Capacitor energy: the complete guide
The energy stored in a capacitor formula
The energy stored in a capacitor formula is E = 1/2 C V^2: capacitance C in farads, voltage V in volts, energy E in joules. Voltage is squared, so doubling the voltage quadruples the stored energy while doubling the capacitance only doubles it. To calculate capacitor energy in watt-hours, divide joules by 3600.
Worked examples
A 100 µF capacitor at 12 V: E = 0.5 × 0.0001 × 144 = 0.0072 J (7.2 mJ); charge Q = CV = 1.2 mC. This is the classic “how many joules in a capacitor” scale of everyday electronics.
A 470 µF capacitor at 25 V: E = 0.5 × 0.00047 × 625 = 0.147 J (147 mJ). This is the energy the capacitor dumps into the circuit when mains power drops — the basis of hold-up time in power supplies.
A 1 F supercapacitor at 5.5 V: E = 0.5 × 1 × 30.25 = 15.1 J (0.0042 Wh). Even a farad-scale supercapacitor energy store is tiny next to batteries — try the battery comparison above.
Capacitor vs battery: energy in context
| Energy store | Typical energy | Capacitor equivalent (at 25 V) |
|---|---|---|
| AA alkaline battery | 2.7 Wh ≈ 9,700 J | 31 F — impossible as one part |
| 18650 Li-ion cell | 12.6 Wh ≈ 45,400 J | 145 F |
| Smartphone battery | 15 Wh ≈ 54,000 J | 173 F |
| Car battery 12 V 50 Ah | 600 Wh ≈ 2.16 MJ | 6,912 F |
| Camera-flash capacitor | ~80 µF at 330 V ≈ 4.4 J | — (reference point) |
The table shows why capacitors are power devices, not energy devices: a single AA battery holds the energy of a 31-farad capacitor bank. Capacitors win on power — releasing their small store in milliseconds for flashes, defibrillators and rail smoothing.
Methodology & assumptions
- All three modes use exact ideal-capacitor math:
E = 1/2 C V^2,Q = CV,C = 2E/V^2,V = sqrt(2E/C), computed in full floating-point precision. - Unit conversions: 1 mF = 10−3 F, 1 µF = 10−6 F, 1 nF = 10−9 F, 1 pF = 10−12 F; 1 Wh = 3600 J exactly.
- The “suggested rating” applies a 2× derating rule of thumb to the operating voltage.
- Real capacitors add tolerance, ESR, leakage and DC-bias capacitance loss (especially X7R/Y5V MLCCs) — results are theoretical; add design margin for critical circuits.