Ohm (Ω)
Definition, derivation and practical use in the International System of Units
Electrical resistance states how strongly a conductor opposes the current flowing through it. The ohm, symbol Ω (the Greek letter omega), is the SI unit of resistance and a derived SI unit. It is fundamental to all electrical engineering, from the sizing of cables to the design of electronic circuits, yet its modern definition and realization are less well known.
As with the base units, it is necessary to distinguish between definition, realization and practical use. Since 2019 the ohm has been anchored in exact constants of nature, and it is realized with a quantum effect that yields the same resistance wherever in the world the experiment is performed.
The definition of the ohm in the SI system
The ohm is defined within the International System of Units (SI) as:
the electrical resistance between two points of a conductor when a constant potential difference of 1 volt applied between these points produces a current of 1 ampere in the conductor.
Expressed in other SI units, 1 Ω = 1 V/A. In base units this becomes 1 Ω = 1 kg·m²·s⁻³·A⁻². The definition rests on:
- the volt, the unit of electric potential difference,
- the ampere, the base unit of electric current, defined through the elementary charge e.
The relation U = R·I, known as Ohm’s law, is what binds the three units together. Since the SI revision of 2019 the von Klitzing constant RK = h/e² is exact, which gives the ohm a direct link to the Planck constant and the elementary charge.
Fact box: History of the ohm
| Year | Event |
| 1827 | Georg Simon Ohm (1789-1854) publishes Die galvanische Kette and formulates Ohm’s law. |
| 1861 | The British Association proposes a practical unit of resistance named after Ohm. |
| 1881 | The International Electrical Congress in Paris adopts the ohm as the unit of resistance; a “legal ohm” is fixed in 1884. |
| 1893 | The “international ohm” is defined in Chicago as the resistance of a mercury column 106.3 cm long, of mass 14.452 1 g and cross-section 1 mm² at 0 °C. |
| 1948 | The absolute ohm replaces the international ohm (9th CGPM). The ohm is part of the SI from 1960. |
| 1980 | Klaus von Klitzing discovers the quantum Hall effect (Nobel Prize 1985). |
| 1990 | The conventional value RK-90 = 25 812.807 Ω is introduced for resistance measurement worldwide. |
| 2019 | The SI revision fixes h and e; RK = h/e² = 25 812.807 45… Ω becomes exact. |
How much is one ohm in practice?
One ohm is the resistance of a conductor in which 1 V drives 1 A. A copper wire with a cross-section of 1 mm² has a resistance of about 0.017 Ω per meter, so one ohm corresponds to roughly 60 meters of such wire. A 60 W incandescent bulb for 230 V has a resistance of about 880 Ω when lit. The resistance of human skin ranges from a few kilohms to several megohms depending on moisture and contact area.
Resistance determines how much power is dissipated in a component according to P = R·I² = U²/R. This is why the unit is decisive when sizing fuses, cables and heating elements.
Definition, realization and use
- The definition states what an ohm is in principle: one volt per ampere, ultimately expressed in h and e.
- The realization is the set of experiments through which national metrology institutes produce the ohm with a known uncertainty.
- The use is the resistance measurement carried out with ohmmeters, bridges and reference resistors in industry and laboratories.
How the ohm is realized
The primary realization of the ohm is based on the quantum Hall effect. In a two-dimensional electron system, cooled to about 1.5 K and placed in a magnetic field of several tesla, the Hall resistance takes exactly quantized values RH = RK/i, where i is an integer (usually i = 2). Because RK = h/e² is fixed exactly, the experiment yields a resistance that is directly traceable to the SI definition.
The value is then transferred with cryogenic current comparators to standard resistors of 1 Ω, 100 Ω and 10 kΩ, with relative uncertainties of the order of 10⁻⁹. These standards in turn calibrate the reference resistors and instruments used in calibration laboratories and industry.
Practical resistance measurement and error sources
The resistance of most materials depends on temperature. For copper, resistance rises by about 0.4 percent per degree Celsius, which makes temperature control necessary in precision measurement. Reference resistors are therefore made of alloys with a very low temperature coefficient.
When measuring small resistances, the resistance of the test leads themselves interferes. The solution is four-terminal (Kelvin) measurement, in which the current is fed through one pair of leads and the voltage is measured across another, so that the lead contribution cancels out. At very high resistances, leakage currents and insulation problems take over instead.
The ohm and other derived units
The ohm is closely tied to the other electrical units and to power through Ohm’s law and the power law.
| Unit | Quantity | Relation to the ohm |
| volt (V) | Voltage | U = R·I |
| ampere (A) | Current | I = U/R |
| siemens (S) | Conductance | 1 S = 1/Ω |
| watt (W) | Power | P = R·I² |
| farad (F) | Capacitance | Time constant τ = R·C, 1 Ω·F = 1 s |
Multiples and common conversions
The ohm is used with SI prefixes from milliohm (mΩ, 10⁻³ Ω) for busbars and contacts, through kilohm (kΩ, 10³ Ω) in electronics, to megohm (MΩ, 10⁶ Ω) in insulation testing. The most common calculation involving the ohm is power dissipation: P = R·I² gives the power in watts, and multiplied by time the energy in joules. Conversions between units of power and energy therefore often follow a resistance measurement. Conversions between units of resistance are handled by the resistance converter.
Summary
The ohm is the SI unit of electrical resistance, defined as one volt per ampere and expressed in base units as kg·m²·s⁻³·A⁻². From the mercury column of 1893 to the quantum Hall effect of today, the unit has moved from a material artefact to a quantity anchored in the Planck constant and the elementary charge.
It is the quantized Hall resistance, and the chain of traceability that starts from it, that makes one ohm the same ohm in every laboratory, whatever the country and the equipment.