Capacitor energy:
½ × C × V² and why voltage matters most

What a capacitor actually stores

A capacitor holds energy in the electric field between two plates. Charging it means moving charge from one plate to the other against the growing voltage, and the work done in doing that is what you recover on discharge. Unlike a battery, a capacitor stores energy electrostatically and can release it very quickly.

Two quantities describe it. Capacitance C, in farads, says how much charge it holds per volt. Voltage V says how hard that charge is pushed. The energy depends on both, but not equally: voltage appears squared.

Capacitors come in many types: electrolytic parts for bulk energy storage, film types for pulses and filtering, ceramic types for high frequencies. They differ in how much charge they hold, how fast they can discharge and how they age, though the energy formula treats them all the same.

Another way to see the voltage dependence is through the field. Doubling the voltage doubles the field between the plates and doubles the charge, and the work to build them up scales with both.

The energy formula and its relatives

The half arises because the voltage builds up gradually as charge is added. The average voltage during charging is half the final voltage, so the energy is charge multiplied by that average.

Convert units before you calculate. 1,000 µF is 1,000 × 10⁻⁶ F = 0.001 F. A frequent source of error is leaving microfarads in the formula and getting an answer a million times too large.

Worked example: 1,000 µF at 12 V

To get a feel for it, 0.072 J is roughly the energy needed to lift a 100 g object by about 7 cm. Small, but released over a millisecond it corresponds to 72 W of power, which is why capacitors can drive brief high-current pulses.

Now vary the inputs. At 24 V the same capacitor stores 0.288 J, four times as much. At 6 V it stores 0.018 J, one quarter. Voltage deserves attention first when you want more energy.

Cross-check with the alternate form: E = ½ × Q × V = 0.5 × 0.012 × 12 = 0.072 J. The identical result confirms that charge and voltage have been handled consistently. Getting two forms to agree is a quick way to catch a unit slip.

Voltage against capacitance

Doubling capacitance only doubles the energy. That is why the voltage rating on a capacitor is so important, and why high-voltage capacitors store far more energy than a bulky low-voltage one of the same farad value.

Series and parallel combinations also change the totals. Two identical capacitors in parallel double the capacitance and so double the energy at the same voltage. In series the capacitance halves but the allowed voltage doubles, so at full rating the pair holds twice the energy of one part, as you would expect from having two parts.

Releasing the energy safely

Energy stays in the capacitor after power is removed. A large or high-voltage capacitor can deliver a painful or dangerous shock and a sudden discharge can weld contacts or damage components. Treat any capacitor in a supply, flash circuit or motor drive as live until it has been discharged through a suitable resistor.

1. 1Switch off and isolate the equipment.
2. 2Discharge through a resistor sized for the voltage and energy, not by shorting with a screwdriver.
3. 3Measure the remaining voltage with a meter before touching.
4. 4Keep in mind that some capacitors rebuild a small voltage after discharge.

The time to discharge through a resistor depends on the product R × C, called the time constant. After about five time constants the capacitor is essentially empty.

A worked time constant: 1,000 µF discharging through 1 kΩ has R × C = 1 s. After five seconds the voltage has fallen to under 1% of its starting value. A 12 V capacitor would be down near 0.08 V, which is why bleeder resistors are used across large supply capacitors.

Where the figure is useful, and where it is not

• Camera flashes and defibrillator-style pulses rely on charging a capacitor slowly and releasing it quickly.
• Power supplies use capacitors to smooth ripple; the energy figure helps estimate how long they carry the load during a dip.
• Hold-up designs compare E with the energy a device needs for a short shutdown.
• Supercapacitors store far more energy but at low voltage, and the same formula applies with careful unit conversion.

Usable energy is lower than the total because a circuit stops working below a minimum voltage. If a device needs at least 9 V, the usable energy of a 12 V capacitor is ½ × C × (12² − 9²) rather than the full ½CV². An electrical energy tool is a convenient companion when you convert joules to watt-hours or kilowatt-hours, though the capacitor formula itself is the one above.

Remember also that leakage, equivalent series resistance and ageing reduce the real performance of electrolytic types. A part that has dried out may hold noticeably less charge than its label, so the formula gives the best case for a healthy component.