Capacitor Stored Energy Calculator

Energy Stored in a Capacitor

A capacitor charged to a voltage V holds energy in its electric field, and that energy works out to E = ½ C V², with E in joules, C in farads and V in volts. Where does the formula come from? Integrate the work needed to push charge against a voltage that keeps rising as the cap fills: E = ∫₀⁹ v dq = ∫₀⁹ (q/C) dq = Q²/(2C). A 1 mF cap at 12 V holds 0.072 J. A 1 F supercapacitor at 2.7 V holds 3.65 J, which is enough to keep an LED lit for minutes.

Watch how voltage dominates here. Double V and you quadruple E; double C and you only double it. That quadratic edge is why pulsed-power gear like camera flashes and defibrillators leans on modest capacitances charged to high voltages (300-2000 V) rather than enormous low-voltage banks. Boylestad and Sedra/Smith both derive E = ½CV² in their opening chapters, and IEC 60384 sets the tolerance, ripple-current and lifetime ratings that decide how much of this energy you can cycle safely.

Applications

Stored capacitor energy shows up all over the place: xenon flashes in cameras, medical defibrillators (usually 200-360 J reaching the patient), railgun and pulsed-laser drivers, automotive supercapacitor banks for regenerative braking, hold-up capacitors in UPS units, and ride-through capacitance on the DC link buses of inverters. EVs and hybrids keep pairing batteries with supercapacitors (IEC 62576), and the reason is their high power density and the fact that they survive millions of cycles.

FAQ

Why is the energy ½CV² and not CV²? Because the voltage climbs from 0 to V while the cap charges, so the average voltage along the way is V/2 and the total work is Q·(V/2) = ½CV². The missing half turns into heat in the charging resistor, and that holds no matter what its value is.

How can I increase the stored energy? Raise the voltage for a quadratic gain, or the capacitance for a linear one. Going up in voltage is usually the better lever, though you're capped by the component's dielectric breakdown rating (IEC 60384).

Is a charged capacitor dangerous? It can be. Big electrolytic capacitors in power supplies and flash circuits hold enough energy to deliver a lethal shock hours after the device has been unplugged. Discharge them through a bleeder resistor and check with a voltmeter before you touch anything.