Summation (Sigma) – Meaning, Copy & Paste, LaTeX, Unicode
Complete mathematical reference, typing shortcuts, character entities, and usage guide for the Summation (Sigma) (∑).
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What Does the ∑ Symbol Mean?
The summation symbol (∑) is an uppercase Greek sigma used in mathematics to represent the compact addition of a sequence of terms. It specifies an index variable, a lower starting limit, and an upper ending limit, instructing you to sum each evaluated term in that range.
Real Numeric Examples
∑_{i=1}^{4} (2i + 1) (2·1+1) + (2·2+1) + (2·3+1) + (2·4+1) = 3 + 5 + 7 + 9 Evaluating the linear expression 2i + 1 for each integer index i from 1 to 4 produces four terms. Adding them together gives 24.
∑_{k=1}^{5} k² 1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 The sum of the squares of the first five natural numbers yields 55.
LaTeX, Unicode, HTML & Keyboard Codes for ∑
Copy individual technical codes and character entities with one click:
\sum U+2211 ∑ ∑ Alt+228 Option + W How to Type ∑ on Every Device and Application
Step-by-step instructions for Windows, Mac, Word, Google Docs, Excel, HTML, LaTeX, and mobile devices:
Windows
Hold down Alt and type 228 (or 8721) on the numeric keypad with Num Lock active. Alternatively, press Win + . to open the Windows Emoji & Symbol panel.
Alt+228 Mac (macOS)
Press Option + W on any standard macOS keyboard. You can also press Cmd + Ctrl + Space to open the Character Viewer and search for 'summation'.
Option + W Microsoft Word
In Word Equation mode (Alt + =), type \sum and press Space. In normal document text, type 2211 and immediately press Alt + X.
\sum Google Docs
Select Insert > Equation, type \sum, and hit Space. Or choose Insert > Special characters and search 'summation'.
\sum Excel / Spreadsheets
Enter =UNICHAR(8721) into any cell to dynamically display the ∑ symbol.
=UNICHAR(8721) HTML & Web
Use the HTML entity ∑ or the numeric decimal entity ∑.
∑ LaTeX (Math Mode)
In LaTeX math mode, write \sum. For boundaries, write \sum_{i=1}^{n} a_i.
\sum Android & iPhone (iOS)
Copy the ∑ symbol directly from this page, or enable a math keyboard extension on iOS or Android.
∑ Commonly Confused With
Distinguish ∑ from visually similar mathematical glyphs and characters:
Greek Capital Sigma
vs ∑U+03A3 (Σ) is the Greek alphabet letter used for linguistic text or population standard deviations, whereas U+2211 (∑) is the dedicated mathematical operator with sizing for limits.
Explore in greek math symbolsProduct Operator
vs ∑The product operator (∏) multiplies consecutive terms together, whereas the summation operator (∑) adds them together.
Explore in algebra symbolsLatin Capital E
vs ∑In low-resolution fonts, capital E can resemble sigma, but E denotes scientific exponent notation (e.g. 1e6) or Euler's number, not a summation index.
Explore in number symbolsFrequently Asked Questions About ∑
Answers to common questions about typing, meaning, and syntax for ∑:
What does the ∑ symbol mean in mathematics?
The ∑ symbol stands for summation, an operation that adds a sequence of numbers or terms together. The notation specifies a starting index (at the bottom) and an ending bound (at the top), generating a concise sum of mathematical terms.
How do you type the ∑ symbol in Microsoft Word?
To type ∑ in Word, press Alt + = to activate the equation editor, type \sum, and hit Space. Alternatively, type the hex code 2211 and press Alt + X to convert it into ∑.
What is the keyboard shortcut for ∑ on Mac?
On macOS, press Option + W on your keyboard to instantly type the summation symbol ∑ into any text field or application.
What is the difference between ∑ and the Greek letter Σ?
While both share Greek origin, U+2211 (∑) is the mathematical n-ary summation operator optimized with sizing for limits, while U+03A3 (Σ) is the Greek uppercase alphabet letter Sigma used for linguistic text and statistical population standard deviation.
How do you write summation in LaTeX?
In LaTeX math mode, write \sum. To add lower and upper bounds, use an underscore and caret: \sum_{i=1}^{n} a_i. In display math ($$...$$ or \displaystyle), the limits render directly above and below the sigma.