O with Slash (ø Ø): The Nordic Letter, Not the Empty Set

Is Ø the empty set symbol or the diameter sign?

No. The o with slash, Ø, is a letter, ∅ is the empty set and ⌀ is the diameter sign, and Unicode files them in different blocks with different jobs. They only look alike. Whether you call it o with line, o with a slash or o with stroke, the letter is one character: U+00F8, or U+00D8 for the capital.

The table sets the letter beside its look-alikes, with the names and categories from UnicodeData.txt (opens in a new tab) and the notes printed in the Unicode code charts for Latin-1 (opens in a new tab), math operators (opens in a new tab) and technical symbols (opens in a new tab).

Character	Code point	Unicode name	Kind of character	What Unicode's charts and data say
ø	U+00F8	LATIN SMALL LETTER O WITH STROKE	lowercase letter (Ll)	Danish, Norwegian, Faroese, IPA; alias "o slash"
Ø	U+00D8	LATIN CAPITAL LETTER O WITH STROKE	uppercase letter (Lu)	points to ∅ as a different character
∅	U+2205	EMPTY SET	math symbol (Sm)	also "null set"; marks a null morpheme in linguistics
⌀	U+2300	DIAMETER SIGN	other symbol (So)	points to ø and to ∅
Ö	U+00D6	LATIN CAPITAL LETTER O WITH DIAERESIS	uppercase letter (Lu)	decomposes into O + U+0308
ⵁ	U+2D41	TIFINAGH LETTER BERBER ACADEMY YAH	other letter (Lo)	grouped with Ø in the confusables data

Why do people mix them up? Unicode's own security data agrees that they look the same. The confusables list (opens in a new tab) behind UTS #39 (opens in a new tab) reduces Ø, ∅, ⌀ and ⵁ to one skeleton: a capital O with U+0338, the combining long solidus overlay. A spoof checker sees one shape. Search, sorting and spell checking see unrelated characters, and a search for Ø does not find ∅.

The shapes differ in the details. StandardizedVariants.txt (opens in a new tab) defines a "zero with long diagonal stroke overlay form" of ∅ and a "short diagonal stroke form" of the digit 0. Both start from a zero, not from the letter O.

Pick by job. Write ∅ for a set with no members, ⌀ beside a size on a drawing, and ø or Ø inside a Danish, Norwegian or Faroese word.

Is ø a letter or an o with an accent?

ø is a letter. The slash is part of its shape, not a mark added to an o, even if "o with slash through it" is how English describes it. Dansk Sprognævn, the Danish language board, prints the alphabet in Retskrivningsreglerne § 1 (opens in a new tab) as a to z followed by æ, ø and å. The accents that Danish text meets, from the acute to the trema and the tilde, appear in a separate list of signs, and the slash through ø is not on it.

Sorting makes the difference visible. § 4 of the same rules (opens in a new tab) tells Danish writers to ignore accents when they alphabetise, so é, è and ë count as e. No rule moves ø. It keeps its own place after æ.

Unicode draws the same line. In UnicodeData.txt (opens in a new tab), é breaks down into e plus a combining acute, and ö into o plus a combining diaeresis. The ø has no breakdown at all.

Letter	Unicode breaks it into	Left after deleting the marks	How Danish rules file it
é	e + U+0301, combining acute accent	e	as e, the accent ignored
ö	o + U+0308, combining diaeresis	o	as ø, a foreign letter
ø	nothing: no decomposition	ø	as ø, its own letter after æ

This shows up in code. Suppose a program strips accents by converting text to the NFD normalization form (opens in a new tab) and deleting the combining marks. Björn comes out as Bjorn. Bjørn comes out unchanged, because there is no mark to delete. A URL slug or a search key made that way keeps the ø.

Where does ø go in alphabetical order?

An o with a slash goes near the very end of the alphabet. The CLDR rules for Danish (opens in a new tab), Norwegian (opens in a new tab) and Faroese (opens in a new tab) place it after z and æ and before å. The CLDR alphabets of Swedish, Finnish and Icelandic have no ø, and their rules file it as a form of ö.

To see it, we sorted given names from AccentPad's facts, with Olav and Zoltán as plain controls. The sorting was done by the locale-aware compare built into Node.js v26, which runs ICU 78.3 with CLDR 48 data.

Sorting rules	Result, first to last
Danish, Norwegian, Faroese	Olav, Zoltán, Ægir, Örjan, Øystein, Åse
Swedish, Finnish	Olav, Zoltán, Åse, Ægir, Örjan, Øystein
Icelandic	Olav, Zoltán, Ægir, Örjan, Øystein, Åse
German, English	Ægir, Åse, Olav, Örjan, Øystein, Zoltán
Raw code point order	Olav, Zoltán, Åse, Ægir, Örjan, Øystein

Under Danish rules Øystein comes after Zoltán and before Åse, and Örjan joins him under ø, as § 4 prescribes. German and English rules treat ø as an o with a mark, so Øystein files among the O names.

The last row is what a sort by raw character values gives. Å is U+00C5, Æ is U+00C6, Ö is U+00D6 and Ø is U+00D8. By coincidence that matches the Swedish row, so a naive sort can look right to a Swedish reader. A Danish reader expects Åse last, and the naive sort puts the name third.

Is ø the same letter as ö?

ø and ö are two spellings of one vowel, split by a border. Danish, Faroese and Norwegian write ø. Swedish, Finnish, Icelandic and German write ö. Each side files the other's letter as its own: Danish § 4 sorts ö as ø, and the CLDR rules for Swedish (opens in a new tab), Finnish (opens in a new tab) and Icelandic (opens in a new tab) sort ø as ö. German is the exception: its CLDR rules (opens in a new tab) file ø with plain o.

	The ø side	The ö side
Alphabets in Unicode CLDR	Danish, Faroese, Norwegian	Swedish, Finnish, Icelandic, German, among others
A letter from the other side is filed	ö as ø	ø as ö (Swedish, Finnish, Icelandic)
The sound in IPA	ø is itself the IPA symbol	German schön is /ʃøːn/ in WikiPron
The word for island	Danish ø, Norwegian øy	Swedish ö
Given names in Wikidata	Bjørn, Torbjørn, Søren	Björn, Torbjörn, Sören

The island row comes from Wiktionary's entries for ø (opens in a new tab), øy (opens in a new tab) and ö (opens in a new tab). The same ö entry notes that older Danish ö merged with ø, as when kjöbe became købe.

Why does a search for bjorn not find Bjørn?

Because Danish, Norwegian, Swedish and Finnish search rules treat the o with slash as a letter, so bjorn typed without the slash is a different word. The same rules treat ø and ö as one letter, so a search for Björn does find Bjørn. English search rules ignore both marks and find all three. Each answer below comes from the Node.js compare used for the sort table, set to search mode with accents ignored.

Search for	Text	Danish or Swedish rules	English rules
Björn	Bjørn	found	found
bjorn	Bjørn	not found	found
bjorn	Björn	not found	found

So a Danish user who searches a Swedish list for Bjørn finds Björn, while a guest who types bjorn without the slash finds neither. If your site serves Nordic users, keep the slash in the data and offer the plain o only as an extra search term.

Which o with a line through it do linguists use?

Linguists use two of them, for opposite jobs. In phonetics, ø is a vowel letter: the Latin-1 code chart (opens in a new tab) lists the IPA among its users, and Wiktionary (opens in a new tab) defines the IPA symbol as a close-mid front rounded vowel. In grammar, the empty set ∅ marks something that is not there. The chart for ∅ (opens in a new tab) says linguists use it for a null morpheme or a phonological zero.

So /ʃøːn/, WikiPron's transcription of German schön, holds a vowel you pronounce. A ∅ in a word analysis marks a slot where nothing is pronounced.

A third shape sits close to ø. The Latin-1 chart points from ø to ɵ, U+0275 LATIN SMALL LETTER BARRED O, a separate letter. Its bar runs straight across the middle. The confusables data reduces ɵ to an o with a short stroke overlay, U+0335, and not to the long slash that ø, ∅ and ⌀ share.