Coulombs to Ampere-Hours Converter

How to Convert Coulombs to Ampere-Hours

To convert an electric charge measurement from coulombs to ampere-hours, divide the charge value by the conversion factor. Since one coulomb is equal to 2.7778 × 10^-4 ampere-hours, you can use this formula:

The charge in ampere-hours is equal to the coulombs divided by 3600.

How Many Ampere-Hours Are in a Coulomb?

There are 2.7778 × 10^-4 ampere-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 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).

Coulombs to Ampere-Hours Conversion Table

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

Related Electric Charge Converters

Convert from Coulombs

Convert to Ampere-Hours