Sigma — Σ / σ
Sigma (Σ σ ς) is the eighteenth letter of the Greek alphabet. The sigma symbol has three forms: uppercase Σ, lowercase σ, and ς, which is used only at the end of a word. In math, Σ means "sum of" (summation), and in statistics σ is the standard deviation; engineers also use σ for stress and electrical conductivity. Copy it with the buttons below, or see how to type Greek letters on any keyboard.
Σ σ
Copy: Σ σ ς
Unicode code points: U+03A3 (uppercase), U+03C3 (lowercase), U+03C2 (final form).
| Uppercase | Σ |
|---|---|
| Lowercase | σ |
| Final form | ς |
| Transliteration | s |
| Pronunciation | SEE‑gh‑mah |
| Numeric value | 200 |
Etymology and Origin
Sigma derives from the Phoenician letter "shin," which represented the "sh" sound. The Greeks adapted it for the "s" sound. Sigma is unique among Greek letters for having three different forms: uppercase Σ, lowercase σ (used in the middle or beginning of words), and final form ς (used only at the end of words).
Pronunciation
- Ancient Greek: [s] as in "sun"
- Modern Greek: [s] as in "sun" (unchanged)
- English usage: SIG-muh [ˈsɪɡmə]
The Three Forms of Sigma
Sigma is the only Greek letter with three distinct written forms:
- Uppercase Σ: Used at the beginning of uppercase words and in mathematical notation
- Lowercase σ: Used at the beginning or middle of lowercase words
- Final form ς: Used exclusively at the end of words in Greek text
Example: The Greek word for "wise" is σοφός (sophos) - note σ at the beginning but final ς at the end.
Uses of Sigma in Mathematics
Sigma is one of the most important symbols in mathematics:
- Summation: Σ denotes the sum of a sequence: Σ(i=1 to n) xᵢ = x₁ + x₂ + ... + xₙ
- Standard Deviation: σ measures spread in a dataset
- Variance: σ² represents variance in statistics
- Sigma Algebra: σ-algebra in measure theory and probability
- Sigma Notation: Compact way to write long sums
- Population Standard Deviation: σ vs sample std dev (s)
Uses in Science and Engineering
- Physics: σ for cross-section area, Stefan-Boltzmann constant (5.67×10⁻⁸)
- Chemistry: σ bonds (sigma bonds) in molecular orbital theory
- Engineering: σ for stress in materials (force per unit area)
- Statistics: Six Sigma quality control methodology
- Electrical: σ for electrical conductivity
- Computer Science: Σ for alphabets in formal language theory
Cultural and Business Uses
- Six Sigma: Business management strategy for process improvement
- Fraternities/Sororities: Many Greek organizations include Sigma
- Sigma Male: Internet archetype (though not academically recognized)
- Photography: Sigma Corporation lens manufacturer
- Military: Special forces units, project codenames
Mathematical Examples with Sigma
Basic summation: Σ(i=1 to 5) i = 1 + 2 + 3 + 4 + 5 = 15
Geometric series: Σ(k=0 to ∞) r^k = 1/(1-r) for |r| < 1
Standard deviation: σ = √[Σ(xᵢ - μ)² / N]
Normal distribution: f(x) = (1/σ√2π) e^(-(x-μ)²/2σ²)
Related Letters
- Stigma (Ϛ ϛ, U+03DA / U+03DB) — a Byzantine ligature of σ + τ used to represent the value 6 in Greek numerals; visually resembles a final sigma but is a distinct character.
- Pi (Π π) — capital Π denotes product notation, the multiplicative analogue of capital Σ for sums. The pair Σ and Π are the two foundational aggregation operators in mathematics.
- Lunate sigma (ϲ Ϲ, U+03F2 / U+03F9) — an alternate sigma shape used in some Byzantine and modern Greek typography; less common than the standard forms.
Writing Tips
- Uppercase Σ: Like the letter "M" turned on its side - top and bottom bars joined by two diagonals meeting in the middle
- Lowercase σ: Circular body with small tail curving right at top
- Final form ς: Elongated with tail descending below baseline - use ONLY at word endings
- Common mistake: Using σ instead of ς at the end of Greek words
- Handwriting: Practice the three forms separately - they're quite distinct
Interesting Facts
- Sigma is the only Greek letter with a special final form (ς)
- In ancient Greek numerals, Σ΄ = 200
- Six Sigma aims for 3.4 defects per million opportunities
- Sigma bonds are stronger than pi (π) bonds in chemistry
- The summation symbol Σ was introduced by Leonhard Euler in 1755
- Sigma is the ancestor of the Latin letter S
- The word "seismic" comes from Greek σεισμός (seismos), meaning earthquake
- Sigma Corporation was founded in 1961 and makes camera lenses
Frequently Asked Questions
How do I type σ?
The easiest way is to use the copy buttons at the top of this page. In Microsoft Word, type 03C3 and press Alt + X. In HTML, use σ (σ) or Σ (Σ). In LaTeX, use \sigma or \Sigma. With a Greek keyboard layout enabled, press S. See how to type Greek letters for every method.
When do you use ς instead of σ?
In Greek text, lowercase sigma is written ς at the end of a word and σ everywhere else, as in σοφός (sophos, "wise"). Uppercase Σ has only one form. On a Greek keyboard, ς is on the W key.
Is Σ the same as the summation sign ∑?
Not quite. Σ (U+03A3) is the Greek letter; ∑ (U+2211) is a separate math operator used for sums. They look alike, and on a Mac Option + W types the summation sign ∑.
What is the difference between σ and Σ in math?
Uppercase Σ means "sum of" a series of terms. Lowercase σ is standard deviation in statistics and stress in engineering.