Charge Converter (mAh, Ah, coulombs)

Understanding the battery charge converter — concept and principle

Battery capacity on phones, power banks and drones is usually printed in milliampere-hours (mAh), while larger batteries use ampere-hours (Ah) and physics and chemistry use the coulomb (C) and the faraday. All of them measure electric charge: how much current a battery can deliver for how long. This converter switches between mAh, Ah, coulombs and faradays (moles of electrons).

How it is calculated

Values are converted to a common base and then to the target unit: result = value × (base per "from" unit) ÷ (base per "to" unit). The factors are:

• 1 Ah = 1,000 mAh
• 1 Ah = 1 A × 3,600 s = 3,600 C, so 1 mAh = 3.6 C
• 1 faraday = F = 96,485.33212 C (charge of one mole of electrons) ≈ 26,801.48 mAh

The principle

Charge is current multiplied by time: Q = I × t. One ampere is one coulomb per second, so a current of 1 A flowing for one hour (3,600 s) moves 3,600 C, which is 1 Ah. A rating of 5,000 mAh therefore means, in the ideal case, 5 A for 1 hour, 1 A for 5 hours or 0.5 A for 10 hours. The faraday links charge to chemistry: the Faraday constant is the elementary charge (e = 1.602176634 × 10⁻¹⁹ C) times the Avogadro constant (6.02214076 × 10²³ mol⁻¹), both exact since the 2019 SI revision. It tells you how many moles of electrons the battery's reactions must transfer.

Worked example

1. Inputs: value = 5,000, from mAh, to Ah.
2. 5,000 mAh ÷ 1,000 = 5 Ah.
3. In coulombs: 5 Ah × 3,600 = 18,000 C.
4. In faradays: 18,000 ÷ 96,485.33212 = 0.1865568538 mol e⁻.

How to read the result

Charge alone is not energy. To compare batteries with different voltages, convert to watt-hours: Wh = Ah × nominal voltage. A 5,000 mAh phone cell at 3.85 V stores 5 × 3.85 = 19.25 Wh, while a 5,000 mAh pack rated at 7.4 V stores about twice as much. Airlines and shipping rules use Wh for this reason. Real runtime is usually below the ideal figure because capacity drops at high current, in the cold and with battery age.

Common mistakes

• Comparing mAh across batteries with different voltages; compare Wh instead.
• Assuming a 20,000 mAh power bank can deliver 20,000 mAh at 5 V USB output. The rating usually refers to the internal 3.6–3.7 V cells, and conversion losses reduce what reaches your device.
• Dividing capacity by peak current to get runtime; average current is what matters.

Frequently asked questions

How many coulombs are in 1 mAh?

Exactly 3.6 C.

How do I convert mAh to Wh?

Wh = mAh × V ÷ 1,000. For example, 3,000 mAh × 3.7 V ÷ 1,000 = 11.1 Wh.

How long will a 5,000 mAh battery last?

Divide by the average current: at 500 mA it is about 10 hours in theory, usually less in practice.

Sources: BIPM, The International System of Units (SI Brochure), 9th edition, 2019 · CODATA recommended values of the fundamental physical constants (NIST) · NIST Special Publication 811 (2008), Appendix B