Last updated

Leeds and Northrup one ohm standard resistance.jpg
A laboratory one-ohm standard resistor, c.1917
General information
Unit system SI
Unit of electrical resistance
Named after Georg Ohm
1 Ω in ...... is equal to ...
    SI base units     kgm 2s −3A −2

The ohm (symbol: Ω, the uppercase Greek letter omega) is the unit of electrical resistance in the International System of Units (SI). It is named after German physicist Georg Ohm. Various empirically derived standard units for electrical resistance were developed in connection with early telegraphy practice, and the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time, and of a convenient scale for practical work as early as 1861. [1]


Following the 2019 redefinition of the SI base units, in which the ampere and the kilogram were redefined in terms of fundamental constants, the ohm is now also defined as an exact value in terms of these constants.


One of the functions of many types of multimeters is the measurement of resistance in ohms. Electronic multi meter.jpg
One of the functions of many types of multimeters is the measurement of resistance in ohms.

The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one volt (V), applied to these points, produces in the conductor a current of one ampere (A), the conductor not being the seat of any electromotive force. [2]

in which the following additional units appear: siemens (S), watt (W), second (s), farad (F), henry (H), weber (Wb), joule (J), coulomb (C), kilogram (kg), and meter (m).

In many cases the resistance of a conductor is approximately constant within a certain range of voltages, temperatures, and other parameters. These are called linear resistors. In other cases resistance varies, such as in the case of the thermistor, which exhibits a strong dependence of its resistance with temperature.

In the US, a double vowel in the prefixed units "kiloohm" and "megaohm" is commonly simplified, producing "kilohm" and "megohm". [3] [4] [5] [6]

In alternating current circuits, electrical impedance is also measured in ohms.

Relation to conductance

The siemens (S) is the SI derived unit of electric conductance and admittance, historically known as the "mho" (ohm spelled backwards, symbol is ℧); it is the reciprocal of the ohm: 1 S = 1 Ω−1.

Power as a function of resistance

The power dissipated by a resistor may be calculated from its resistance, and the voltage or current involved. The formula is a combination of Ohm's law and Joule's law:

where P is the power, R is the resistance, V is the voltage across the resistor, and I is the current through the resistor.

A linear resistor has a constant resistance value over all applied voltages or currents; many practical resistors are linear over a useful range of currents. Non-linear resistors have a value that may vary depending on the applied voltage (or current). Where alternating current is applied to the circuit (or where the resistance value is a function of time), the relation above is true at any instant, but calculation of average power over an interval of time requires integration of "instantaneous" power over that interval.

Since the ohm belongs to a coherent system of units, when each of these quantities has its corresponding SI unit (watt for P, ohm for R, volt for V and ampere for I, which are related as in § Definition) this formula remains valid numerically when these units are used (and thought of as being cancelled or omitted).


The rapid rise of electrotechnology in the last half of the 19th century created a demand for a rational, coherent, consistent, and international system of units for electrical quantities. Telegraphers and other early users of electricity in the 19th century needed a practical standard unit of measurement for resistance. Resistance was often expressed as a multiple of the resistance of a standard length of telegraph wires; different agencies used different bases for a standard, so units were not readily interchangeable. Electrical units so defined were not a coherent system with the units for energy, mass, length, and time, requiring conversion factors to be used in calculations relating energy or power to resistance. [7]

Two different methods of establishing a system of electrical units can be chosen. Various artifacts, such as a length of wire or a standard electrochemical cell, could be specified as producing defined quantities for resistance, voltage, and so on. Alternatively, the electrical units can be related to the mechanical units by defining, for example, a unit of current that gives a specified force between two wires, or a unit of charge that gives a unit of force between two unit charges. This latter method ensures coherence with the units of energy. Defining a unit for resistance that is coherent with units of energy and time in effect also requires defining units for potential and current. It is desirable that one unit of electrical potential will force one unit of electric current through one unit of electrical resistance, doing one unit of work in one unit of time, otherwise, all electrical calculations will require conversion factors.

Since so-called "absolute" units of charge and current are expressed as combinations of units of mass, length, and time, dimensional analysis of the relations between potential, current, and resistance show that resistance is expressed in units of length per time – a velocity. Some early definitions of a unit of resistance, for example, defined a unit resistance as one quadrant of the Earth per second.

The absolute-unit system related magnetic and electrostatic quantities to metric base units of mass, time, and length. These units had the great advantage of simplifying the equations used in the solution of electromagnetic problems, and eliminated conversion factors in calculations about electrical quantities. However, the centimeter–gram–second, CGS, units turned out to have impractical sizes for practical measurements.

Various artifact standards were proposed as the definition of the unit of resistance. In 1860 Werner Siemens (1816–1892) published a suggestion for a reproducible resistance standard in Poggendorff's Annalen der Physik und Chemie . [8] He proposed a column of pure mercury, of one square millimeter cross section, one meter long: Siemens mercury unit. However, this unit was not coherent with other units. One proposal was to devise a unit based on a mercury column that would be coherent – in effect, adjusting the length to make the resistance one ohm. Not all users of units had the resources to carry out metrology experiments to the required precision, so working standards notionally based on the physical definition were required.

In 1861, Latimer Clark (1822–1898) and Sir Charles Bright (1832–1888) presented a paper at the British Association for the Advancement of Science meeting [9] suggesting that standards for electrical units be established and suggesting names for these units derived from eminent philosophers, 'Ohma', 'Farad' and 'Volt'. The BAAS in 1861 appointed a committee including Maxwell and Thomson to report upon standards of electrical resistance. [10] Their objectives were to devise a unit that was of convenient size, part of a complete system for electrical measurements, coherent with the units for energy, stable, reproducible and based on the French metrical system. [11] In the third report of the committee, 1864, the resistance unit is referred to as "B.A. unit, or Ohmad". [12] By 1867 the unit is referred to as simply ohm. [13]

The B.A. ohm was intended to be 109 CGS units but owing to an error in calculations the definition was 1.3% too small. The error was significant for preparation of working standards.

On 21 September 1881 the International Electrical Congress defined a practical unit of ohm for the resistance, based on CGS units, using a mercury column 1 mm2 in cross-section, approximately 104.9 cm in length at 0 °C, similar to the apparatus suggested by Siemens.

A legal ohm, a reproducible standard, was defined by the international conference of electricians at Paris in 1884 as the resistance of a mercury column of specified weight and 106 cm long; this was a compromise value between the B. A. unit (equivalent to 104.7 cm), the Siemens unit (100 cm by definition), and the CGS unit. [14] Although called "legal", this standard was not adopted by any national legislation. The "international" ohm was recommended by unanimous resolution at the International Electrical Congress 1893 in Chicago. [15] The unit was based upon the ohm equal to 109 units of resistance of the C.G.S. system of electromagnetic units. The international ohm is represented by the resistance offered to an unvarying electric current in a mercury column of constant cross-sectional area 106.3 cm long of mass 14.4521 grams and 0 °C. This definition became the basis for the legal definition of the ohm in several countries. In 1908, this definition was adopted by scientific representatives from several countries at the International Conference on Electric Units and Standards in London. [15] The mercury column standard was maintained until the 1948 General Conference on Weights and Measures, at which the ohm was redefined in absolute terms instead of as an artifact standard.

By the end of the 19th century, units were well understood and consistent. Definitions would change with little effect on commercial uses of the units. Advances in metrology allowed definitions to be formulated with a high degree of precision and repeatability.

Historical units of resistance

Unit [16] DefinitionValue in B.A. ohmsRemarks
Absolute foot/second × 107using imperial units0.3048considered obsolete even in 1884
Thomson's unitusing imperial units0.3202100 million ft/s (30,480 km/s), considered obsolete even in 1884
Jacobi copper unitA specified copper wire 25 ft (7.620 m) long weighing 345 gr (22.36 g)0.6367Used in 1850s
Weber's absolute unit × 107Based on the meter and the second0.9191
Siemens mercury unit 1860. A column of pure mercury0.9537100 cm and 1 mm2 cross section at 0 °C
British Association (B.A.) "ohm" 18631.000Standard coils deposited at Kew Observatory in 1863 [17]
Digney, Breguet, Swiss9.266–10.420Iron wire 1 km long and 4 mm2 cross section
Matthiessen13.591 mi (1.609 km) of 116-inch-diameter (1.588 mm) pure annealed copper wire at 15.5 °C
Varley25.61One mile of special 116-inch-diameter copper wire
German mile57.44A German mile (8,238 yd or 7,533 m) of iron wire 16 in (4.233 mm) diameter
Abohm 10−9Electromagnetic absolute unit in centimeter–gram–second units
Statohm 8.987551787×1011Electrostatic absolute unit in centimeter–gram–second units

Realization of standards

The mercury column method of realizing a physical standard ohm turned out to be difficult to reproduce, owing to the effects of non-constant cross section of the glass tubing. Various resistance coils were constructed by the British Association and others, to serve as physical artifact standards for the unit of resistance. The long-term stability and reproducibility of these artifacts was an ongoing field of research, as the effects of temperature, air pressure, humidity, and time on the standards were detected and analyzed.

Artifact standards are still used, but metrology experiments relating accurately dimensioned inductors and capacitors provided a more fundamental basis for the definition of the ohm. Since 1990 the quantum Hall effect has been used to define the ohm with high precision and repeatability. The quantum Hall experiments are used to check the stability of working standards that have convenient values for comparison. [18]

Following the 2019 redefinition of the SI base units, in which the ampere and the kilogram were redefined in terms of fundamental constants, the ohm is now also defined in terms of these constants.


The symbol Ω was suggested, because of the similar sound of ohm and omega, by William Henry Preece in 1867. [19] In documents printed before Second World War the unit symbol often consisted of the raised lowercase omega (ω), such that 56 Ω was written as 56ω.

Historically, some document editing software applications have used the Symbol typeface to render the character Ω. [20] Where the font is not supported, the same document may be displayed with a "W" ("10 W" instead of "10 Ω", for instance). As W represents the watt, the SI unit of power, this can lead to confusion, making the use of the correct Unicode code point preferable.

Where the character set is limited to ASCII, the IEEE 260.1 standard recommends using the unit name "ohm" as a symbol instead of Ω.

In the electronics industry it is common to use the character R instead of the Ω symbol, thus, a 10 Ω resistor may be represented as 10R. This is part of the RKM code. It is used in many instances where the value has a decimal place. For example, 5.6 Ω is listed as 5R6, or 2200 Ω is listed as 2K2. This method avoids overlooking the decimal point, which may not be rendered reliably on components or when duplicating documents.

Unicode encodes the symbol as U+2126OHM SIGN, distinct from Greek omega among letterlike symbols, but it is only included for backward compatibility and the Greek uppercase omega character U+03A9ΩGREEK CAPITAL LETTER OMEGA (Ω, Ω) is preferred. [21] In MS-DOS and Microsoft Windows, the alt code ALT 234 may produce the Ω symbol. In Mac OS, ⌥ Opt+Z does the same.

See also

Notes and references

  1. "Ohm's Law - Statement, Formula, Solved Examples, Verification, FAQs". BYJUS. Retrieved 2023-02-07.
  2. BIPM SI Brochure: Appendix 1, p.46 (pdf)
  3. SASB/SCC14 – SCC14 – Quantities, Units, and Letter Symbols (2002-12-30). IEEE/ASTM SI 10-2002: IEEE/ASTM Standard for Use of the International System of Units (SI): The Modern Metric System.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
  4. Thompson, Ambler; Taylor, Barry N. (November 2008) [March 2008]. "Chapter 9.3 Spelling unit names with prefixes". Guide for the Use of the International System of Units (SI) (PDF) (2nd corrected printing, 2008 ed.). Gaithersburg, Maryland, USA: National Institute of Standards and Technology, U.S. Department of Commerce. CODEN   NSPUE3. NIST Special Publication 811. Archived (PDF) from the original on 2021-01-31. Retrieved 2021-01-31. p. 31: Reference [6] points out that there are three cases in which the final vowel of an SI prefix is commonly omitted: megohm (not megaohm), kilohm (not kiloohm), and hectare (not hectoare). In all other cases in which the unit name begins with a vowel, both the final vowel of the prefix and the vowel of the unit name are retained and both are pronounced. (85 pages)
  5. "NIST Guide to the SI". Gaithersburg, Maryland, USA: National Institute of Standards and Technology (NIST), Physical Measurement Laboratory. 2016-08-25 [2016-01-28]. Chapter 9: Rules and Style Conventions for Spelling Unit Names, 9.3: Spelling unit names with prefixes. Special Publication 811. Archived from the original on 2021-01-31. Retrieved 2021-01-31.
  6. Aubrecht II, Gordon J.; French, Anthony P.; Iona, Mario (2012-01-20). "About the International System of Units (SI) Part IV. Writing, Spelling, and Mathematics". The Physics Teacher . 50 (2): 77–79. Bibcode:2012PhTea..50...77A. doi:10.1119/1.3677278.
  7. Hunt, Bruce J. (1994). "The Ohm Is Where the Art Is: British Telegraph Engineers and the Development of Electrical Standards" (PDF). Osiris. 2. 9: 48–63. doi:10.1086/368729. S2CID   145557228. Archived from the original on 2014-03-08. Retrieved 2014-02-27.
  8. Siemens, Werner (1860). "Vorschlag eines reproducirbaren Widerstandsmaaßes". Annalen der Physik und Chemie (in German). 186 (5): 1–20. Bibcode:1860AnP...186....1S. doi:10.1002/andp.18601860502.
  9. Clark, Latimer; Bright, Sir Charles (1861-11-09). "Measurement of Electrical Quantities and Resistance". The Electrician . 1 (1): 3–4. Retrieved 2014-02-27.
  10. Report of the Thirty-First Meeting of the British Association for the Advancement of Science; held at Manchester in September 1861. September 1861. pp. xxxix–xl.
  11. Williamson, A.; Wheatstone, C.; Thomson, W.; Miller, W. H.; Matthiessen, A.; Jenkin, Fleeming (September 1862). Provisional Report of the Committee appointed by the British Association on Standards of Electrical Resistance. Thirty-second Meeting of the British Association for the Advancement of Science. London: John Murray. pp. 125–163. Retrieved 2014-02-27.
  12. Williamson, A.; Wheatstone, C.; Thomson, W.; Miller, W. H.; Matthiessen, A.; Jenkin, Fleeming; Bright, Charles; Maxwell, James Clerk; Siemens, Carl Wilhelm; Stewart, Balfour; Joule, James Prescott; Varley, C. F. (September 1864). Report of the Committee on Standards of Electrical Resistance. Thirty-fourth Meeting of the British Association for the Advancement of Science. London: John Murray. p. Foldout facing page 349. Retrieved 2014-02-27.
  13. Williamson, A.; Wheatstone, C.; Thomson, W.; Miller, W. H.; Matthiessen, A.; Jenkin, Fleeming; Bright, Charles; Maxwell, James Clerk; Siemens, Carl Wilhelm; Stewart, Balfour; Varley, C. F.; Foster, G. C.; Clark, Latimer; Forbes, D.; Hockin, Charles; Joule, James Prescott (September 1867). Report of the Committee on Standards of Electrical Resistance. Thirty-seventh Meeting of the British Association for the Advancement of Science. London: John Murray. p. 488. Retrieved 2014-02-27.
  14. "The Electrical Congress Of Paris, 1884". Nature. 30 (758): 26–27. May 1884. doi: 10.1038/030026a0 . Retrieved 2023-12-23.
  15. 1 2 Fleming, John Ambrose (1911). "Units, Physical"  . In Chisholm, Hugh (ed.). Encyclopædia Britannica . Vol. 27 (11th ed.). Cambridge University Press. pp. 738–745, see page 742. An Electrical Congress was held in Chicago, U.S.A. in August 1893, to consider......and at the last one held in London in October 1908 were finally adopted
  16. Gordon Wigan (trans. and ed.), Electrician's Pocket Book, Cassel and Company, London, 1884
  17. Historical Studies in International Corporate Business. Teich p34
  18. R. Dzuiba and others, Stability of Double-Walled Maganin Resistors in NIST Special Publication Proceedings of SPIE, The Institute, 1988 pp. 63–64
  19. Preece, William Henry (1867), "The B.A. unit for electrical measurements", Philosophical Magazine , vol. 33, p. 397, retrieved 2017-02-26
  20. E.g. recommended in HTML 4.01: "HTML 4.01 Specification". W3C. 1998. Section 24.1 "Introduction to character entity references". Retrieved 2018-11-22.
  21. Excerpts from The Unicode Standard, Version 4.0 , accessed 11 October 2006

Related Research Articles

<span class="mw-page-title-main">Ampere</span> SI base unit of electric current

The ampere, often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb (C) moving past a point per second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.

The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism.

In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, power is sometimes called activity. Power is a scalar quantity.

<span class="mw-page-title-main">Resistor</span> Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

<span class="mw-page-title-main">International System of Units</span> Modern form of the metric system

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

<span class="mw-page-title-main">Volt</span> SI derived unit of voltage

The volt is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI).

<span class="mw-page-title-main">Electrical impedance</span> Opposition of a circuit to a current when a voltage is applied

In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.

<span class="mw-page-title-main">Metric system</span> Metre-based systems of measurement

The metric system is a decimal-based system of measurement. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela.

<span class="mw-page-title-main">Coulomb</span> SI derived unit of electric charge

The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is equal to the electric charge delivered by a 1 ampere current in 1 second and is defined in terms of the elementary charge e, at about 6.241509×1018 e.

<span class="mw-page-title-main">Ohm's law</span> Law of electrical current and voltage

Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the three mathematical equations used to describe this relationship:

<span class="mw-page-title-main">Electrical resistance and conductance</span> Opposition to the passage of an electric current

The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is electrical conductance, measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with mechanical friction. The SI unit of electrical resistance is the ohm, while electrical conductance is measured in siemens (S).

<span class="mw-page-title-main">Henry (unit)</span> SI unit of inductance

The henry is the unit of electrical inductance in the International System of Units (SI). If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber turn, that coil has a self inductance of 1 henry.‌ The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.

<span class="mw-page-title-main">Farad</span> SI unit of electric capacitance

The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI), equivalent to 1 coulomb per volt (C/V). It is named after the English physicist Michael Faraday (1791–1867). In SI base units 1 F = 1 kg−1⋅m−2⋅s4⋅A2.

In physics, the weber is the unit of magnetic flux in the International System of Units (SI). The unit is derived from the relationship 1 Wb = 1 V⋅s (volt-second). A magnetic flux density of 1 Wb/m2 is one tesla.

In electromagnetism, the impedance of free space, Z0, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is,

A conventional electrical unit is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.

The watt is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution.

The International System of Electrical and Magnetic Units is an obsolete system of units used for measuring electrical and magnetic quantities. It was proposed as a system of practical international units by unanimous recommendation at the International Electrical Congress, discussed at other Congresses, and finally adopted at the International Conference on Electric Units and Standards in London in 1908. It was rendered obsolete by the inclusion of electromagnetic units in the International System of Units (SI) at the 9th General Conference on Weights and Measures in 1948.

The siemens is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is equal to the reciprocal of one ohm and is also referred to as the mho. The siemens was adopted by the IEC in 1935, and the 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.

<span class="mw-page-title-main">History of the metric system</span> History of the metric system measurement standards

The history of the metric system began during the Age of Enlightenment with measures of length and weight derived from nature, along with their decimal multiples and fractions. The system became the standard of France and Europe within half a century. Other measures with unity ratios were added, and the system went on to be adopted across the world.