Convert between 12 units: Coulombs, mAh, Franklin, Elementary Charge & More
Enter a value in any field to see instant conversions across all 12 electric charge units. Our comprehensive calculator covers everything from elementary charges to kilocoulombs with precise scientific conversion factors for accurate results in physics, electrical engineering, and practical applications.
Our calculator employs internationally recognized conversion factors based on fundamental physical constants and unit definitions. All conversions are performed relative to the coulomb as the base SI unit:
Coulomb (C): The fundamental SI unit of electric charge. One coulomb represents the charge of approximately 6.242 × 10¹⁸ elementary charges. In practical terms, this is an enormous amount of charge – lightning bolts typically carry only a few coulombs.
Sub-units for Smaller Measurements:
Ampere-hour (Ah): The workhorse unit of electrical engineering. A battery rated at 1 Ah can theoretically provide 1 ampere of current for 1 hour, or equivalently, 0.5 amperes for 2 hours. Essential for sizing electrical systems and energy storage.
Milliampere-hour (mAh): The standard unit for small portable devices. Smartphone batteries typically range from 3,000-5,000 mAh, while hearing aid batteries might be 50-300 mAh.
Ampere-second (A⋅s): Equivalent to coulombs but emphasizes the time-current relationship. Often used in electroplating calculations and short-duration electrical processes.
Franklin (Fr): Also called statcoulomb, this CGS unit is much smaller than the coulomb and convenient for atomic and molecular scale calculations. One franklin is defined as the charge that experiences a force of one dyne when placed one centimeter from an identical charge.
Abcoulomb (abC): From the electromagnetic CGS system, equal to 10 coulombs. Historically important in magnetic field calculations and still used in some specialized physics applications.
Elementary Charge (e): The fundamental unit of electric charge carried by a single proton or electron. This is the smallest amount of charge that can exist freely and forms the basis for all other electrical phenomena.
Electric charge is one of the most fundamental properties of matter, governing everything from the behavior of atoms to the operation of complex electronic devices. Understanding the complete spectrum of charge units – from the tiny elementary charge to practical ampere-hours – is crucial for anyone working in electrical engineering, physics, or related fields.
Electric charge is an intrinsic property of certain particles that determines how they interact electromagnetically. Unlike mass, which is always positive, electric charge can be either positive or negative. This dual nature creates the attractive and repulsive forces that shape our physical world, from the structure of atoms to the operation of electronic devices.
Research on electrostatic phenomena shows that all electric charge exists in discrete packets. The fundamental unit of charge – the elementary charge carried by a proton or electron – equals exactly 1.602176634 × 10⁻¹⁹ coulombs (as defined in the 2019 SI revision). This quantization means that every measurable electric charge is an integer multiple of this elementary unit, from the picocoulombs in sensitive electronic components to the thousands of ampere-hours in electric vehicle batteries.
The evolution of electric charge units reflects humanity's growing understanding of electromagnetic phenomena and the need for standardized measurement systems across different scientific traditions.
The Foundation - Charles-Augustin de Coulomb (1736-1806): The story begins with French physicist Charles-Augustin de Coulomb, whose pioneering work in the 1780s established the mathematical foundation for understanding electrostatic forces. Using his famous torsion balance, Coulomb discovered that the force between two charged objects varies inversely with the square of the distance between them - now known as Coulomb's Law. His work laid the groundwork for quantifying electric charge, though the modern coulomb unit wasn't established until much later.
The CGS System Revolution (1870s-1880s): The centimeter-gram-second (CGS) system of units, developed in the 1870s, created the first systematic approach to electrical measurements. This system gave birth to two important units still used today:
The SI Revolution and Modern Definitions: The International System of Units (SI), officially adopted in 1960, revolutionized electrical measurements. The coulomb was originally defined through the ampere, which itself was defined by the force between current-carrying wires. However, the 2019 redefinition of SI units marked a historic shift: the coulomb is now defined directly in terms of the elementary charge, making it one of the most precisely defined units in science.
Practical Engineering Units: As electrical technology advanced, engineers needed practical units for real-world applications:
The Quantum Era and Elementary Charge: The discovery of the electron by J.J. Thomson in 1897 and Robert Millikan's famous oil drop experiment (1909) revealed that electric charge comes in discrete packets. Millikan's precise measurement of the elementary charge (1.602 × 10⁻¹⁹ coulombs) became fundamental to modern physics and quantum mechanics.
Modern Metrology: Today's electric charge measurements achieve unprecedented precision. The 2019 redefinition of the ampere in terms of the elementary charge creates a direct link between quantum physics and practical electrical engineering, ensuring that your smartphone battery capacity measurement shares the same fundamental basis as cutting-edge quantum computing research.
In today's technology-driven world, understanding charge units has immediate practical implications. Battery manufacturers constantly work with ampere-hours to specify battery capacity. A smartphone battery typically holds 3-4 Ah, meaning it can theoretically supply 3-4 amperes for one hour or 1 ampere for 3-4 hours.
Several persistent misconceptions about electric charge are commonly encountered:
Misconception: "Ampere-hours measure energy stored in batteries."
Reality: Ampere-hours measure charge capacity, not energy. Energy storage depends on both charge and voltage (measured in watt-hours).
Misconception: "Franklin units are obsolete and irrelevant."
Reality: Franklin units remain valuable in electrostatic calculations and atomic physics, where they often simplify mathematical expressions.
Different approaches are recommended for various applications:
For Battery Design: Start with ampere-hour requirements based on device current consumption and desired operating time. Convert to coulombs when performing detailed electrochemical calculations.
For Electrostatic Analysis: Use Franklin units for initial calculations involving Coulomb's law, then convert to SI units for integration with other electromagnetic calculations.
For General Electronics: Stick with coulombs and ampere-hours, as these integrate seamlessly with standard electrical measurements and specifications.
The ongoing redefinition of SI units in terms of fundamental constants affects how we understand electric charge. The 2019 redefinition of the ampere in terms of the elementary charge creates a more fundamental basis for charge measurements, potentially improving precision in quantum electronics and metrology.
As quantum technologies advance, increased importance of single-electron charge measurements is anticipated, where understanding the relationship between coulombs and elementary charges becomes crucial for device operation.
This guide is based on established electrical engineering principles and verified conversion factors. All formulas and conversion factors presented here are verified against authoritative sources including NIST standards and international physics references. The practical examples represent common applications found in electrical engineering and physics education.
Electric charge measurements span an enormous range of applications, from quantum physics (elementary charges) to industrial power systems (kilocoulombs). Different fields use different units for convenience - physicists prefer units that simplify their equations, while engineers choose units that match their practical measurements. Our comprehensive converter bridges all these applications.
Milliampere-hours (mAh) are used for small portable devices like smartphones, tablets, and hearing aids, while ampere-hours (Ah) describe larger batteries in cars, boats, and home energy storage systems. 1 Ah = 1,000 mAh, so a 4,000 mAh phone battery equals 4 Ah.
Franklin units (statcoulombs) are most useful in electrostatic calculations and atomic physics problems where the CGS system simplifies mathematical expressions. They're particularly common in older physics literature, plasma physics, and when working with Coulomb's law in its simplest mathematical form.
The elementary charge (e) is the electric charge of a single proton or electron - the smallest amount of charge that can exist freely. It's fundamental to quantum physics and forms the basis for the modern definition of the coulomb. Understanding elementary charges is essential for quantum electronics and nanotechnology.
Our conversion factors are based on exact definitions (for SI units) and internationally accepted standards (for CGS units). The elementary charge and speed of light values used are from the 2019 SI redefinition, providing accuracy suitable for virtually all scientific and engineering applications.
Electric charge units span over 20 orders of magnitude! When converting between very different scales (like elementary charges to ampere-hours), the numbers become extremely large or small. Scientific notation (like 1.23e+15) keeps these results readable and precise.
Yes, this converter uses the same standards and conversion factors employed throughout the electrical industry. From smartphone battery specifications (mAh) to power system analysis (kC), these are the units and conversions that professional electrical engineers use daily.
The abcoulomb comes from the electromagnetic CGS system and equals exactly 10 coulombs. It was designed to simplify magnetic force calculations in the CGS system. While less common today, it's still used in some specialized physics applications and historical literature.
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While we strive for accuracy in all conversions and educational content, this calculator is provided for informational and educational purposes only. The conversion factors used are based on internationally recognized standards and authoritative sources including NIST and BIPM.
Important: For critical applications in electrical engineering, scientific research, or safety-related systems, we recommend verifying results with official standards documentation and consulting with qualified professionals. Electrical calculations involving high voltages, currents, or energy storage systems should always be reviewed by licensed electrical engineers.
This tool should not be used as the sole basis for critical engineering decisions, safety calculations, or professional electrical work without proper verification and professional oversight. ConversionCalculator.net assumes no liability for any damages, losses, or consequences arising from the use of this calculator or the information provided.