Coulombs to Milliampere-Hours Converter

How to Convert Coulombs to Milliampere-Hours

To convert an electric charge measurement from coulombs to milliampere-hours, divide the charge value by the conversion factor. Since one coulomb is equal to 0.2777778 milliampere-hours, you can use this formula:

The charge in milliampere-hours is equal to the coulombs divided by 3.6.

How Many Milliampere-Hours Are in a Coulomb?

There are 0.2777778 milliampere-hours in one coulomb.

What Is a Coulomb?

The coulomb (symbol: C) is the SI derived unit of electric charge. It is named after the French physicist Charles-Augustin de Coulomb, who formulated Coulomb's law describing the electrostatic force between charged particles. One coulomb is defined as the amount of electric charge transported by a constant current of one ampere in one second. In terms of fundamental constants, since the 2019 redefinition of SI base units, the coulomb is defined by taking the elementary charge e to be exactly 1.602176634 × 10⁻¹⁹ coulombs. A single coulomb represents a very large amount of charge in everyday terms. A typical lightning bolt transfers about 5 coulombs of charge, and the charge stored in a standard AA battery is roughly 5,000 coulombs (about 1.4 ampere-hours). A static electricity shock might involve only a few microcoulombs. The coulomb is related to other SI units as: 1 C = 1 A·s (ampere-second). It can also be expressed as: 1 C = 1 F·V (farad-volt) or 1 C = 1 J/V (joule per volt).

One coulomb is equal to:

• 1,000 millicoulombs (mC)
• 1,000,000 microcoulombs (μC)
• 1,000,000,000 nanocoulombs (nC)
• 1,000,000,000,000 picocoulombs (pC)
• 0.1 abcoulombs (abC)
• ≈ 2,997,920,000 statcoulombs (stC)
• ≈ 6.2415 × 10¹⁸ electron charges (e)
• ≈ 0.000278 ampere-hours (Ah)
• ≈ 0.2778 milliampere-hours (mAh)

What Is a Milliampere-Hour?

The milliampere-hour (symbol: mAh) is a unit of electric charge equal to one thousandth of an ampere-hour. It represents the charge conveyed by a current of one milliampere flowing for one hour, which equals 3.6 coulombs. Milliampere-hours are the most common unit for rating the capacity of small rechargeable batteries used in portable electronics. Smartphone batteries are typically rated at 3,000–5,000 mAh, wireless earbuds at 30–60 mAh per earbud, and laptop batteries at 40,000–100,000 mAh (or equivalently 40–100 Wh at a given voltage). The milliampere-hour provides an intuitive measure of battery life: a 3,000 mAh battery can theoretically supply 3,000 mA (3 A) for one hour, or 300 mA for 10 hours, or 100 mA for 30 hours. However, actual battery life depends on many factors including discharge rate, temperature, and battery age. While not an SI unit, the milliampere-hour is ubiquitous in the consumer electronics industry and is printed on virtually every rechargeable battery. It has become the de facto standard for communicating battery capacity to consumers.

One milliampere-hour is equal to:

• 3.6 coulombs (C)
• 3,600 millicoulombs (mC)
• 3,600,000 microcoulombs (μC)
• 3.6 × 10⁹ nanocoulombs (nC)
• 3.6 × 10¹² picocoulombs (pC)
• 0.36 abcoulombs (abC)
• ≈ 1.079 × 10¹⁰ statcoulombs (stC)
• ≈ 2.247 × 10¹⁹ electron charges (e)
• 0.001 ampere-hours (Ah)

Understanding Electric Charge

Electric charge is a fundamental physical property of matter that causes it to experience a force when placed in an electromagnetic field. Charge comes in two types: positive and negative. Like charges repel each other, while opposite charges attract, as described by Coulomb's law.

The SI unit of electric charge is the coulomb (C), defined as the charge transported by a constant current of one ampere in one second. In the microscopic world, charge is quantized — it always appears in integer multiples of the elementary charge e ≈ 1.602 × 10⁻¹⁹ C, which is the magnitude of charge carried by a single electron or proton.

Electric charge is conserved in all physical processes: the total charge in an isolated system never changes. This conservation law is one of the most fundamental principles in physics and is closely related to the gauge symmetry of electromagnetism.

Measurement Systems

Three main unit systems are used for electric charge:

• SI (International System): Uses the coulomb and its metric prefixes (mC, μC, nC, pC). This is the modern standard used worldwide in science and engineering.
• CGS-ESU (Electrostatic): Uses the statcoulomb (or franklin), defined through Coulomb's law with the proportionality constant set to 1. Common in theoretical physics.
• CGS-EMU (Electromagnetic): Uses the abcoulomb, where 1 abC = 10 C. Historically used in electromagnetic theory.

Practical Charge Units

In addition to the fundamental units, two practical units are widely used:

• Ampere-hour (Ah): Equal to 3,600 C. Used for battery capacity ratings of large batteries (car batteries, industrial cells).
• Milliampere-hour (mAh): Equal to 3.6 C. The standard unit for consumer electronics battery capacity (smartphones, tablets, wireless devices).
• Electron charge (e): The fundamental quantum of charge, ≈ 1.602 × 10⁻¹⁹ C. Used in atomic and particle physics.

Electric Charge in Everyday Life

• A typical lightning bolt transfers about 5 coulombs of charge
• A static electricity shock involves about 1–10 microcoulombs
• A smartphone battery (3,000 mAh) stores about 10,800 coulombs
• A car battery (60 Ah) stores about 216,000 coulombs
• A single electron carries 1.602 × 10⁻¹⁹ coulombs

Tips for Electric Charge Conversions

• For SI prefix conversions (C, mC, μC, nC, pC), each step is a factor of 1,000. Moving from a larger prefix to a smaller one means multiplying by 1,000 for each step.
• To convert between coulombs and ampere-hours, remember: 1 Ah = 3,600 C. Divide coulombs by 3,600 to get ampere-hours.
• Battery capacity in mAh can be converted to coulombs by multiplying by 3.6. For example, a 5,000 mAh battery stores 18,000 coulombs.
• The electron charge (e) involves extremely large or small numbers. When converting to/from electron charges, scientific notation is essential.
• CGS units (statcoulombs, abcoulombs) are rarely used in modern practice. If you encounter them in older literature, remember: 1 abC = 10 C, and 1 C ≈ 3 × 10⁹ stC.
• When working with battery specifications, note that capacity (mAh or Ah) alone doesn't determine energy storage — you also need to know the voltage. Energy (Wh) = Capacity (Ah) × Voltage (V).

Coulombs to Milliampere-Hours Conversion Table

The following table shows conversions from coulombs to milliampere-hours.

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