Statcoulombs to Ampere-Hours Converter

How to Convert Statcoulombs to Ampere-Hours

To convert an electric charge measurement from statcoulombs to ampere-hours, divide the charge value by the conversion factor. Since one statcoulomb is equal to 9.2657 × 10^-14 ampere-hours, you can use this formula:

The charge in ampere-hours is equal to the statcoulombs divided by 1.0793 × 10¹³.

How Many Ampere-Hours Are in a Statcoulomb?

There are 9.2657 × 10^-14 ampere-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 While largely superseded by SI units in modern engineering, the statcoulomb and CGS-ESU system remain important in theoretical physics and older scientific literature.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 Ampere-Hour?

The ampere-hour (symbol: Ah) is a unit of electric charge commonly used to measure the capacity of batteries and other energy storage devices. One ampere-hour is defined as the electric charge conveyed by a steady current of one ampere flowing for one hour. Since one hour equals 3,600 seconds and one ampere is one coulomb per second, one ampere-hour equals exactly 3,600 coulombs. This makes the ampere-hour a convenient practical unit for expressing large quantities of charge found in batteries. Ampere-hours are the standard unit for rating battery capacity. For example, a typical car battery might be rated at 50–100 Ah, meaning it can theoretically deliver 50–100 amperes for one hour, or proportionally less current for longer periods. Large industrial batteries and electric vehicle batteries may be rated in the hundreds or thousands of ampere-hours. While not an SI unit, the ampere-hour is widely accepted in electrical engineering, consumer electronics, and the battery industry. It provides an intuitive measure of how much charge a battery can store and deliver, making it easier for consumers and engineers to compare battery capacities across different products.

One ampere-hour is equal to:

• 3,600 coulombs (C)
• 3,600,000 millicoulombs (mC)
• 3.6 × 10⁹ microcoulombs (μC)
• 3.6 × 10¹² nanocoulombs (nC)
• 3.6 × 10¹⁵ picocoulombs (pC)
• 360 abcoulombs (abC)
• ≈ 1.079 × 10¹³ statcoulombs (stC)
• ≈ 2.247 × 10²² electron charges (e)
• 1,000 milliampere-hours (mAh)

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 Ampere-Hours Conversion Table

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

Related Electric Charge Converters

Convert from Statcoulombs

Convert to Ampere-Hours