Summation Symbol (∑): How to Type, Copy, and Use It
The summation symbol, ∑, is the big sigma that means “add all of these up.” You’ll see it in maths, statistics, and finance, usually with a little index below it and a limit above. It looks like the Greek capital letter Σ, but the maths operator is actually a different character. It isn’t on an English keyboard, so most people copy it or use a shortcut. This page has both, plus how to read a summation and why programmers use a loop instead.
If you just need the symbol, copy ∑ (or the Greek sigma Σ) from the grid below. If you want the shortcuts and how it works, the sections below cover both.
In a hurry?
- Copy it: click ∑ in the grid below.
- On Windows: hold Alt and type 8721.
- On a Mac: press Option + w.
- In Word: type 2211 then press Alt + X.
- In HTML: write ∑ (or ∑).
Table of Contents
Copy and paste the summation symbol
The summation operator and the sigma letters, with the codes you’re likely to need. Use the grid above to copy with one click; this table is the reference.
| Symbol | Name | Unicode | Windows | HTML |
|---|---|---|---|---|
| ∑ | n-ary summation | U+2211 | Alt + 8721 | ∑ |
| Σ | Greek capital sigma | U+03A3 | Alt + 931 | Σ |
| σ | Greek small sigma | U+03C3 | Alt + 963 | σ |
| ∏ | n-ary product | U+220F | Alt + 8719 | ∏ |
The ∑ isn’t on a standard keyboard, so it takes a shortcut, a code, or a copy. The sections below cover each device, then the difference between the operator and the letter that trips people up.
How to type the summation symbol on any device
Type ∑ on Windows
Use the Alt code: turn on Num Lock, hold Alt, and type 8721 on the numeric keypad for ∑. On a laptop with no keypad, press Windows + . for the symbol panel and search “summation” or “sigma.”
Type ∑ on Mac
On a Mac, press Option + w for ∑. It’s a single shortcut with no dead-key step, which makes the Mac the easiest place to type it.
Type ∑ on iPhone and Android
Neither phone keyboard has ∑ as standard, so copying is easiest on mobile. A Greek keyboard gives you the letter Σ, and some maths keyboard apps include the ∑ operator; otherwise copy it from the grid above.
Type ∑ in Microsoft Word
Type 2211 then press Alt + X to convert the code into ∑. Or use Insert → Symbol, where ∑ sits among the mathematical operators. For a full summation with limits above and below, use the equation editor (Alt + =) and pick the large-operator sigma, which draws the index and limit in the right places.
Type ∑ on Linux
Press Ctrl + Shift + U, type 2211, then Enter. That Unicode input works in most GTK and Qt apps.
Add ∑ in HTML and CSS
In HTML, ∑ is ∑ or the numeric ∑ (the Greek letter Σ is Σ). In CSS, a ∑ in a content value is the escaped code point \2211.
∑ the operator vs Σ the Greek letter
Here’s the distinction that almost no guide makes: the maths summation sign and the Greek capital letter are two different characters that look nearly identical. The summation operator ∑ is U+2211 (“n-ary summation”), a mathematical symbol. The Greek capital sigma Σ is U+03A3, a letter of the Greek alphabet. On screen they’re almost the same shape, but the operator is usually drawn a little larger and heavier, sized to sit over an index and a limit.
Which should you use? For a real sum, use the operator ∑ (U+2211) — it’s the correct character, it renders at the right size in equations, and screen readers and maths software recognise it as “summation.” Reach for the Greek Σ only when you actually mean the letter (a variable, a name, the summation in casual text where the operator isn’t available). It’s the same situation as π, where the Greek letter and the maths use overlap but the precise character matters — more on that in the [pi symbol](/pi-symbol/) guide.
| Character | Name | Use it for |
|---|---|---|
| ∑ | summation operator (U+2211) | actual sums |
| Σ | Greek capital sigma (U+03A3) | the letter, variables |
How to read a summation: the parts of ∑
A summation looks intimidating but it’s just a compact set of instructions. Take ∑ from i = 1 to n of i. Reading it piece by piece: the i = 1 below the sigma is the starting point and the index (the counter); the n above is where you stop; and the expression to the right of the sigma is what you add up each time.
So that example says: start with i = 1, work out the expression, add 1 to i, do it again, and keep going until i reaches n — then add all those results together. ∑ from i=1 to 5 of i means 1 + 2 + 3 + 4 + 5 = 15. Once you see the sigma as “a loop that adds,” every summation becomes readable: bottom is where you start, top is where you stop, and the right-hand side is what you’re summing.
| Part | Where | Means |
|---|---|---|
| index (i = 1) | below | start value and counter |
| limit (n) | above | stop value |
| expression | to the right | what to add each step |
∑ in code: use a loop or sum(), not the symbol
In programming there’s no ∑ operator — a summation is a loop or a built-in function. The sigma notation maps almost directly onto a for loop: the index and limits become the loop range, and the expression becomes what you add to a running total. ∑ from i=1 to n of i is just total = 0; for i in range(1, n+1): total += i.
Most languages also give you a shortcut. Python has sum() (sum(range(1, n+1))), JavaScript has reduce(), and spreadsheets have =SUM(A1:A10) — which is literally the summation sign turned into a function, and where most people meet ∑ in disguise. So the intimidating sigma is one of the friendliest symbols to translate into code: it’s a loop that keeps a total, or a single call to sum.
| Sigma notation | In code |
|---|---|
| ∑ of a list | sum(list) / =SUM(range) |
| ∑ from i=1 to n | for i in range(1, n+1) |
| running total | total += value |
∑ vs ∏: adding versus multiplying
The summation sign has a twin that does the same job for multiplication: the capital pi ∏ (U+220F), the product operator. Where ∑ adds a sequence of terms, ∏ multiplies them. So ∏ from i=1 to 4 of i means 1 × 2 × 3 × 4 = 24 (which is also 4 factorial).
They’re read exactly the same way — index below, limit above, expression to the right — and they’re deliberately paired: sigma for sums, pi for products, just as Σ and Π sit next to each other in the Greek alphabet. If you can read a summation, you can read a product; only the operation changes. The product operator, and the difference between capital Π and lowercase π, are covered in the [pi symbol](/pi-symbol/) guide.
Sigma beyond sums: σ, standard deviation, and ‘six sigma’
The sigma family reaches well past maths class, mostly through its lowercase form, σ. In statistics, σ (lowercase sigma) is the standard deviation — a measure of how spread out data is — while the capital ∑ appears in the formulas that calculate it (you sum the squared differences). So the two sigmas work together: ∑ does the adding, σ names the result.
That’s also where the business world picked it up. “Six Sigma”, the quality-management method, is named after σ: a “six sigma” process is so tightly controlled that defects fall six standard deviations from the mean — astronomically rare. And in everyday shorthand, people write σ for volatility in finance or “3σ event” for something far outside the norm. So if you’re reaching for a sigma, check whether you want the capital ∑ (a sum) or the lowercase σ (a spread) — they’re both in the grid above.
∑ in URLs and encoding
In a URL, ∑ is percent-encoded as %E2%88%91 (its three UTF-8 bytes). In code, the escape for the character in a string is \u2211 in JavaScript, Java, JSON, and Python (the Greek Σ is \u03A3). If ∑ ever shows as garbled characters or a box, the page is being read in the wrong encoding — serve it as UTF-8.
Copy-paste HTML codes
Every code for the summation sign and the sigmas in one place. Click a cell and copy.
| Symbol | Named entity | Numeric entity | URL (percent) code |
|---|---|---|---|
| ∑ | ∑ | ∑ | %E2%88%91 |
| Σ | Σ | Σ | %CE%A3 |
| σ | σ | σ | %CF%83 |
| ∏ | ∏ | ∏ | %E2%88%8F |
In a CSS content value, use \2211 for ∑. For its multiplying twin and the sigma-pi pairing, see the [pi symbol](/pi-symbol/) guide, and for every operator the [math symbols Alt codes](/math-symbols-on-keyboard-alt-codes/) reference.
Troubleshooting
My ∑ shows as a box or garbled text
That’s an encoding mismatch: the UTF-8 bytes for ∑ are being read as an older encoding. Set the file, database, and page charset to UTF-8 and ∑ displays correctly.
My summation sign looks like a plain Greek letter
You may have the Greek capital Σ (U+03A3) instead of the summation operator ∑ (U+2211). For a real sum, use the operator — type 2211 then Alt + X, Option + w on a Mac, or copy ∑ from the grid above.
Alt + 8721 isn’t working
That decimal code needs app support. If it fails, type 2211 then Alt + X in Word, use Option + w on a Mac, or copy ∑ from the grid above.
FAQ
How do I type the summation symbol?
On Windows, hold Alt and type 8721. On a Mac, press Option + w. In Word, type 2211 then Alt + X. In HTML, write ∑. Or click ∑ in the grid above.
Is ∑ the same as the Greek letter Σ?
No. The summation operator ∑ (U+2211) is a maths symbol; the Greek capital sigma Σ (U+03A3) is a letter. They look almost identical, but for a real sum use the operator, which is sized for equations and recognised as “summation.”
How do I read a summation?
The value below the sigma is the start and the counter, the value above is where you stop, and the expression to the right is what you add each step. So ∑ from i=1 to 5 of i means 1 + 2 + 3 + 4 + 5 = 15.
How do I do a summation in code or Excel?
Use a loop or a sum function, not the ∑ symbol: sum(range(1, n+1)) in Python, =SUM(A1:A10) in Excel. The sigma maps directly onto a for loop with a running total.
How do I write ∑ in HTML?
Use ∑ or ∑ (the Greek Σ is Σ). In a URL, ∑ is percent-encoded as %E2%88%91.
