Capacitance & Voltage to Charge (Q = C × V)

In 2026, a medical-device firmware engineer hand-tuning the energy delivery on a biphasic AED needs to know — fast and without rounding artefacts — exactly how much charge is sitting on a 40 µF storage capacitor at 5 kV before the discharge SCR fires. The Charge Balance Scale on this page exists because that exact intuition (Q grows linearly with V, energy grows quadratically) is the difference between a 200 J safe shock and a 360 J refractory rescue per IEC 60601-2-4 §201.12.4. This page is also pitched at hobbyists chasing the same equation through their first 470 µF PSU cap.

The earliest quantitative treatment of electric charge belongs to Charles-Augustin de Coulomb, a French military engineer who in 1785 published a sequence of seven memoirs describing his torsion-balance experiments. By measuring the twist of a fine silver wire suspending a charged pith-ball, Coulomb established that the force between two point charges falls off as 1/r² and rises linearly with the product of the charges — the law that bears his name. The SI unit of electric charge was named for him at the 11th CGPM in 1960 in formal recognition.

Michael Faraday, working at the Royal Institution in London through the 1830s, formalized the relationship between charge and the device we now call a capacitor. Faraday introduced the term "capacity" in 1834 and described what he then called "specific inductive capacity" — the property of a dielectric to store charge per unit voltage. His electrochemical work (Faraday's laws of electrolysis, 1834) also gave the world the relationship between charge transferred and substance deposited, leading to the "faraday" (F = 96,485 C/mol) as a separate unit honouring him in physical chemistry.

The mathematical edifice that ties charge, capacitance, current and voltage together into a coherent theory belongs to James Clerk Maxwell. His 1865 paper "A Dynamical Theory of the Electromagnetic Field" and the 1873 Treatise on Electricity and Magnetism placed Q = ∫ I dt = C × V on the same footing as the other field equations. Maxwell's displacement-current term — the time derivative of D-field through a capacitor — explained how AC current "flows" through a dielectric without any net electron motion.

On the standards side, IEC 60384 (Fixed Capacitors for Use in Electronic Equipment) and its many sub-parts have governed the industrial production of capacitors since 1962. The voltage-derating tables, tolerance codes (J, K, M), and life-test cycles in this calculator's reference panel all trace back to this IEC standard. For high-voltage pulse caps the relevant standard is IEC 61071, and for supercaps IEC 62391 — both define how Q = C × V applies in their respective non-ideal regimes (DC-bias derating, ESR-limited charge transfer, leakage current).

The SI redefinition that took effect on World Metrology Day, 20 May 2019, recast the coulomb from a derived quantity (1 A × 1 s) into an exact fundamental count: 1 C ≡ 6.241509074 × 10¹⁸ elementary charges, since the elementary charge e is now defined as exactly 1.602176634 × 10⁻¹⁹ C. The ampere and the coulomb are thus literally quantized — every reading on the balance scale corresponds to an exact integer of electrons, even if that integer has 18 digits.

The 2020s saw the supercapacitor (EDLC) cross the 3000 F per unit threshold — essentially making the farad a practical unit in handheld gear for the first time since Faraday named it. The defibrillator preset and supercap preset on the balance scale span seven decades of capacitance (10⁻⁶ to 10⁻²) but only one decade of voltage (3 V to 5 kV) — illustrating why the charge balance must be drawn on a log scale for both pans to make sense visually. Engineers building EV regen-braking buffers and grid VAR-compensation banks live in this exact corner of the Q = CV equation every day.