Volt (V)
Definition, derivation and practical use in the International System of Units
Electric potential difference, or voltage, is the quantity that drives current through a circuit and states how much energy each unit of charge carries. The volt, symbol V, is the SI unit of voltage and one of the most widely used derived SI units. It appears everywhere from batteries and wall sockets to power lines and nerve signals, yet few people know how it is defined and how it is realized in a measurement laboratory.
As with the base units, it is necessary to distinguish three levels: definition, realization and practical use. The volt is a derived unit, which means its definition is built on other SI units and, ultimately, on fixed constants of nature.
The definition of the volt in the SI system
The volt is defined within the International System of Units (SI) as:
the electric potential difference between two points of a conductor which, when a constant current of 1 ampere flows between them, dissipates a power of 1 watt.
Expressed in other SI units, 1 V = 1 W/A = 1 J/C. In base units this becomes 1 V = 1 kg·m²·s⁻³·A⁻¹. The definition therefore rests on:
- the ampere, the base unit of electric current, defined through the elementary charge e,
- the watt, the unit of power, which in turn rests on the kilogram, the meter and the second.
Since the SI revision of 2019, both the elementary charge e and the Planck constant h have exact numerical values. This allows the volt to be realized directly from constants of nature, without a detour through conventional reference values.
Fact box: History of the volt
| Year | Event |
| 1800 | Alessandro Volta (1745-1827) presents the voltaic pile, the first chemical battery. |
| 1881 | The International Electrical Congress in Paris adopts the volt as the practical unit of potential difference. |
| 1893 | The “international volt” is fixed in Chicago through the Clark cell (1.434 V at 15 °C), later replaced by the Weston cell (1.018 3 V). |
| 1948 | The absolute volt replaces the international volt (9th CGPM). The volt is part of the SI from 1960. |
| 1962 | Brian Josephson predicts the Josephson effect, which ties voltage to frequency. |
| 1990 | The conventional value KJ-90 = 483 597.9 GHz/V is introduced so that all national laboratories realize the same volt. |
| 2019 | The SI revision fixes e and h; the Josephson constant KJ = 2e/h becomes exact and the volt is realized directly in the SI. |
What is a volt in practice?
One volt corresponds to an energy of one joule per coulomb of charge. An ordinary AA cell delivers about 1.5 V, a car battery 12 V and the European mains supply 230 V between line and neutral. Nerve impulses in the body operate at voltages around 70 mV, while high-voltage direct-current (HVDC) transmission lines can run at several hundred kilovolts.
Voltage by itself does no work. Only when a current flows is the voltage converted into power according to P = U·I, and into energy over time according to W = U·I·t. This is why the volt must always be read together with the ampere, the watt and the joule.
Definition, realization and use
- The definition states what a volt is in principle: one watt per ampere, ultimately expressed in constants of nature.
- The realization is the set of experiments through which national metrology institutes produce the volt with a known uncertainty.
- The use is the voltage measurement carried out with voltmeters and reference sources in industry, laboratories and everyday life.
How the volt is realized
The primary realization of the volt is based on the Josephson effect. When a superconducting tunnel junction is irradiated with microwaves of frequency f, voltage steps of size U = n·f/KJ appear, where n is an integer and KJ = 2e/h is the Josephson constant. Because e and h have been fixed exactly since 2019, the voltage is directly traceable to a frequency, and hence to the second.
In practice, arrays of thousands of junctions in series are used, giving voltages up to 10 V with relative uncertainties of the order of 10⁻⁹. This voltage is then used to calibrate secondary references, chiefly Zener-based voltage standards, which in turn calibrate voltmeters and calibrators in calibration laboratories.
Practical voltage measurement and error sources
Ordinary measurement with a voltmeter is affected by several factors. The instrument’s input resistance loads the circuit and can lower the measured voltage, especially in high-resistance circuits. Thermoelectric voltages arise at junctions between different metals and can cause errors at the microvolt level. Reference values drift with temperature and time, which makes regular calibration necessary.
For alternating voltage there is the added question of which value is meant: peak value, root-mean-square (RMS) value or mean value. The mains voltage of 230 V is an RMS value; the peak value is about 325 V.
The volt and other derived units
The volt enters the definition of several other electrical units, and several relations tie it to power and energy.
| Unit | Quantity | Relation to the volt |
| ampere (A) | Electric current | Base unit; 1 V = 1 W/A |
| watt (W) | Power | P = U·I |
| ohm (Ω) | Resistance | U = R·I, 1 Ω = 1 V/A |
| farad (F) | Capacitance | C = Q/U, 1 F = 1 C/V |
| joule (J) | Energy | W = U·Q, 1 J = 1 V·C |
Multiples and common conversions
The volt is used with SI prefixes across a very wide range: millivolt (mV, 10⁻³ V) for sensor signals, kilovolt (kV, 10³ V) in power distribution and megavolt (MV, 10⁶ V) in high-voltage engineering and particle accelerators. Since voltage times current gives power and power times time gives energy, conversions of power and energy are the most common applications in which the volt takes part, for example between watts and kilowatts or between joules and kilowatt-hours. Conversions between units of voltage are handled by the voltage converter.
Summary
The volt is the SI unit of electric potential difference, defined as one watt per ampere and expressed in base units as kg·m²·s⁻³·A⁻¹. Through the 2019 SI revision the unit is anchored in exact values of the elementary charge and the Planck constant, and it is realized with the Josephson effect, which ties voltage to frequency.
From quantum voltage standards to a simple voltmeter runs an unbroken chain of traceability. That chain is what makes a volt mean the same thing in every laboratory, workshop and home in the world.