Perpendicular and Parallel Symbols (⊥ ∥): Meaning and How to Type Them

The perpendicular symbol ⊥ means "is at a right angle to": AB ⊥ CD says that line AB meets line CD at exactly 90°. The parallel symbol ∥ means "never meets, same direction": AB ∥ CD says the two lines stay the same distance apart forever. You can type ⊥ as \perp and ∥ as \parallel in LaTeX, insert both from the Character Viewer on a Mac or with Alt + X codes in Word, and copy them from the list below on any device.

This guide covers what each symbol means in geometry, vectors, and logic, the difference between the two Unicode "perpendicular" characters, the easy-to-confuse double pipe used for norms, and how to type every related sign on Windows, Mac, phones, HTML, and LaTeX.

Copy and Paste the Perpendicular and Parallel Symbols

• ⊥ — up tack, used as the perpendicular sign (U+22A5)
• ⟂ — perpendicular, the dedicated geometry character (U+27C2)
• ∥ — parallel to (U+2225)
• ∦ — not parallel to (U+2226)
• ⊤ — down tack, "top" in logic (U+22A4)
• ∠ — angle (U+2220)
• ∡ — measured angle (U+2221)
• ∢ — spherical angle (U+2222)
• ∟ — right angle (U+221F)
• ⊾ — right angle with arc (U+22BE)
• ‖ — double vertical line, used for vector norms (U+2016)

What the Perpendicular Symbol Means

Two lines, rays, or segments are perpendicular when they intersect at a right angle. The statement is written with the symbol between the two names:

• AB ⊥ CD — segment AB is perpendicular to segment CD
• ℓ ⊥ m — line ℓ is perpendicular to line m
• The altitude of a triangle is perpendicular to the base it meets: AD ⊥ BC

A small square drawn in the corner of a diagram marks the same relationship visually, and ∟ or ⊾ reproduce that corner mark in text. Perpendicular lines have slopes that are negative reciprocals of each other, so a line with slope 2 is perpendicular to a line with slope −1/2, and a horizontal line is perpendicular to every vertical one.

Orthogonal Vectors

In linear algebra ⊥ widens from lines to vectors and subspaces. Two vectors are orthogonal when their dot product is zero, written u ⊥ v ⟺ u · v = 0. The symbol also names the orthogonal complement: if W is a subspace of V, then W⊥ (read "W perp") is the set of every vector in V that is orthogonal to all of W. The superscript position is the clue that you are looking at a complement rather than a relation between two objects.

⊥ and ⟂: Two Code Points for One Sign

Unicode has two characters that look like an inverted T. U+22A5 ⊥ is named UP TACK and lives in the Mathematical Operators block; it is the one every keyboard shortcut, Alt code, and LaTeX command produces, and it is what you should use for "perpendicular" in ordinary writing. U+27C2 ⟂ is named PERPENDICULAR and was added later in the Miscellaneous Mathematical Symbols-A block so that geometry could have a relation symbol distinct from the logic constant. Most fonts draw them identically, so the practical difference is small: use ⊥ unless a style guide or a Unicode-aware math font (unicode-math in LuaLaTeX or XeLaTeX maps \perp to U+27C2) asks for the other.

The Up Tack in Logic and Type Theory

Outside geometry, ⊥ is the constant false (also called "bottom" or "falsum"), and its mirror ⊤ is true ("top" or "verum"). In lattice theory ⊥ and ⊤ are the least and greatest elements. The symbol is the same U+22A5 character in every case; only the context tells you whether you are reading about right angles or about falsehood.

What the Parallel Symbol Means

Lines are parallel when they lie in the same plane and never intersect, no matter how far they are extended. Parallel lines have equal slopes, and a transversal crossing them creates equal corresponding angles, which is the fact most parallel-line proofs rely on.

• AB ∥ CD — segment AB is parallel to segment CD
• ℓ ∥ m — line ℓ is parallel to line m
• ∦ negates the statement: ℓ ∦ m means the lines are not parallel and will meet somewhere

Vectors are parallel when one is a scalar multiple of the other, so u ∥ v means u = kv for some nonzero k. Physics uses the same symbol for components: E∥ is the part of a field parallel to a surface, and E⊥ is the part perpendicular to it, the pair you see in boundary conditions for electromagnetism.

∥ Versus the Norm Bars ‖

The parallel sign ∥ (U+2225) is a relation, like = or <, and it belongs between two objects. The double vertical line ‖ (U+2016) is a delimiter that wraps a single object, as in ‖v‖ for the length of a vector or ‖A‖ for a matrix norm. The two characters look alike, and many people type the parallel sign by hitting the pipe key twice, which is a third thing again: || is two ASCII vertical bars (U+007C), which programming languages read as logical OR. In LaTeX the distinction is enforced by the commands: \parallel is a relation with space on both sides, while \| (identical to \Vert) is an ordinary symbol with no relation spacing, so \|v\| hugs its contents. Writing x \| y to mean "x is parallel to y" typesets with the wrong spacing and reads as a norm to anyone skimming the equation.

How to Type the Perpendicular and Parallel Symbols

Windows: Neither symbol is in the Windows-1252 code page, so there is no four-digit Alt code that works everywhere. The reliable route is Word's Alt + X trick: type the hex code 22A5 and press Alt + X to convert it into ⊥, or 2225 for ∥. In Word, WordPad, and most Office apps, holding Alt and typing the decimal value 8869 (for ⊥) or 8741 (for ∥) on the numeric keypad also works because those apps interpret long Alt codes as Unicode. In Word's Insert → Symbol dialog, set the subset to Mathematical Operators and both symbols sit next to each other.

Mac: There is no Option-key shortcut for either sign. Open the Character Viewer with Control + Command + Space, type "perpendicular" or "parallel" into the search box, and double-click the result. If you use the symbols often, add a text replacement in System Settings → Keyboard so that typing ;perp expands to ⊥.

iPhone and Android: The stock keyboards do not include ⊥ or ∥. Paste them from this page, or set up a text replacement in Settings → General → Keyboard → Text Replacement on iOS (Gboard has the same option under Dictionary on Android). The ∠ angle symbol is also missing from phone keyboards, so the same workaround applies.

Google Docs and Word: In Google Docs choose Insert → Special characters and search for "perpendicular" or "parallel", or draw the shape in the search box. In Word use Insert → Symbol → More Symbols, or type the Unicode value and press Alt + X. Both apps also accept the symbols in their equation editors, where typing \perp or \parallel followed by a space converts to the symbol.

Perpendicular and Parallel in LaTeX

\perp and \parallel are defined by the LaTeX kernel and work in any math environment. \bot prints the same ⊥ glyph but is classified as an ordinary symbol rather than a relation, so A \bot B runs the letters together while A \perp B gets proper relation spacing; use \perp for geometry and \bot for the logic constant. \nparallel (not parallel), \measuredangle, and \sphericalangle require the amssymb package. For orthogonal complements write W^{\perp}.

1\documentclass{article}
2\usepackage{amsmath}
3\usepackage{amssymb}
4\begin{document}
5Geometry: $AB \perp CD$, $\ell \parallel m$, and $p \nparallel q$.
6
7Angles: $\angle ABC = 90^{\circ}$, $\measuredangle ABC$, $\sphericalangle ABC$.
8
9Vectors: $\mathbf{u} \perp \mathbf{v} \iff \mathbf{u} \cdot \mathbf{v} = 0$,
10and the orthogonal complement $W^{\perp}$.
11
12Norm versus parallel: $\|\mathbf{v}\| = 1$ but $\mathbf{u} \parallel \mathbf{v}$.
13
14Logic: $\bot$ is false and $\top$ is true; $p \land \neg p \equiv \bot$.
15
16Circuits: $R_{\text{eq}} = R_1 \parallel R_2 = \frac{R_1 R_2}{R_1 + R_2}$.
17\end{document}
Copy

Every command above is math-mode only, so wrap it in $...$ when it appears in a sentence. For a wider tour of relation and geometry symbols with their codes and commands, see https://tools.useoctree.com/symbols/geometry and https://tools.useoctree.com/symbols/relations, and for the degree sign used with angle measures see https://www.useoctree.com/blog/degree-symbol-how-to-type.

Related Symbols

Congruence ≅ and similarity ∼ complete the geometry toolkit; see https://www.useoctree.com/blog/congruent-symbol-meaning-how-to-type for ≅, https://www.useoctree.com/blog/not-equal-sign-meaning-how-to-type for ≠, and https://www.useoctree.com/learn/mathematical-expressions for the basics of math mode.

FAQ

What does ⊥ mean in math?

Between two lines, segments, or vectors, ⊥ means "is perpendicular to": AB ⊥ CD says the two meet at a right angle, and u ⊥ v says the vectors have a dot product of zero. As a superscript, W⊥ is the orthogonal complement of W. Standing alone in logic, ⊥ means false.

What is the difference between ⊥ and ⟂?

They are two Unicode code points for the same shape. ⊥ (U+22A5, "up tack") is the one produced by keyboards, Alt codes, and \perp, and it serves for both geometry and logic. ⟂ (U+27C2, "perpendicular") was added specifically for geometry. Either is acceptable for right angles; ⊥ is far more widely supported.

How do I type the parallel symbol on a keyboard?

In LaTeX write \parallel. In Word type 2225 and press Alt + X, or hold Alt and type 8741 on the numeric keypad. On a Mac open the Character Viewer (Control + Command + Space) and search "parallel". In HTML use ∥. Avoid typing two pipe characters ||, which is a different symbol.

What is the difference between \parallel and \| in LaTeX?

\parallel is a relation symbol meaning "is parallel to" and gets space on both sides. \| is a delimiter used for norms and absolute values of vectors, as in \|v\|, with no relation spacing. They look alike in print but typeset and read differently.

Is ⊥ the same as the right-angle symbol?

Not quite. ⊥ states a relationship between two lines in a formula, while the right angle marks ∟ (U+221F) and ⊾ (U+22BE) reproduce the little square drawn in the corner of a diagram. Use ⊥ in equations and the square in figures.

Writing Geometry Cleanly in Your Documents

Use \perp for right angles and orthogonality, \parallel for parallel lines, and \| only when you are measuring a norm. Octree, the AI LaTeX editor at https://www.useoctree.com, autocompletes these commands as you type and shows the compiled result instantly, so the spacing in AB ⊥ CD comes out right the first time.