Farad (F)

Definition, derivation and practical use in the International System of Units

Capacitance is a measure of how much electric charge a component can store per volt of applied voltage. The quantity is central to electronics, power engineering and measurement, and its SI unit, the farad (F), is one of the derived SI units. The unit is named after the English physicist and chemist Michael Faraday (1791-1867).

The farad is also one of the units whose size is most often misjudged: a whole farad is, in practice, a very large capacitance. To understand the unit it is necessary, as for the meter and the kilogram, to distinguish between definition, realization and practical use.

The definition of the farad in the SI system

Within the International System of Units (SI), the farad is defined as:

the capacitance of a capacitor that holds an electric charge of 1 coulomb when the voltage between its plates is 1 volt.

In formula form: 1 F = 1 C/V = 1 A·s/V. Expressed in SI base units, the farad is s⁴·A²·m⁻²·kg⁻¹. The definition therefore rests on:

the ampere, the base unit of electric current, defined through the elementary charge e,
the second, defined through the hyperfine transition frequency of the caesium-133 atom,
the volt, the derived unit of electric potential difference.

Fact box: the history of the farad

Year	Event
1837	Michael Faraday describes dielectrics and how an insulating material affects the charge stored in a capacitor.
1861	Latimer Clark and Charles Bright propose the name farad for the unit of capacitance.
1881	The International Electrical Congress in Paris adopts the farad as a practical unit.
1893	The so-called international electrical units are fixed in Chicago.
1948	Transition to absolute electrical units, defined from the mechanical units.
1960	The farad becomes a derived unit of the newly established SI.
2019	The SI revision fixes e and h; the farad can be realized directly from constants of nature.

What is a farad in practice?

A 1 F capacitor charged to 1 V stores a charge of 1 C, which corresponds to roughly 6.24 × 10¹⁸ elementary charges. In electronics that is a great deal. Common components sit instead at picofarads (pF), nanofarads (nF) and microfarads (µF): a decoupling capacitor on a circuit board is often 100 nF, an electrolytic capacitor in a power supply a few hundred µF.

So-called supercapacitors reach hundreds or thousands of farads, but only at low voltages of a few volts. The stored energy is given by W = ½·C·U², so both the capacitance and the voltage decide how much energy a capacitor can hold.

Definition, realization and use

The definition states what a farad is in principle and is entirely abstract: one coulomb per volt.
The realization refers to the experiments by which national metrology institutes produce a known capacitance traceable to the SI.
The use refers to the measurement of capacitance in electronics development, production and calibration.

The distinction matters because the farad is rarely measured directly from its definition. It is derived instead through other electrical quantities with very low measurement uncertainty.

How the farad is realized

The classical primary method is the calculable capacitor, often called the Thompson-Lampard capacitor after the theorem published in 1956. Its capacitance follows from a single length measurement: the capacitance per meter of electrode is a constant of about 2 pF/m, given by constants of nature and the geometry. The farad could thereby be traced to the meter.

Since 1990, and definitively after the SI revision of 2019, capacitance is instead realized from the quantum Hall resistance R_K = h/e², which now has an exact value. In a so-called quadrature bridge, the impedance 1/(ω·C) of a capacitor at a known angular frequency ω is compared with a resistance traceable to the ohm. The farad is thus traced to the Planck constant, the elementary charge and the second.

Practical measurement and sources of error

In laboratories and production, capacitance is measured with LCR meters, which drive the component with an alternating voltage of known frequency and compute the capacitance from the current and its phase. The result depends on several factors:

The temperature dependence of the dielectric: ceramic capacitors can change their capacitance by tens of percent across their temperature range.
Frequency dependence: losses in the dielectric and parasitic inductance make the measured capacitance vary with the measurement frequency.
Stray impedances: measurement leads and nearby conductors contribute capacitance of their own, which at small values calls for a shielded three-terminal measurement.

Traceable calibration therefore relies on reference capacitors with stable dielectrics, such as fused silica or air, held at a controlled temperature.

The farad and other derived units

The farad is tied to several of the electrical units of the SI:

Unit	Quantity	Relation to the farad
coulomb (C)	Electric charge	Q = C · U
volt (V)	Electric potential difference	U = Q / C
ohm (Ω)	Electrical resistance	Time constant τ = R · C
joule (J)	Energy	W = ½ · C · U²
henry (H)	Inductance	Resonant frequency f = 1 / (2π√(LC))

Multiples and common conversions

Because one farad is so large, the unit is almost always used with an SI prefix: 1 pF = 10⁻¹² F, 1 nF = 10⁻⁹ F, 1 µF = 10⁻⁶ F and 1 mF = 10⁻³ F. Conversion between the prefixes goes by a factor of 1,000 per step, so 1 µF = 1,000 nF = 1,000,000 pF.

The energy a capacitor stores can be converted to other energy units with the energy converter, and the power it can deliver over a given time with the power converter. Conversions between units of capacitance are handled by the capacitance converter.

Summary

The farad is the SI unit of capacitance and is defined as one coulomb per volt. The unit is derived from the ampere, the second and the volt, and it is realized today with very low uncertainty from the quantum Hall resistance and a known frequency.

In practice a whole farad is an unusually large capacitance, which is why the unit almost always appears with a prefix. The interplay between a strict definition, a traceable realization and a carefully performed measurement makes the farad a reliable unit in both electronics and metrology.