Farads to Amp Hours Converter
A 100 farad supercapacitor swinging through 5 volts holds charge worth about 0.139 amp-hours.
Quick answer: Multiply the farads by the voltage swing, then divide by 3,600. For example, 100 F over 5 V is 0.1389 Ah, 10 F over 2.7 V is 0.0075 Ah and 3,000 F over 2.7 V is 2.25 Ah.
The farads to amp hours formula
Amp-hours equal farads times voltage swing, divided by 3,600.
The farad is one coulomb per volt, and one amp-hour is 3,600 coulombs.
Take 100 F over 5 V. 100 × 5 ÷ 3,600 gives 0.1389 Ah.
Take 10 F over 2.7 V. 10 × 2.7 ÷ 3,600 gives 0.0075 Ah.
Charge from capacitance
One farad is one coulomb per volt, so a capacitor moves the charge in coulombs equal to its farads times the voltage change (Wikipedia: Farad).
One amp-hour is one amp for 3,600 seconds, which is 3,600 coulombs. So divide the coulombs by 3,600.
How to convert farads to amp hours step by step
- Read the capacitance in farads and the voltage swing in volts.
- Multiply the two to get coulombs.
- Divide by 3,600 to get amp-hours.
- Multiply by 1,000 for milliamp-hours.
Example 1: 100 F over 5 V
- Start with 100 F over 5 V.
- 100 × 5 ÷ 3,600 = 0.1389.
- The charge is 0.1389 Ah.
100 F over 5 V = 0.1389 Ah
Example 2: 10 F over 2.7 V
- Start with 10 F over 2.7 V.
- 10 × 2.7 ÷ 3,600 = 0.0075.
- The charge is 0.0075 Ah.
10 F over 2.7 V = 0.0075 Ah
Example 3: 3,000 F over 2.7 V
- Start with 3,000 F over 2.7 V.
- 3,000 × 2.7 ÷ 3,600 = 2.25.
- The charge is 2.25 Ah.
3,000 F over 2.7 V = 2.25 Ah
The three examples below use common sizes.
Each one shows the sum in full.
farads to amp hours conversion table
| Capacitance and voltage swing | Charge (Ah) | Charge (mAh) |
|---|---|---|
| 1 F over 5 V | 0.001389 Ah | 1.389 mAh |
| 10 F over 2.7 V | 0.0075 Ah | 7.5 mAh |
| 10 F over 5 V | 0.0139 Ah | 13.889 mAh |
| 50 F over 2.7 V | 0.0375 Ah | 37.5 mAh |
| 100 F over 2.7 V | 0.075 Ah | 75 mAh |
| 100 F over 5 V | 0.1389 Ah | 138.89 mAh |
| 100 F over 12 V | 0.3333 Ah | 333.33 mAh |
| 350 F over 2.7 V | 0.2625 Ah | 262.5 mAh |
| 500 F over 2.7 V | 0.375 Ah | 375 mAh |
| 1,000 F over 2.7 V | 0.75 Ah | 750 mAh |
| 3,000 F over 1.35 V | 1.125 Ah | 1,125 mAh |
| 3,000 F over 2.7 V | 2.25 Ah | 2,250 mAh |
The highlighted row is the default of the calculator. The last column gives mAh.
A quick mental shortcut for farads to amp hours
Multiply the farads by the volts and divide by about 3,600. 100 F over 5 V is 500 coulombs, and 500 divided by 3,600 is about 0.139 Ah.
Double the voltage swing and the charge doubles.
Use the voltage swing, not the top voltage
A supercapacitor cannot give up all its charge. It is useful only between its top voltage and the lowest voltage your circuit accepts.
So enter the difference between the two voltages as the swing.
Charge is not energy
Amp-hours count charge only. A battery keeps its voltage nearly steady while a capacitor loses voltage as it discharges.
To compare with a battery, use the energy page instead.
Size of the farad
Commercial capacitors run from about 0.1 pF up to 5,000 F, and the largest are supercapacitors (Wikipedia: Farad).
Even 3,000 F over 2.7 V comes to only 2.25 Ah.
Quick conversion answers
| Conversion | Result |
|---|---|
| 100 F over 5 V | 0.1389 Ah |
| 10 F over 2.7 V | 0.0075 Ah |
| 350 F over 2.7 V | 0.2625 Ah |
| 3,000 F over 2.7 V | 2.25 Ah |
Where this conversion is used
Designers size a supercapacitor to hold up a small circuit for a short time.
Hobbyists compare the charge in a supercapacitor with a small battery.
Common mistakes to avoid
- Using the full voltage as the swing. The usable swing is smaller.
- Comparing Ah with a battery directly. The voltage falls as a capacitor discharges.
- Forgetting the 3,600. Without it the answer is in coulombs.
- Mixing farads with microfarads. A microfarad is one millionth of a farad.
Related converters
More capacitance and voltage swings
0.5 F over 5 V is 0.0006944 Ah. 2 F over 5.5 V is 0.003056 Ah. 5 F over 2.7 V is 0.00375 Ah.
25 F over 2.7 V is 0.01875 Ah. 58 F over 16 V is 0.2578 Ah. 120 F over 48 V is 1.6 Ah.
220 F over 2.7 V is 0.165 Ah. 650 F over 2.7 V is 0.4875 Ah. 5,000 F over 2.7 V is 3.75 Ah.
Doubling the first number
1 F over 5 V is 0.001389 Ah. 4 F over 5.5 V is 0.006111 Ah. 10 F over 2.7 V is 0.0075 Ah.
50 F over 2.7 V is 0.0375 Ah. 116 F over 16 V is 0.5156 Ah. 240 F over 48 V is 3.2 Ah.
440 F over 2.7 V is 0.33 Ah. 1,300 F over 2.7 V is 0.975 Ah. 10,000 F over 2.7 V is 7.5 Ah.
The same supercapacitor with different voltage swings
100 F over 1 V is 0.02778 Ah. 100 F over 2.7 V is 0.075 Ah. 100 F over 5 V is 0.1389 Ah.
100 F over 12 V is 0.3333 Ah.
Frequently asked questions
How do I convert farads to amp-hours?
Multiply the farads by the voltage swing, then divide by 3,600.
How many Ah is 100 F over 5 V?
About 0.1389 Ah, which is 138.9 mAh.
Why divide by 3,600?
One amp-hour is 3,600 coulombs.
Can I compare this with a battery?
Only roughly. A battery holds its voltage and a capacitor does not.
What voltage swing should I use?
The top voltage minus the lowest voltage your circuit can accept.
What is a coulomb?
The charge that one amp carries in one second.
Sources
- Wikipedia: Farad (en.wikipedia.org)
