Omega

How to read it

Dictionary.com gives the American pronunciations oh-MEG-uh, oh-MEE-guh and oh-MAY-guh; the Collins English Dictionary gives British OH-mi-guh /ˈəʊmɪɡə/. The name means “great o”, and Collins describes it as a long vowel, as against Omicron, “small o”. As the last letter, omega also means the end or the last of a series, and Dictionary.com points to the phrase “alpha and omega”, the first and last letters together (see Alpha).

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Capital and small forms

Unicode has a separate ohm sign but says the preferred representation of the ohm is the Greek capital omega, U+03A9, and the two are canonically equivalent. The upside-down ℧, the mho, is an archaic unit of conductance, now the siemens. The pi variant ϖ looks like a small omega (see Pi).

The ohm

Ω is the symbol for the ohm, the SI unit of electrical resistance: one volt per ampere (NIST SP 330). The SI defines it as the resistance between two points of a conductor when one volt across them produces a current of one ampere. A 10 kΩ resistor is 10,000 ohms. NIST’s Guide for the Use of the SI sets the unit symbol Ω upright; in italic, Ω is the quantity solid angle.

Omega in maths and physics

ω is angular frequency, 2π divided by the period, ω = 2π/T, in inverse seconds (OpenStax University Physics). In statistical physics Ω is the number of accessible states in S = k ln Ω, which links entropy to the Boltzmann constant (NIST SP 330). In computer science Ω gives a lower bound on how fast a function grows, as O gives an upper bound (MIT 6.006; see Omicron).

In quantum physics

The energy of a matter wave is E = ħω, de Broglie’s relation (OpenStax University Physics); ω also appears in the time-modulation factor e^(−iωt) of the wave function Ψ. In particle physics Ω⁻ is the omega baryon, which OpenStax lists at 1672 MeV.