Joules to Volts on a Capacitor

In 2026, a biomedical engineer designing the next-generation Zoll AED has to convert a target 200-joule biphasic discharge into a terminal voltage on a 32 µF polypropylene capacitor without leaving the bench. The math — V = √(2E/C) = 3536 V — is trivial once you know it, but the dozens of cap families with different ESR, leakage and self-resonance make picking the right starting point harder than the math. This calculator collapses all of that into a single page with named presets and a visual that makes the inverse-square relationship between energy and voltage obvious.

The capacitor was discovered accidentally in 1745 by Ewald Georg von Kleist in Pomerania and independently by Pieter van Musschenbroek at the University of Leyden in 1746. Both were trying to "store" the static electricity produced by friction machines. Their Leyden jars — glass jars half-filled with water, lined inside and out with metal foil — stored on the order of 1 nF at a few kV, enough to deliver a sharp shock to a chain of 200 monks holding hands as Jean-Antoine Nollet demonstrated to King Louis XV in 1746. The energy was perhaps 0.05 J — a thousandth of what a modern AED stores.

Michael Faraday’s work on electromagnetic induction in 1831 led to the unit that bears his name: 1 farad = 1 coulomb of charge per 1 volt of potential. Faraday’s laboratory capacitors stored about 10⁻⁸ F. The mismatch between Faraday’s named unit and practical components was so severe that capacitor datasheets used µF (microfarads) as the default unit for the next 150 years. That changed in the 1990s when Brian Conway and Maxwell Technologies commercialised the electrical double-layer capacitor (EDLC) — commonly called a supercapacitor — with capacitance literally on the order of single farads. Today’s Maxwell BCAP3000 stores 3000 F in a 60 mm can.

The defibrillator capacitor is the most safety-critical application of energy-stored calculation. Paul Zoll demonstrated external transthoracic defibrillation in 1956 at Beth Israel Hospital, Boston, using a 240-joule monophasic pulse on a 16 µF capacitor at 5500 V. By 1962 Bernard Lown had refined the technique to the synchronised cardioversion still standard today. Modern AEDs use biphasic pulses on 32-80 µF polypropylene film caps storing 150–360 J; the H-bridge between the capacitor and the electrodes reshapes the discharge into a chopped 4–12 ms biphasic waveform that defibrillates with less peak voltage and less myocardial damage than the original monophasic technique.

The energy formula itself was nailed down by Lord Kelvin and James Clerk Maxwell in the 1860s as part of the broader formalisation of electromagnetic energy density. Maxwell’s 1873 Treatise on Electricity and Magnetism first stated U = ½CV² in modern form. Combined with James Prescott Joule’s 1841 heating-law work — which established that electrical and mechanical energy were interconvertible units, the joule itself — the framework for converting between capacitor energy and voltage was complete by 1875. Every formula on this page is older than the lightbulb.

International standards now govern safe use of stored electrical energy. IEC 60664 sets the 50 V DC touch-safe threshold for low-voltage equipment, while IEC 61010 defines a 350 mJ stored-energy limit on accessible terminals of laboratory measurement equipment. NFPA 70E in the United States and IEC 60364 internationally require permanently-installed bleed resistors across capacitor banks above the threshold so that the bank fully discharges within 1 minute of de-energisation. The widget's safety callout above 50 V mirrors these limits.

By 2026, the dominant emerging use of capacitor energy-to-voltage conversion is grid ride-through and KERS (kinetic energy recovery) in transit. Bombardier MITRAC trams, Mazda i-ELOOP cars and CATL grid-scale modules all rely on EDLC arrays sized in joules of swing energy against a target DC bus voltage. The conversion V = √(2E/C) decides whether a single 3000 F Maxwell BCAP3000 at 2.7 V (10,935 J) or a series stack of 18 modules at 48.6 V (10,935 J still, but spread across 18 cans) is the right choice. The page's log-scale slider deliberately spans 1 µF to 10 kF so both ends of the design space are reachable.