Short answer: Tap any symbol below to copy it. In Word, turn on Math AutoCorrect and type \int for ∫ or \partial for ∂. Anywhere else, type the hex code and press Alt + X — 222B then Alt + X gives ∫.
Calculus notation is compact by design: one character can stand for an operation that takes a paragraph to describe. That compactness is also why the symbols get muddled — ∂ ∆ ∇ δ Δ all descend from the same visual family and mean five different things. There’s a section on that below. For the logic and set notation that usually sits alongside this, see set theory symbols, or browse the full maths collection.
Need something outside maths? The full copy-and-paste symbol keyboard has every mark on one page.
Integrals
| Symbol | Means | Code point | HTML | Word / LaTeX |
|---|---|---|---|---|
| ∫ | integral | U+222B | ∫ | \int |
| ∬ | double integral | U+222C | ∬ | \iint |
| ∭ | triple integral | U+222D | ∭ | \iiint |
| ∮ | contour integral (closed path) | U+222E | ∮ | \oint |
| ∯ | surface integral | U+222F | ∯ | \oiint |
∫ is a stretchy operator, and that has a practical consequence. In proper maths typesetting the integral sign grows vertically to match the height of what it encloses, and its limits sit tucked above and below the hook. The plain Unicode character does none of that — it’s one fixed glyph. Inline, in a sentence, that’s fine. In a displayed equation with a tall fraction, a pasted ∫ will look visibly undersized next to it. That’s the point where you want LaTeX or MathML rather than a character, and there’s markup for both further down.
Derivatives and vector operators
| Symbol | Means | Code point | HTML | Word / LaTeX |
|---|---|---|---|---|
| ∂ | partial derivative | U+2202 | ∂ | \partial |
| ∇ | nabla / del — gradient, divergence, curl | U+2207 | ∇ | \nabla |
| ∆ | increment, “change in” | U+2206 | ∆ | \increment |
| ′ ″ ‴ | first, second, third derivative | U+2032–U+2034 | ′ | \prime |
| ∘ | function composition | U+2218 | ∘ | \circ |
| ⋅ | dot product | U+22C5 | ⋅ | \cdot |
| × | cross product | U+00D7 | × | \times |
The prime marks double as feet and inches notation — that use is covered in the prime symbol guide. In calculus they’re derivative order, and they are not apostrophes: f′(x) uses U+2032, while f'(x) uses a typewriter apostrophe and will sort and search differently.
Series, limits and infinity
| Symbol | Means | Code point | HTML | Word / LaTeX |
|---|---|---|---|---|
| ∑ | summation | U+2211 | ∑ | \sum |
| ∏ | product | U+220F | ∏ | \prod |
| ∐ | coproduct | U+2210 | ∐ | \coprod |
| ∞ | infinity | U+221E | ∞ | \infty |
| → | tends to (in limits) | U+2192 | → | \to |
| ℓ | script small l (lengths, ℓᵖ spaces) | U+2113 | ℓ | \ell |
“lim” itself is just the three letters, set upright rather than italic — there’s no single character for it. In LaTeX that’s \lim, which handles the styling and the subscript placement.
Relations you’ll meet in analysis
| Symbol | Means | Code point | HTML | Word / LaTeX |
|---|---|---|---|---|
| ≡ | identically equal to | U+2261 | ≡ | \equiv |
| ≢ | not identically equal | U+2262 | ≢ | \nequiv |
| ≅ | congruent to | U+2245 | ≅ | \cong |
| ∝ | proportional to | U+221D | ∝ | \propto |
| ∼ | asymptotically similar | U+223C | ∼ | \sim |
| ⌈ ⌉ | ceiling | U+2308 / U+2309 | ⌈ | \lceil \rceil |
| ⌊ ⌋ | floor | U+230A / U+230B | ⌊ | \lfloor \rfloor |
| ∛ ∜ | cube root, fourth root | U+221B / U+221C | ∛ | \cbrt |
For ≈ ≤ ≥ ≠ see comparison symbols; for √ on its own, the square root symbol.
A caution on ∼ and ≈. The tilde operator ∼ (U+223C) is a mathematical relation. The ASCII tilde ~ (U+007E) is a punctuation character that happens to look like it. In a paper, x ~ y and x ∼ y are different characters, and the ASCII one sits on a different baseline in most fonts.
The delta family — five symbols, one shape
This is the part worth reading twice. Five characters look related and mean entirely different things.
| Symbol | Unicode name | Code point | Means |
|---|---|---|---|
| ∆ | Increment | U+2206 | “change in” — ∆x, ∆t |
| Δ | Greek capital letter delta | U+0394 | The Greek letter, and the discriminant |
| δ | Greek small letter delta | U+03B4 | Small quantity, variation, Dirac delta |
| ∂ | Partial differential | U+2202 | Partial derivative |
| ∇ | Nabla | U+2207 | Gradient, divergence, curl |
Three things to take from that table:
∂ is not a stylised d, and it is not a delta. It’s its own character with its own code point, and it exists precisely because ∂f/∂x means something different from df/dx. Typing an italic d and calling it a partial derivative is wrong in the same way that typing Σ for a summation is wrong.
∆ and Δ are genuinely interchangeable in practice. U+2206 Increment exists for the “change in” sense and U+0394 is the Greek letter, but most fonts draw them identically, most authors use whichever their keyboard produced, and both are widely accepted. If you want to be precise, use ∆ for ∆x and Δ for the Greek letter — see the delta symbol guide for the letter’s own story. This is the one pair in this article where being pragmatic is defensible.
∇ is not an upside-down delta, even though that’s how everyone describes it. Its name is nabla, after a Hebrew harp of that shape, and it’s a separate character. Read aloud it’s usually “del”.
Word and Outlook: type them by name
The fastest route in Word, and it’s off by default outside equations:
- File → Options → Proofing → AutoCorrect Options
- Open the Math AutoCorrect tab
- Tick Use Math AutoCorrect rules outside of math regions
- Check Replace text as you type is on, then OK
Now \int + space gives ∫, \partial gives ∂, \infty gives ∞. The commands are the LaTeX ones, so the tables above double as your shortcut list.
Two side effects to expect: Word inserts in Cambria Math, which can carry into the following text — Ctrl + Space resets to the paragraph style. And the trigger space is consumed, so you may need to delete one.
For a real equation rather than a loose symbol, press Alt + = (Windows) or Control + Option + = (Mac) to open the equation editor, where the same commands build properly-sized, properly-stacked notation — including a stretchy integral with its limits in the right place.
Alt + X works anywhere in Word: type 222B, press Alt + X, get ∫. If a digit or a letter a–f sits immediately before the code, put a space first or Word will absorb it.
Windows, Mac and everywhere else
Windows outside Word: classic Alt + 0NNN codes reach only code point 255, and every symbol here except × and ± sits above that — see why Alt codes don’t work. Use Character Map, or copy from the grid above.
Mac: there is no Option shortcut for any of these, and pages that list one have invented it. Open the Character Viewer with Control + Command + Space and search by Unicode name — “integral”, “nabla”, “partial”. For repeated use, add Unicode Hex Input (System Settings → Keyboard → Text Input → Edit → + → Others), then hold Option and type the four-digit hex code.
ChromeOS and Linux: Ctrl + Shift + U, type the hex code, press Enter.
Google Docs: Insert → Special characters, then search by name or draw the shape — the sketch box is unusually good at ∫ and ∂. Docs also has its own equation editor under Insert → Equation, which accepts \int and \partial style commands directly.
Phones: none of these are on the standard keyboards. Copy them, or store the ones you use as text replacements (iPhone: Settings → General → Keyboard → Text Replacement).
In LaTeX, HTML and MathML
The LaTeX commands are in the tables above, used inside maths mode. Full coverage in LaTeX math symbols.
For a symbol inline in prose, a numeric reference or the pasted character is fine:
html
<p>As n → ∞, the sum ∑ converges.</p>
<!-- renders: As n → ∞, the sum ∑ converges. -->For an actual expression, use MathML — this is where the stretchy-operator problem is solved for you:
html
<math display="block">
<mrow>
<msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup>
<msup><mi>x</mi><mn>2</mn></msup>
<mi>d</mi><mi>x</mi>
</mrow>
</math>The <mo> element tells the browser this ∫ is an operator, so it stretches and takes its limits properly, and <msubsup> places the bounds where they belong instead of trailing after the sign.
There’s an accessibility argument too. A screen reader meeting ∫ in prose reads its Unicode name — “integral” — which is correct and useful. It reads an italic d standing in for ∂ as “d”, losing the distinction entirely, and reads Σ used as a summation as “sigma”. Using the right code point isn’t pedantry; it’s the difference between notation that survives being read aloud and notation that doesn’t.
Troubleshooting
| Problem | Fix |
|---|---|
Alt + 0NNN produces nothing | These code points are above 255. Use \command in Word, hex + Alt + X, or copy. × (0215) and ± (0177) are the exceptions |
\int isn’t converting in Word | Tick Use Math AutoCorrect rules outside of math regions under File → Options → Proofing → AutoCorrect Options |
| The integral sign looks too small next to my fraction | ∫ is a stretchy operator and the plain character can’t stretch. Use the equation editor, MathML <mo>, or LaTeX |
| My font changed after inserting | Word switches to Cambria Math. Ctrl + Space returns to normal style |
| Alt + X swallowed the preceding characters | Word takes the hex digits before the cursor. Put a space before the code |
| Symbol shows as a box | Font coverage — ∯, ∐, ∜ and ⌈⌉⌊⌋ are the thinnest. See symbols showing as boxes |
| My ∂ pasted as a plain d | You had an italic d, not U+2202. Copy ∂ from above |
| My ∑ won’t work in a maths tool | You likely have Greek Σ (U+03A3), not ∑ (U+2211) — see set theory symbols |
f'(x) looks wrong in print | That’s a typewriter apostrophe. The prime is ′ (U+2032) |
Which method should you use?
| If you… | Do this |
|---|---|
| Need one symbol now | Copy it from the grid above |
| Write maths in Word regularly | Turn on Math AutoCorrect and learn the \ names |
| Are writing a real equation | The equation editor (Alt + =), not loose characters |
| Are on a Mac | Character Viewer, or add Unicode Hex Input |
| Write papers | LaTeX — see LaTeX math symbols |
| Publish maths on the web | Numeric references inline, MathML for expressions |
| Need the logic and set notation too | Set theory symbols |
For Greek letters as letters — α β θ λ π σ — see the Greek alphabet guide.
Frequently asked questions
How do I type the integral symbol ∫?
In Word with Math AutoCorrect enabled, type \int followed by a space. Otherwise type the hex code 222B and press Alt + X. On a Mac, open the Character Viewer with Control + Command + Space and search “integral”. On ChromeOS or Linux, press Ctrl + Shift + U, type 222B, then Enter. Or copy it from this page.
What is the difference between ∂ and δ and ∆?
They are three separate characters. ∂ (U+2202) is the partial differential, used in partial derivatives such as ∂f/∂x. δ (U+03B4) is the Greek small letter delta, used for small quantities and variations. ∆ (U+2206) is the increment sign, meaning “change in”, as in ∆x. The partial differential is not a stylised d and not a delta.
Is ∇ an upside-down delta?
It looks like one, but it’s a distinct character with its own name: nabla (U+2207), usually read aloud as “del”. It denotes the gradient, and with a dot or cross the divergence and curl. The Greek capital delta Δ is U+0394 and a different character entirely.
Is there an Alt code for calculus symbols?
Almost never. Classic Alt + 0NNN codes only reach code points up to 255, and nearly all calculus symbols sit above that. The multiplication sign × (Alt + 0215) and plus-minus ± (Alt + 0177) are exceptions. For the rest, use Word’s \command shortcuts, hex plus Alt + X, or copy them.
Why does my integral sign look too small?
Because the plain Unicode character is a single fixed glyph, while a properly typeset integral stretches to match the height of the expression it encloses and places its limits above and below the hook. For displayed equations, use Word’s equation editor, MathML, or LaTeX rather than a pasted character.
How do I write derivative primes correctly?
Use the prime character ′ (U+2032) rather than a typewriter apostrophe, so f′(x) rather than f'(x). Double and triple primes for higher derivatives are ″ (U+2033) and ‴ (U+2034). They’re the same characters used for feet and inches — see the prime symbol guide.
Written by Igor R. Tested on Windows 11, macOS, iOS, Android, ChromeOS, Linux, Microsoft Word and Google Docs. Last updated August 2026. Symbol code points follow the Unicode Standard.