Statcoulombs to Milliampere-Hours Converter

How to Convert Statcoulombs to Milliampere-Hours

To convert an electric charge measurement from statcoulombs to milliampere-hours, divide the charge value by the conversion factor. Since one statcoulomb is equal to 9.2657 × 10^-11 milliampere-hours, you can use this formula:

The charge in milliampere-hours is equal to the statcoulombs divided by 1.0793 × 10¹⁰.

How Many Milliampere-Hours Are in a Statcoulomb?

There are 9.2657 × 10^-11 milliampere-hours in one statcoulomb.

What Is a Statcoulomb?

The statcoulomb (symbol: stC, also called the franklin or esu of charge) is the unit of electric charge in the centimetre–gram–second electrostatic system of units (CGS-ESU). It is defined as the amount of charge that exerts a force of one dyne on an equal charge one centimetre away in vacuum. One statcoulomb is approximately equal to 3.336 × 10⁻¹⁰ coulombs, making it a very small unit of charge compared to the coulomb. Conversely, one coulomb equals approximately 2.998 × 10⁹ statcoulombs. The conversion factor between coulombs and statcoulombs involves the speed of light in vacuum (c ≈ 2.998 × 10¹⁰ cm/s), reflecting the fundamental relationship between electric and magnetic units in the CGS system. This connection to the speed of light is one of the key features of Gaussian units used in theoretical physics. While largely superseded by SI units in modern engineering, the statcoulomb and CGS-ESU system remain important in theoretical physics and older scientific literature. Many classic electromagnetism textbooks, particularly those covering Gaussian units, express charge in statcoulombs.

One statcoulomb is equal to:

• ≈ 3.336 × 10⁻¹⁰ coulombs (C)
• ≈ 3.336 × 10⁻⁷ millicoulombs (mC)
• ≈ 3.336 × 10⁻⁴ microcoulombs (μC)
• ≈ 0.3336 nanocoulombs (nC)
• ≈ 333.6 picocoulombs (pC)
• ≈ 3.336 × 10⁻¹¹ abcoulombs (abC)
• ≈ 2.082 × 10⁹ electron charges (e)
• ≈ 9.266 × 10⁻¹⁴ ampere-hours (Ah)

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).

Statcoulombs to Milliampere-Hours Conversion Table

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

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