Charge Conversion
Value:
Popular Charge Converters:
What is a Charge Converter?
An electric charge converter is a tool that converts between units of electric charge such as coulombs, ampere-hours, milliampere-hours, and faradays. It is essential for battery capacity calculations, electronics design, and electrochemistry applications.
History of Charge Measurement
The coulomb is named after Charles-Augustin de Coulomb, who quantified electric charge in the 1780s. The ampere-hour emerged in the 19th century as a practical unit for battery capacity. Michael Faraday introduced the faraday constant for electrochemistry, and Robert Millikan measured the elementary charge in 1909.
About This Charge Converter
This electric charge converter supports 15 units including coulomb, ampere-hour, milliampere-hour, faraday, abcoulomb, statcoulomb, franklin, and elementary charge. It handles both SI and CGS units for electrical engineering and physics.
Understanding Electric Charge and Its Units
Electric charge is a fundamental physical property of matter that causes it to experience electromagnetic force. The SI unit of charge is the coulomb (C), defined as the amount of charge transported by a current of one ampere flowing for one second. In practical applications — especially battery technology — charge is commonly expressed in ampere-hours (Ah) or milliampere-hours (mAh), which directly indicate how long a battery can sustain a given current.
Charge conversion is essential in electrical engineering, battery design, electrochemistry, and physics. A smartphone battery rated at 4000 mAh stores 14,400 coulombs of charge. Understanding the relationship between coulombs and ampere-hours allows engineers to calculate battery life, charging times, electroplating thickness, and capacitor energy storage. The conversion bridges the theoretical world of physics (coulombs) with the practical world of electronics (mAh).
How to Convert Between Electric Charge Units
Electric charge conversion is based on the fundamental relationship between current, charge, and time: Q = I × t (charge = current × time):
- Identify the source unit (e.g., milliampere-hours) and target unit (e.g., coulombs).
- Use the key relationship: 1 Ah = 3600 C (since 1 hour = 3600 seconds and 1 A × 1 s = 1 C).
- For mAh to C: multiply mAh by 3.6 (since 1 mAh = 3.6 C).
- For conversions involving elementary charge (e): 1 e = 1.602176634 × 10⁻¹⁹ C (exact by definition since 2019).
- Verify direction: Ah to C gives larger numbers (×3600); C to Ah gives smaller numbers (÷3600).
Key Electric Charge Conversion Formulas
Essential relationships between charge units in physics and electrical engineering:
- 1 ampere-hour (Ah) = 3600 coulombs (C)
- 1 milliampere-hour (mAh) = 3.6 coulombs
- 1 coulomb = 1 ampere × 1 second
- 1 coulomb = 6.24151 × 10¹⁸ elementary charges (e)
- 1 elementary charge = 1.602176634 × 10⁻¹⁹ C (exact)
- 1 faraday = 96,485.33212 C (charge of 1 mole of electrons)
- 1 abcoulomb (CGS) = 10 coulombs
Worked Examples — Electric Charge Conversions
Example 1: A smartphone battery is rated at 5000 mAh. How many coulombs of charge can it store?
Solution:
Conversion: 1 mAh = 3.6 C.
Multiply: 5000 × 3.6 = 18,000 C.
Answer: 5000 mAh = 18,000 coulombs. This means 18,000 ampere-seconds of charge storage.
Example 2: An electroplating process deposits 2 faradays of charge. How many ampere-hours is this?
Solution:
1 faraday = 96,485.33 C.
Total charge: 2 × 96,485.33 = 192,970.66 C.
Convert to Ah: 192,970.66 ÷ 3600 = 53.60 Ah.
Answer: 2 faradays = 53.6 Ah. This is the charge needed to deposit one mole of a divalent metal.
Example 3: A capacitor stores 0.05 C of charge. Express this in milliampere-hours.
Solution:
Conversion: 1 C = 1/3.6 mAh = 0.2778 mAh.
Multiply: 0.05 × 0.2778 = 0.01389 mAh.
Answer: 0.05 C ≈ 0.0139 mAh — illustrating why capacitors store far less charge than batteries.
Example 4: How many electrons flow through a wire carrying 2 A for 10 seconds?
Solution:
Total charge: Q = I × t = 2 × 10 = 20 C.
Electrons per coulomb: 6.24151 × 10¹⁸.
Total electrons: 20 × 6.24151 × 10¹⁸ = 1.248 × 10²⁰.
Answer: Approximately 1.25 × 10²⁰ electrons pass through the wire in 10 seconds.
Electric Charge Conversion Quick Reference
Common charge unit conversions for electronics and physics:
| From | To |
|---|---|
| 1 Ah | 3600 C |
| 1 mAh | 3.6 C |
| 1 C | 0.000278 Ah |
| 1 C | 0.278 mAh |
| 1 µAh | 0.0036 C |
| 1 faraday | 96,485.33 C |
| 1 e | 1.602 × 10⁻¹⁹ C |
| 1 abcoulomb | 10 C |
| 1 statcoulomb | 3.336 × 10⁻¹⁰ C |
| 1 kAh | 3.6 × 10⁶ C |
| 1 C | 6.242 × 10¹⁸ e |
| 1 Wh ÷ V | 1 Ah |
Understanding Charge Measurement Systems
The SI system uses the coulomb as the derived unit of charge (1 C = 1 A·s). Since 2019, the coulomb is defined in terms of the elementary charge constant e = 1.602176634 × 10⁻¹⁹ C exactly. This anchors the electrical units to a fundamental constant of nature. In practice, the coulomb is inconveniently large for everyday electronics (a typical lightning bolt delivers about 5 C, and a single electron carries an incredibly tiny fraction of a coulomb).
The practical system used in battery technology employs ampere-hours (Ah) and milliampere-hours (mAh). These units directly express the time-current relationship: a 2000 mAh battery can theoretically supply 2000 mA for 1 hour, or 1000 mA for 2 hours, or 500 mA for 4 hours (idealized — real batteries are less linear). The CGS system uses the statcoulomb (electrostatic) and abcoulomb (electromagnetic), mostly encountered in older physics texts. The faraday unit (96,485 C) represents the charge on one mole of electrons and is fundamental to electrochemistry calculations.
Real-World Applications of Charge Conversion
Battery Technology
Battery capacity in mAh must be converted to coulombs for fundamental physics calculations. A 10,000 mAh power bank stores 36,000 C — essential for calculating charging times, energy density, and comparing with supercapacitor storage.
Electroplating & Electrochemistry
Faraday's laws of electrolysis require charge in coulombs to calculate mass deposited. Plating 1 mole of copper requires 2 faradays (192,971 C) because Cu²⁺ needs 2 electrons per ion. Industrial plating shops track amp-hours for process control.
Electric Vehicle Design
EV batteries are rated in kWh (energy) and Ah (charge capacity). Converting between these requires knowing the nominal voltage. A 75 kWh battery at 400V nominal has 187.5 Ah capacity = 675,000 coulombs of stored charge.
Particle Physics
Accelerator beam currents are measured in amperes, and integrated luminosity involves total charge delivered. Converting particle counts to coulombs (via elementary charge) is routine in experimental physics data analysis.
Lightning Research
Lightning bolts transfer charge measured in coulombs (typically 1-5 C per flash). Researchers convert between charge, peak current, and duration to characterize storm severity and design protection systems.
Common Pitfalls in Charge Conversion
The most common error is confusing energy (Wh) with charge (Ah). They are related by voltage: Wh = Ah × V. A 5000 mAh battery at 3.7V stores 18.5 Wh of energy, not 5 Wh. Another frequent mistake is assuming battery mAh ratings are linear — a 4000 mAh battery does NOT supply 4000 mA for exactly 1 hour because internal resistance causes voltage drop under high current, and batteries have minimum cutoff voltages. Also, be careful with temperature effects: battery capacity (in mAh) decreases at low temperatures, so a "3000 mAh" battery in freezing conditions may deliver only 2000 mAh of usable charge. Finally, note that mAh measures charge only — two batteries with the same mAh but different voltages store different amounts of energy.
Key Takeaways
- 1 Ah = 3600 C is the essential conversion between practical and SI charge units.
- Battery mAh ratings tell you charge capacity: multiply by 3.6 to get coulombs.
- The elementary charge e = 1.602 × 10⁻¹⁹ C links microscopic physics to macroscopic electrical measurements.
- One faraday (96,485 C) is the charge per mole of electrons — the bridge between chemistry and electricity.
- Charge (Q) = Current (I) × Time (t): this dimensional relationship underlies all charge unit conversions.
- For battery life estimation: hours = capacity (mAh) ÷ current draw (mA), assuming constant discharge.
Metric Conversion Factor Tables for Charge Converter
| Units to convert | Multiply By The Number | Convert as Unit |
|---|---|---|
| Coulomb (C) | 0.000277778 | Ampere-hour (Ah) |
| Coulomb (C) | 0.277778 | Milliampere-hour (mAh) |
| Coulomb (C) | 0.001 | Kilocoulomb (kC) |
| Coulomb (C) | 1 | Ampere-second (A*s) |
| Coulomb (C) | 0.00001036 | Faraday (F) |
| Ampere-hour (Ah) | 3600 | Coulomb (C) |
| Ampere-hour (Ah) | 1000 | Milliampere-hour (mAh) |
| Milliampere-hour (mAh) | 3.6 | Coulomb (C) |
| Milliampere-hour (mAh) | 0.001 | Ampere-hour (Ah) |
| Faraday (F) | 96485.3321 | Coulomb (C) |
| Faraday (F) | 26.8015 | Ampere-hour (Ah) |
| Abcoulomb (abC) | 10 | Coulomb (C) |
| Statcoulomb (statC) | 3.33564e-10 | Coulomb (C) |
| Elementary charge (e) | 1.60218e-19 | Coulomb (C) |
| Kilocoulomb (kC) | 1000 | Coulomb (C) |
Chargeconverters & it's abbreviations
| Unit | Abbreviation | Unit | Abbreviation | Unit | Abbreviation |
|---|---|---|---|---|---|
| coulomb | C | megacoulomb | MC | kilocoulomb | kC |
| millicoulomb | mC | microcoulomb | µC | nanocoulomb | nC |
| picocoulomb | pC | abcoulomb | abC | ampere-hour | Ah |
| milliampere-hour | mAh | ampere-second | A·s | faraday | F |
| statcoulomb | statC | franklin | Fr | elementary charge | e |
Frequently Asked Questions
How do I convert coulombs to ampere-hours?
Divide the coulomb value by 3600 to get ampere-hours. For example, 7200 C ÷ 3600 = 2 Ah.
What is the difference between Ah and mAh?
Ah (ampere-hours) and mAh (milliampere-hours) both measure battery capacity. 1 Ah = 1000 mAh. Phone batteries are typically rated in mAh (e.g., 5000 mAh), while car batteries use Ah (e.g., 60 Ah).
How many coulombs are in one ampere-hour?
One ampere-hour equals exactly 3600 coulombs. This is because 1 Ah = 1 ampere flowing for 3600 seconds (1 hour).
What is a faraday in terms of coulombs?
One faraday equals approximately 96,485.33 coulombs. It represents the total charge of one mole of electrons and is fundamental to electrochemistry calculations.
What is the elementary charge?
The elementary charge (e) is the electric charge of a single proton, equal to approximately 1.602 × 10⁻¹⁹ coulombs. It is the smallest unit of free charge found in nature.
Complete list of Charge conversion units and its conversion.
- 1 coulomb [C] = 0.000277778 ampere-hour [Ah]
coulombs to Ah → - 1 coulomb [C] = 0.277778 milliampere-hour [mAh]
coulombs to mAh → - 1 coulomb [C] = 1 ampere-second [A*s]
C to A*s →
- 1 ampere-hour [Ah] = 3600 coulomb [C]
Ah to coulombs → - 1 ampere-hour [Ah] = 1000 milliampere-hour [mAh]
Ah to mAh → - 1 ampere-hour [Ah] = 0.03731 faraday [F]
Ah to faraday →
- 1 faraday [F] = 26.8015 ampere-hour [Ah]
faraday to Ah → - 1 abcoulomb [abC] = 10 coulomb [C]
abC to coulombs → - 1 statcoulomb [statC] = 3.33564e-10 coulomb [C]
statC to coulombs →
- 1 coulomb [C] = 0.001 kilocoulomb [kC]
C to kC → - 1 coulomb [C] = 0.00001036 faraday [F]
C to faraday → - 1 coulomb [C] = 0.1 abcoulomb [abC]
C to abC →
- 1 milliampere-hour [mAh] = 3.6 coulomb [C]
mAh to coulombs → - 1 milliampere-hour [mAh] = 0.001 ampere-hour [Ah]
mAh to Ah → - 1 faraday [F] = 96485.3321 coulomb [C]
faraday to coulombs →
- 1 elementary charge [e] = 1.60218e-19 coulomb [C]
e to coulombs → - 1 kilocoulomb [kC] = 1000 coulomb [C]
kC to C → - 1 megacoulomb [MC] = 1000000 coulomb [C]
MC to C →