Capacitor Energy
E = ½CV²
Quick answer
This calculator solves E = ½CV² for Energy. With Capacitance 100 µF, Voltage 12 V, the result is 7.2 mJ. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The energy stored in a capacitor is proportional to the capacitance and the square of the voltage across it. The quadratic voltage relationship means that doubling the voltage quadruples the stored energy, which is why high-voltage capacitors can be extremely dangerous even at small capacitance values. This energy is stored in the electric field between the capacitor plates. Supercapacitors exploit this principle with very high capacitance values (farads rather than microfarads) to serve as short-term energy storage devices that bridge the gap between batteries and conventional capacitors.
Variables
- E — Energy in joules (J)
- C — Capacitance in farads (F)
- V — Voltage across the capacitor (V)
Practical Notes
A fully charged camera flash capacitor (typically 300µF at 300V) stores about 13.5 joules, enough to be lethal. Always discharge capacitors safely before working on circuits. The energy can also be expressed as E = Q²/(2C) or E = QV/2.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| E | Energy | mJ | µJ, mJ, J, kJ, Wh, kWh |
| C | Capacitance | µF | pF, nF, µF, mF, F |
| V | Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Capacitance 100 µF, Voltage 12 V
- 2. The relation: E = ½CV²
- 3. Substitute: C = 100 µF, V = 12 V
- 4. Result: Energy = 7.2 mJ
Worked examples
Minimum range
Given: Capacitance 100 nF, Voltage 0.33 V
Result: Energy = 0.005445 µJ
Low range
Given: Capacitance 1 µF, Voltage 3.3 V
Result: Energy = 5.445 µJ
Typical
Given: Capacitance 100 µF, Voltage 12 V
Result: Energy = 7.2 mJ
High range
Given: Capacitance 1 mF, Voltage 0.23 kV
Result: Energy = 26.45 J
Maximum range
Given: Capacitance 10 mF, Voltage 2.3 kV
Result: Energy = 7.347 Wh
Solving for each variable
Solve for Energy
Capacitance 100 nF, Voltage 0.33 V → 0.005445 µJ
Solve for Capacitance
Energy 100 µJ, Voltage 0.33 V → 1.837 mF
Solve for Voltage
Energy 100 µJ, Capacitance 100 nF → 44.72 V
How Energy changes with Capacitance
| Capacitance (input) | Energy (result) |
|---|---|
| 10 µF | 0.72 mJ |
| 25 µF | 1.8 mJ |
| 50 µF | 3.6 mJ |
| 75 µF | 5.4 mJ |
| 100 µF | 7.2 mJ |
| 150 µF | 10.8 mJ |
| 0.2 mF | 14.4 mJ |
| 0.4 mF | 28.8 mJ |
| 0.7 mF | 50.4 mJ |
| 1 mF | 72 mJ |
The same result in other units
| Unit | Value |
|---|---|
| µJ | 7200 |
| mJ | 7.2 |
| J | 0.0072 |
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<p><a href="https://vbatpower.com/formulas/capacitor-energy/">Capacitor Energy</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Capacitor Energy?
Use E = ½CV². With Capacitance 100 µF, Voltage 12 V, Energy works out to 7.2 mJ.
What is the formula for Capacitor Energy?
The formula is E = ½CV². The energy stored in a capacitor is proportional to the capacitance and the square of the voltage across it.
How do you find Capacitance when you know the other values?
Rearrange for Capacitance: with Energy 100 µJ, Voltage 0.33 V, Capacitance is 1.837 mF.
How do you find Voltage when you know the other values?
Rearrange for Voltage: with Energy 100 µJ, Capacitance 100 nF, Voltage is 44.72 V.
What units does Capacitor Energy use?
Energy is shown in µJ, mJ, J. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Capacitors formulas →Need more features?
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