Article — Capacitor Energy Calculator
Capacitor energy calculator
A capacitor stores energy equal to E = ½CV², in joules, when C is in farads and V in volts. A 100 µF capacitor at 12 V holds 7.2 millijoules. A 1 farad supercapacitor at 2.7 V holds 3.65 joules — close to a thousand times more for the same voltage class.
The expression looks simple, but the V² term has consequences. Double the voltage and you quadruple the energy. That is why a small ceramic cap charged to a few hundred volts can deliver a sharper shock than a much larger electrolytic at 12 V. It is also why supercapacitors are stuck at low voltages — the dielectric in a double-layer cell breaks down above about 2.7 V, so they trade voltage for huge capacitance.
What is capacitor energy?
Capacitor energy is the electrical potential energy stored in the electric field between two conductors separated by a dielectric. When a capacitor is connected to a source, charge flows onto the plates until the voltage across the cap matches the source. That charging work — pushing charge against a rising field — becomes stored energy you can later draw back as current.
Unlike a battery, the capacitor stores no chemical energy. There is no electrochemical reaction, no ion shuttle, no degradation per cycle. That is why a healthy ceramic capacitor can be charged and discharged for billions of cycles without measurable wear, while a lithium-ion cell starts losing capacity after a few hundred.
The largest capacitor banks in the world live at fusion research facilities. The Z Machine at Sandia National Laboratories uses 36 capacitor banks holding 22 megajoules total, discharged into a target in 100 nanoseconds — peak power around 80 trillion watts, roughly 80× the entire planet's electrical generation for that brief instant.
The capacitor energy formula
The standard form is E = ½CV². Three equivalent forms drop out depending on what you know:
E = ½CV² given C and VE = Q²/(2C) given Q and CE = ½QV given Q and VQ = CV charge from C, VIf your numbers come in non-SI units, convert before plugging in. 1 µF = 10⁻⁶ F. 1 nF = 10⁻⁹ F. 1 pF = 10⁻¹² F. The calculator above handles the conversion automatically — type in the natural unit and pick from the dropdown.
Why ½CV² and not CV²?
The half comes from integration, not from efficiency. As charge accumulates on the plates, the voltage rises linearly from zero up to the final V. Each tiny packet of charge dq is pushed against the instantaneous voltage v, not the final V. Total work is W = ∫v dq from 0 to Q, which evaluates to ½QV. Substituting Q = CV gives ½CV².
A common misconception: connect a charged cap to an identical empty one and you "lose half the energy." That is true — half goes to heat in the wires and EM radiation. The ½ in the formula is not what causes that loss; the loss happens because charge equilibration is dissipative regardless of the formula's prefactor.
Capacitor energy by type
Different capacitor families occupy radically different points on the C-vs-V chart, which means radically different energy regimes.
- Ceramic (MLCC): 1 pF to 100 µF, 6.3 V to 3 kV. A typical 100 nF decoupler at 5 V stores 1.25 µJ.
- Aluminum electrolytic: 1 µF to 10 mF, 6.3 V to 450 V. A 1000 µF/35 V smoothing cap stores 0.6 joules.
- Film (polypropylene): 1 nF to 100 µF, 50 V to 2 kV. Common in motor-run circuits and audio crossovers.
- Tantalum: 0.1 µF to 1 mF, 4 V to 50 V. High stability, low ESR, but unforgiving of overvoltage.
- Supercapacitor (EDLC): 0.1 F to 3000 F, 2.5 V to 2.7 V per cell. A 100 F/2.7 V cell stores 364.5 joules.
- Photo flash: 100–500 µF at 300–360 V. A 470 µF/330 V flash cap stores 25.6 joules — enough to ignite paper if shorted.
An electrolytic cap above about 30 V can deliver a painful or dangerous shock long after the device is unplugged. Camera flash capacitors, microwave HV caps, and any motor-start cap can hold lethal charge for hours. Always bleed through a 1 kΩ to 10 kΩ resistor before touching the terminals.
Capacitor energy vs battery energy
Capacitors and batteries are not interchangeable, and the reason is energy density. A typical AA alkaline cell stores about 9.4 kJ in 23 grams — roughly 400 J per gram. A 100 F supercapacitor at 2.7 V weighs around 20 grams and stores 365 J total, or about 18 J/g. The supercap stores twenty times less energy per gram, but it can dump that energy in milliseconds instead of hours.
That is why hybrid buses use both — a battery for energy and a supercap bank for the regenerative braking spike. The cap absorbs the kilowatt-second pulse, then trickles it back to the battery.
Common capacitor energy mistakes
The forehead-slap errors usually come from units rather than physics.
Always convert capacitance to farads and voltage to volts before applying E = ½CV². A 100 µF cap at 50 V is not 100 × 50² / 2 = 125,000 joules — it is 0.125 joules. The factor of 10⁻⁶ catches everyone the first time.
- Forgetting micro: 100 µF means 100 × 10⁻⁶ F, not 100 F. Order-of-magnitude error.
- Working voltage vs rated voltage: Energy uses the actual voltage across the cap, not the cap's rating.
- Ignoring ESR: Equivalent series resistance dissipates energy as heat during fast charge/discharge.
- Series stack assumption: Two 1000 µF caps in series make 500 µF, not 2000 µF.
- Polarity: Reversing an electrolytic destroys it. The formula does not warn you.
Real-world capacitor energy uses
Capacitor energy storage powers nearly everything that needs a fast burst. Defibrillators dump 200–360 joules from a 100–200 µF cap charged to 2 kV across a patient's chest in 10 milliseconds. Pulsed lasers fire from cap banks because no battery can deliver kilojoules in microseconds. Coilgun and railgun prototypes use multi-megajoule banks. Even your camera flash and the kick on a car starter rely on the same equation.
On the small end, every digital chip you own depends on tiny decoupling capacitors that store nanojoules — just enough to ride out the current spikes when the chip switches. Without them, the supply rail collapses and the chip resets. The math is identical to the railgun's: E = ½CV². Only the exponents change.