Capacitor Energy Calculator

A charged capacitor is a spring made of electric field. Enter the capacitance and the voltage across it, and this calculator returns the energy it stores and the charge on its plates — the two numbers behind camera flashes, defibrillators and every “do not open, charged capacitor” warning ever printed.

Where the Half Comes From

The energy formula E = ½ C V² carries a half that puzzles every newcomer, and the resolution is the charging story: the first charge arrives against no opposing voltage (nearly free), the last arrives against the full V (full price) — so the average price per unit charge is V/2, and the total is Q × V/2 = ½CV². The other half of the source's expenditure became heat in the charging resistance, independently of that resistance's size — one of electronics' small exact theorems, and the reason capacitor charging from a fixed voltage is capped at 50% efficiency no matter how good the components get (inductive charging dodges it; resistive charging cannot). The charge itself obeys the simpler covenant Q = CV, and the two formulas together are the capacitor's complete identity card: how much it holds, and what the holding is worth in joules.

Worked Example: A Humble Hundred Microfarads

The defaults price a component from any parts drawer: 100 µF at 25 V. Energy = ½ × 100×10⁻⁶ × 625 = 0.03125 J (31.25 mJ), holding Q = 100×10⁻⁶ × 25 = 2.50 mC of separated charge. Thirty-one millijoules sounds like nothing — it would lift a paperclip by three centimetres — until the delivery time enters: a capacitor can return its store in microseconds, and 31 mJ in 10 µs is a 3.1 kW pulse, which is why small capacitors bite, weld relay contacts and fire strobes. Scale the example to a camera flash (300 µF at 330 V) and the same formula returns about 16 J delivered in a millisecond — the arithmetic of every photograph ever taken by flash, computed by this page's single line.

Capacitors Versus Batteries: The Power–Energy Trade

Set this page beside a battery's ledger and the two storage philosophies divide the world: batteries store far more energy per kilogram (chemical bonds beat electric fields by orders of magnitude) but release it at chemistry's pace, while capacitors store little and release it at the speed of a closing switch — power density versus energy density, the eternal trade. Supercapacitors narrow the gap from the capacitor side (farads by the thousand, joules by the kilojoule), which is why they buffer regenerative braking and memory backup: applications that need a sprinter, not a marathoner. The calculator serves both citizens — enter farads-scale values in microfarads (a 10 F supercap is 10,000,000 µF) and the same ½CV² prices a bus's brake-energy buffer as happily as a strobe's.

The Defibrillator: This Formula at the Bedside

A defibrillator is this page with a paddles attachment: a capacitor bank charged to a few thousand volts stores a few hundred joules (a typical 200 J shock is, in calculator terms, a modest capacitance at a serious voltage — the V² doing the heavy lifting), then dumps it through the chest in milliseconds along a shaped waveform. The dose is prescribed in joules because the formula prices the store exactly, and the device's charge button is a nurse entering numbers into ½CV² with an anxious finger. Camera flash, ignition coil, backup RAM and the defibrillator share one component and one equation; the difference is only which row of the parts catalogue, and how much the answer matters.

The Railgun Temptation

Every few years a headline rediscovers that capacitor banks can release their store almost instantaneously, and a pulsed-power machine — railgun, coilgun, high-field magnet — is born in a laboratory with a wall of capacitors priced by this page's formula, cell by cell: the bank's total joules are the sum auditors check, and its power is those joules divided by a discharge time the switches dare. The formula's square law steers the whole architecture toward the highest voltage insulation permits, because energy density bought with volts costs no extra cans. The calculator's modest 31 mJ example and a megajoule bank differ only in the number of zeros the same line of algebra is asked to carry — which is what a real formula means by scale.

The Leyden Jar: Where the Formula Was Born

The capacitor's first draft, the Leyden jar of 1745, stored its charge in glass and foil and delivered shocks that entertained salons and terrified demonstrators in roughly equal measure — Franklin coined "battery" for a rack of them and flew his kite into the same physics. Those jars held, by this page's arithmetic with their picofarad-scale capacitances and kilovolt charges, on the order of a joule — enough to kill a turkey (Franklin did) and to make a roomful of monks leap in unison (an abbot did, for science). The formula has not changed since the jars; only the dielectrics, the voltages and the respect have improved. Every joule the calculator prices today descends from that first, sparking bookkeeping.

Related Tools

More from the Physics Calculators hub: the Capacitive Reactance Calculator — this component in alternating current — and the Kinetic Energy Calculator, whose ½mv² is this page's formula wearing mechanics' clothes.

Frequently Asked Questions

Why is the energy proportional to V squared?

Because voltage does double duty: raising V both stores more charge (Q = CV, linear in V) and makes each unit of that charge worth more energy (each coulomb was lifted through the voltage it now faces). Two linear effects multiply into the square — the same reason kinetic energy squares the speed (more momentum, carried faster) and this hub's spring energy squares the stretch. Squared terms are nature's way of charging rent twice on the same improvement, and the capacitor's version is why high-voltage design is energy-dense long before it is large: the worked example's modest 31 mJ becomes 3.1 J at 250 V — a hundredfold for a tenfold voltage — with the capacitance untouched.

How dangerous is a charged capacitor?

By this page's number, delivered fast: the hazard is energy × delivery rate through a body, and the rules of thumb are that joules above ~10 J demand real respect, charged high-voltage capacitors (microwave ovens, photo flashes, old CRTs) can hold lethal stores for days after unplugging, and the safe ritual — discharge through a resistor, verify with a meter — exists because the store is silent and invisible. The calculator quantifies the first half of safety (how much energy); the second half (how fast your body would receive it) is why technicians treat even "small" high-voltage electrolytics as loaded. Compute the joules; then behave as if they are all addressed to you.

What is the energy density of a supercapacitor?

Commercial supercapacitors reach roughly 5–10 Wh per kilogram — against lithium batteries' 150–250 — while delivering power at ten times the battery's rate and surviving a million cycles, which is the trade stated as a product category. In this page's units: a 3,000 F, 2.7 V cell stores ½ × 3,000 × 7.29 ≈ 10.9 kJ ≈ 3 Wh, in a can the size of a drinks bottle. The formula scales without complaint from picofarads to kilofarads; only the packaging changes, and the calculator's microfarad input wants the supercap's value multiplied by a million — arithmetic the reader is now equipped to do without flinching.

Where does the stored energy physically live?

In the electric field between the plates — the dielectric's strained polarisation is the store, which is why the energy density can be written as ½εE² (permittivity times the field squared, per unit volume): double the field, quadruple the density, until the dielectric breaks down and the capacitor fails as a tiny lightning bolt. Breakdown field strength is therefore the real ceiling on capacitor energy, and the industry's history is dielectric materials science — better films, ceramics and electrolytes holding stronger fields — chased by exactly the incentive the square law provides. The calculator counts the joules; the field picture explains both their address and their limit.

How fast can a capacitor discharge?

Into a resistance R, the discharge is exponential with time constant RC — the hub's RC world — reaching 63% spent in one time constant and effectively empty in five; into a near-short (a strobe tube, a spark), the limit becomes the circuit's stray inductance and the capacitor's own equivalent series resistance, and microseconds or less are routine. That delivery speed is the entire point of the flash, the defibrillator and the pulsed magnet: the energy is modest, the rate is the superpower, and the calculator's joules divided by your discharge time is the peak power — a third figure, hiding in the two it prints, that explains the component's whole career.

Do capacitors in series store more or less?

Less than either alone, by the series rule (reciprocals add): two 100 µF in series make 50 µF — but the pair tolerates twice the voltage, and since energy squares the voltage, the series bank at double voltage stores twice the single capacitor's energy at its own rating. Banks are designed exactly so: series strings for voltage headroom, parallel strings for capacitance, the total energy always the sum of the cells' ½CV² at their working voltages. The calculator prices the unit cell; bank design is that price, multiplied by honest bookkeeping — and derating, because electrolytics age by losing capacitance, and the store shrinks with them.