Farads to Joules Converter
A 100 farad capacitor charged to 5 volts stores 1,250 joules of energy.
Quick answer: Square the voltage, multiply by the farads, then halve the result. For example, 100 F at 5 V is 1,250 J, 1 F at 12 V is 72 J and 3,000 F at 2.7 V is 10,935 J.
The farads to joules formula
Energy in joules equals half times capacitance in farads times voltage squared.
Doubling the voltage makes the stored energy four times larger.
Take 100 F at 5 V. 0.5 × 100 × 5² gives 1,250 J.
Take 1 F at 12 V. 0.5 × 1 × 12² gives 72 J.
The energy stored in a capacitor
The energy stored in a charged capacitor is half the capacitance times the square of the voltage across it (TutorChase: Energy stored in a charged capacitor).
Because the voltage is squared, doubling it quadruples the energy.
How to convert farads to joules step by step
- Read the capacitance in farads and the voltage across it.
- Multiply the voltage by itself.
- Multiply by the farads, then halve it.
- Read the energy in joules, or divide by 3,600 for watt-hours.
Example 1: 100 F at 5 V
- Start with 100 F at 5 V.
- 0.5 × 100 × 5² = 1,250.
- The energy is 1,250 J.
100 F at 5 V = 1,250 J
Example 2: 1 F at 12 V
- Start with 1 F at 12 V.
- 0.5 × 1 × 12² = 72.
- The energy is 72 J.
1 F at 12 V = 72 J
Example 3: 3,000 F at 2.7 V
- Start with 3,000 F at 2.7 V.
- 0.5 × 3,000 × 2.7² = 10,935.
- The energy is 10,935 J.
3,000 F at 2.7 V = 10,935 J
The three examples below use common sizes.
Each one shows the sum in full.
farads to joules conversion table
| Capacitance and voltage | Energy (J) | Energy (Wh) |
|---|---|---|
| 1 F at 5 V | 12.5 J | 0.003472 Wh |
| 1 F at 12 V | 72 J | 0.02 Wh |
| 10 F at 2.7 V | 36.45 J | 0.0101 Wh |
| 10 F at 5 V | 125 J | 0.0347 Wh |
| 50 F at 5 V | 625 J | 0.1736 Wh |
| 100 F at 2.7 V | 364.5 J | 0.1013 Wh |
| 100 F at 5 V | 1,250 J | 0.3472 Wh |
| 100 F at 12 V | 7,200 J | 2 Wh |
| 350 F at 2.7 V | 1,275.75 J | 0.3544 Wh |
| 1,000 F at 2.7 V | 3,645 J | 1.013 Wh |
| 3,000 F at 2.7 V | 10,935 J | 3.038 Wh |
| 5,000 F at 2.7 V | 18,225 J | 5.063 Wh |
The highlighted row is the default of the calculator. The last column gives Wh.
A quick mental shortcut for farads to joules
Square the volts, multiply by the farads, then halve it. For 100 F at 5 V that is 25 x 100 / 2, which is 1,250 J.
Double the farads and the energy doubles.
Why the voltage is squared
The energy depends on the voltage twice over. A higher voltage means more charge on the plates, and each bit of charge also sits at a higher voltage.
That is why a small rise in voltage adds a lot of energy.
A worked example with a 12 volt capacitor
A 1 F capacitor at 12 V stores 0.5 x 1 x 144, which is 72 J. At 6 V the same capacitor stores only 18 J.
Halving the voltage cuts the energy to a quarter.
Safety with stored energy
A charged capacitor can release its energy in a flash. Even a few hundred joules can burn skin or start a fire if it is shorted.
Discharge large capacitors with a proper resistor and check the voltage before touching them.
Quick conversion answers
| Conversion | Result |
|---|---|
| 100 F at 5 V | 1,250 J |
| 1 F at 12 V | 72 J |
| 10 F at 2.7 V | 36.45 J |
| 3,000 F at 2.7 V | 10,935 J |
Where this conversion is used
Designers compare the energy in capacitors for memory backup and flash circuits.
Students practise energy formulas for capacitors.
Common mistakes to avoid
- Skipping the half. The energy is half of C times V squared.
- Forgetting to square the voltage. The energy grows with the square.
- Using microfarads as farads. The answer would be one million times too large.
- Using the rated voltage when the capacitor is only partly charged. Use the voltage that is really across it.
Related converters
More capacitance and voltage pairs
0.01 F at 5 V is 0.125 J. 0.1 F at 5 V is 1.25 J. 0.5 F at 12 V is 36 J.
2 F at 16 V is 256 J. 5 F at 50 V is 6,250 J. 25 F at 3 V is 112.5 J.
220 F at 2.7 V is 801.9 J. 500 F at 2.7 V is 1,823 J. 2,000 F at 2.7 V is 7,290 J.
Doubling the first number
0.02 F at 5 V is 0.25 J. 0.2 F at 5 V is 2.5 J. 1 F at 12 V is 72 J.
4 F at 16 V is 512 J. 10 F at 50 V is 12,500 J. 50 F at 3 V is 225 J.
440 F at 2.7 V is 1,604 J. 1,000 F at 2.7 V is 3,645 J. 4,000 F at 2.7 V is 14,580 J.
The same capacitor at different voltages
100 F at 1 V is 50 J. 100 F at 2.7 V is 364.5 J. 100 F at 5 V is 1,250 J.
100 F at 12 V is 7,200 J.
Frequently asked questions
How do I convert farads to joules?
Multiply half the capacitance in farads by the voltage squared.
How many joules is 100 F at 5 V?
1,250 J.
Why is the voltage squared?
Both the charge and the voltage it sits at rise together.
How do I get watt-hours?
Divide the joules by 3,600.
What happens if I halve the voltage?
The energy falls to a quarter.
Is a charged capacitor dangerous?
It can be. Discharge large ones safely before touching them.
Sources
- TutorChase: Energy stored in a charged capacitor (tutorchase.com)
- Wikipedia: Farad (en.wikipedia.org)
