Summation symbol
The summation symbol ∑ is maths’ most useful piece of shorthand: “add them all up”. With an index below and a limit above, one compact sign replaces a whole column of additions — ∑ as i runs from 1 to 4 of i simply means 1 + 2 + 3 + 4. Copy ∑ here, take its notation apart piece by piece, and learn how it differs from the Greek letter it was borrowed from.
Copy the summation sign and its family
Sums at work, ready to copy
Anatomy of a sum
| Part | What it tells you |
|---|---|
| ∑ — the sign itself | “Sum”: add every term the formula generates, in order |
| The index below (i = 1) | The counter and its starting value — the first term uses i = 1 |
| The limit above (n or 4) | Where the counter stops — the last term uses that value |
| The expression after it | The recipe for each term: i alone gives 1, 2, 3…; i² gives the squares 1, 4, 9… |
Two characters wear this shape, and the difference is a favourite trap. ∑ (U+2211) is a dedicated mathematical operator — spaced like an operator, born for formulas when Leonhard Euler introduced it in 1755. Σ (U+03A3) is the Greek capital letter sigma, the letter the operator’s shape was borrowed from; it belongs to Greek words and text. Equation editors insert the true ∑; spreadsheets paint Σ on the AutoSum button. In casual notes either survives — in typeset maths, the operator is the correct twin. Its smaller sibling σ works a different job entirely, measuring standard deviation in statistics.
How to type it
| Platform | Method |
|---|---|
| Windows (Word) | Type 2211 then Alt + X (Word’s equation editor turns it into full sigma notation with limits) |
| Mac | No single key — Character Viewer (search “summation” or “n-ary”) or copy from here |
| HTML / LaTeX | HTML: the “sum” entity name (ampersand + sum;) or code 8721. LaTeX: \sum, with limits as _ and ^ |
| Excel / Sheets | The SUM function does the adding — paste ∑ into labels and titles where the sign itself is the text |
Explore more
Sigma’s letter home is the Greek alphabet, the average built on ∑ lives at the mean symbol, the multiplying twin ∏ shares a page with the pi symbol, and everything gathers in the math symbols collection.
Frequently asked questions
How do you read a summation aloud?
“The sum, as i runs from 1 to n, of …” — name the counter, its start, its stop, then the expression. ∑ with i from 1 to 4 of i reads exactly that way and unpacks to 1 + 2 + 3 + 4 = 10: the notation is a compressed instruction, not a mystery.
Is there a shortcut for adding 1 + 2 + … + n?
Yes — the pairing trick credited to the young Gauss: pair the first and last terms (each pair sums to n + 1), and there are n/2 pairs, giving n(n + 1)/2. For 1 to 10: 10 × 11 / 2 = 55 — the same answer the ∑ k card above carries.
∑ or Σ — does it matter which I paste?
For homework, notes and messages, no reader will mind. For published maths, yes: ∑ (U+2211) is the operator with correct spacing and limit placement; Σ (U+03A3) is a letter that merely looks the part. When in doubt, paste the operator from this page.
What does the smaller σ mean?
In statistics, lowercase sigma σ is the standard deviation — how widely values spread around their mean; in Greek text it is simply the letter s (written ς at the end of a word). Same family, three different trades: letter, spread, and — as capital ∑ — the great adder.