.com/media/pg/BMV-700H/en/battery-capacity-and-peukert-exponent.html)
8. [NBS Circular 60, 2nd edition: Electric Units and Standards](https://nvlpubs.nist.gov/nistpubs/Legacy/circ/nbscircular60e2.pdf)
9. [The so-called international electrical units, NBS Bulletin](https://nvlpubs.nist.gov/nistpubs/bulletin/01/nbsbulletinv1n1p39_A2b.pdf)
10. [Battery Capacity, U.S. Navy training document](https://media.defense.gov/2014/Jun/20/2002655900/-1/-1/1/140620-N-ZZ182-6548.pdf)
11. [DOE-HDBK-1084-95, Primer on Lead-Acid Storage Batteries](https://archives.standards.doxcelerate.com/documents/doe-hdbk-1084-95-primer-on-lead-acid-storage-batteries)
12. [Battery Capacity Testing Methods, Maccor Knowledge Center](https://www.maccor.com/battery-testing-knowledge-center/fundamentals/battery-capacity-testing-methods.html)
13. [Storage batteries, U.S. Ordnance Department publication, govinfo](https://www.govinfo.gov/content/pkg/GOVPUB-W-18972922f0429c9ad06058a0009b4150/pdf/GOVPUB-W-18972922f0429c9ad06058a0009b4150.pdf)
14. [Best power banks in Australia, TechRadar](https://www.techradar.com/best/best-power-banks-australia)
15. [IEC 61960-4:2024, Coin secondary lithium cells and batteries, IEC Webstore](https://webstore.iec.ch/en/publication/76834)

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*Topic: Encyclopedia › Physical world and mathematics › Measurement and time › Units and unit systems › Units by physical quantity › Units of electricity and magnetism*

*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*

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License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license