Omega — Ω / ω
Omega (Ω ω) is the twenty-fourth and last letter of the Greek alphabet. The omega symbol is written Ω in uppercase and ω in lowercase; its name means "great O", for the long o sound. Ω is the symbol for the ohm, the unit of electrical resistance, and ω stands for angular velocity and angular frequency. Because it comes last, "alpha and omega" means the beginning and the end. Copy it with the buttons below, or see how to type Greek letters on any keyboard.
Ω ω
Copy: Ω ω
Unicode code points: U+03A9 (uppercase), U+03C9 (lowercase).
| Uppercase | Ω |
|---|---|
| Lowercase | ω |
| Transliteration | ō |
| Pronunciation | oh‑MEH‑ghah |
| Numeric value | 800 |
Etymology and Origin
Omega literally means "great O" (ὦ μέγα) to distinguish it from omicron ("little o"). It was added in the East Ionic alphabet around the 7th century BCE to represent the long "o" sound. The phrase "alpha and omega" (beginning and end) comes from the Christian Book of Revelation, where God declares "I am the Alpha and the Omega."
Pronunciation
- Ancient Greek: [ɔː] as long "o" in "door"
- Modern Greek: [o] as in "go"
- English usage: oh-MAY-guh or oh-MEE-guh [oʊˈmeɪɡə] or [oʊˈmiːɡə]
The Ohm - Unit of Electrical Resistance
The uppercase omega (Ω) is the standard symbol for ohm, the SI unit of electrical resistance, named after German physicist Georg Ohm. One ohm is defined as the resistance through which a current of one ampere flows when a potential difference of one volt is applied.
- Ohm's Law: V = IR, where R is measured in ohms (Ω)
- Common values: kΩ (kilohms), MΩ (megohms), mΩ (milliohms)
- Symbol origin: Chosen because Ohm starts with O, and Ω looks distinctive
Uses of Omega in Mathematics
- Big-Omega Notation: Ω(n) describes lower bound of algorithm complexity
- First Uncountable Ordinal: ω₁ in set theory
- Solid Angle: Ω measured in steradians
- Omega Constant: Ω ≈ 0.5671432904 (solution to Ω e^Ω = 1)
- Wright Omega Function: ω(z) solves ω + ln ω = z (related to Lambert W)
- Chaitin's Constant: Ω represents algorithmic probability
Uses in Science and Engineering
- Physics: Angular velocity (ω = 2πf), angular frequency
- Electrical Engineering: Impedance (measured in ohms Ω)
- Cosmology: Ω (density parameter) determines universe geometry
- Particle Physics: Omega baryon (Ω⁻), omega meson
- Biochemistry: Omega-3 and omega-6 fatty acids
- Astronomy: ω for argument of periapsis in orbital mechanics
Cultural and Symbolic Uses
- "Alpha and Omega": Beginning and end, used in Christianity
- Omega Watches: Luxury Swiss watchmaker (est. 1848)
- Fraternities/Sororities: Final letter, symbolizes completion
- Video Games: Omega Weapon (Final Fantasy), Omega symbol in Undertale
- Comics: Darkseid's Omega Effect (DC Comics)
- Brands: Often used to suggest finality, completion, excellence
Mathematical Examples with Omega
Ohm's Law: If V = 12V and I = 2A, then R = V/I = 6Ω
Angular velocity: ω = 2πf, where f is frequency in Hz
Big-Omega: Algorithm with runtime Ω(n²) takes at least quadratic time
Solid angle: Full sphere = 4π steradians ≈ 12.566 sr
Cosmology: If Ω > 1, universe is closed; if Ω < 1, universe is open
Related Letters
- Omicron (Ο ο) — "small o", paired with omega in ancient Greek to mark short vs. long vowel quantity. Modern Greek pronounces both [o].
- Alpha (Α α) — the first letter, paired with omega in the phrase "alpha and omega" to mean "the entirety of something" or "beginning and end".
- Eta (Η η) — the long-e counterpart to omega's long o; in classical Greek they marked the long-vowel pair.
Writing Tips
- Uppercase Ω: Looks like a horseshoe or open circle with two feet extending downward
- Lowercase ω: Like a rounded "w" - three curved strokes forming valleys
- Common mistake: Don't confuse Ω with the astrological symbol for Aries (♈)
- Handwriting: Lowercase ω should have smooth, flowing curves - practice the three-bump shape
- Similarity: Uppercase Ω resembles inverted horseshoe magnet symbol
Interesting Facts
- Omega is the 24th and final letter of the Greek alphabet
- In ancient Greek numerals, Ω΄ = 800
- Omega Watches was the first watch worn on the Moon (1969, Apollo 11)
- Omega-3 fatty acids are essential nutrients found in fish oil
- "Alpha and Omega" appears in Revelation 1:8, 21:6, and 22:13
- The ohm symbol (Ω) was proposed by William Preece in 1867
- Georg Ohm discovered his law in 1827 but faced initial skepticism
- Omega Nebula (M17) is a star-forming region in Sagittarius
Frequently Asked Questions
How do I type ω?
The easiest way is to use the copy buttons at the top of this page. In Microsoft Word, type 03C9 and press Alt + X. In HTML, use ω (ω) or Ω (Ω). In LaTeX, use \omega or \Omega. With a Greek keyboard layout enabled, press V. See how to type Greek letters for every method.
How do I type the ohm symbol Ω?
Use uppercase omega Ω (U+03A9). On a Mac, Option + Z types it. A separate "ohm sign" (U+2126) exists, but Unicode treats it as equivalent to Ω and recommends the Greek letter.
What does "alpha and omega" mean?
Alpha is the first letter and omega the last, so "the alpha and the omega" means the beginning and the end, or everything. The phrase comes from the Book of Revelation.
What does ω mean in physics?
Angular velocity or angular frequency, measured in radians per second. For a wave, ω = 2πf, where f is the frequency in hertz.