diagonal

See also: Diagonal

English

Etymology

From Middle French diagonal, from Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”), from διά (diá, “across”) + γωνία (gōnía, “angle”).

Pronunciation

• (Received Pronunciation, General American) IPA^(key): /daɪ̯ˈæɡ(ə)nəl/

  • Audio (Southern England):

    (file)

    • (Upper Midwestern US, Northwestern US, Canada, /æ/ raising) IPA^(key): /daɪ̯ˈeɪ̯ɡ(ə)nəl/
• (Australia) IPA^(key): /dɑɪ̯ˈæɡənəl/
  • (South Australia, l-vocalization) IPA^(key): /dɑɪ̯ˈæɡənəu̯/
• Rhymes: -æɡənəl, -æɡnəl
• Hyphenation: di‧ag‧o‧nal

Adjective

diagonal (not comparable)

diagonal stairs

1. (geometry) Joining two nonadjacent vertices (of a polygon or polyhedron).
2. Having slanted or oblique lines or markings.
3. Having a slanted or oblique direction.
   • 2011 January 12, Saj Chowdhury, “Liverpool 2 - 1 Liverpool”, in BBC‎^[1]:

     The visitors' undoing was caused by a diagonal ball from the right which was nodded into the six-yard area by Ian Evatt and finished off by Campbell.

4. Of or related to the cater-corner (diagonally opposite) legs of a quadruped, whether the front left and back right or front right and back left.

Synonyms

• (having a slanted or oblique direction): aslant, aslope, slanted, slanting, sloped, sloping

Derived terms

• bidiagonal
• brachydiagonal
• clinodiagonal
• diagonal cutters
• diagonalisation
• diagonality
• diagonalize
• diagonalness
• diagonalwise
• diagrid
• dikes
• dykes
• equidiagonal
• gyrodiagonal
• heptadiagonal
• macrodiagonal
• nondiagonal
• offdiagonal
• orthodiagonal
• pandiagonal
• pentadiagonal
• quasidiagonal
• subdiagonal
• superdiagonal
• tridiagonal

Translations

geometry: joining two nonadjacent vertices

• Arabic: مَائِل (māʔil), قُطْرِيّ (ar) (quṭriyy)
• Bulgarian: диагона́лен (diagonálen)
• Catalan: diagonal (ca)
• Chinese:

  Mandarin: 對角 / 对角 (zh) (duìjiǎo)

• Czech: úhlopříčný (cs), diagonální (cs)
• Dutch: diagonaal (nl)
• Esperanto: diagonala
• Finnish: lävistävä, diagonaalinen (fi)
• French: diagonale (fr)
• German: diagonal (de), schräg (de)
• Greek:

  Ancient Greek: διαγώνιος (diagṓnios)

• Hebrew: אלכסוני (alakhsony)
• Hindi: विकर्ण (hi) (vikarṇ)
• Hungarian: átlós (hu)
• Italian: diagonale (it)
• Japanese: 筋交い (ja) (すじかい, sujikai), 対角 (ja) (たいかく, taikaku)
• Latin: diagonalis, diagonios
• Persian: تراگوشه (tarâguše), تراکنج (tarâkonj)
• Polish: przekątny, skośny (pl), diagonalny (pl)
• Portuguese: diagonal (pt)
• Romanian: diagonal (ro)
• Russian: диагона́льный (ru) (diagonálʹnyj), диагона́ль (ru) f (diagonálʹ)
• Slovak: diagonálny (sk)
• Spanish: diagonal (es)
• Swedish: diagonal (sv)
• Tagalog: hilis
• Ukrainian: діагона́льний (diahonálʹnyj)

having a slanted or oblique direction

• Bulgarian: кос (bg) (kos)
• Catalan: diagonal (ca)
• Chinese:

  Mandarin: 對角 / 对角 (zh) (duìjiǎo)

• Dutch: diagonaal (nl)
• Finnish: vino (fi), viisto (fi), vinottainen
• Hebrew: אלכסוני (alakhsony)
• Hungarian: rézsútos (hu), ferde (hu), átlós (hu)
• Italian: diagonale (it)
• Macedonian: кос (kos)
• Portuguese: diagonal (pt)
• Romanian: diagonal (ro), oblic (ro), înclinat (ro)
• Russian: диагона́льный (ru) (diagonálʹnyj), косо́й (ru) (kosój)
• Spanish: diagonal (es)
• Swedish: diagonal (sv)

of, or relating the legs of quadruped

• Finnish: diagonaalinen (fi)
• Swedish: diagonal (sv)

Noun

diagonal (plural diagonals)

1. (geometry) A line joining non-adjacent vertices of a polygon.
2. Anything forming or resembling such a line, particularly:
   1. (geometry) A line or plane at an oblique angle to another.
   2. (fashion) A line or cut across a fabric at an oblique angle to its sides.
   3. (typography, uncommon) Synonym of slash ⟨/⟩.
      • 1965, Dmitri A. Borgmann, Language on Vacation, page 240:

        Initial inquiries among professional typists uncover names like slant, slant line, slash, and slash mark. Examination of typing instruction manuals discloses additional names such as diagonal and diagonal mark, and other sources provide the designation oblique.

Synonyms

• (oblique line or cut across a fabric): bias
• (oblique punctuation mark): See slash

Antonyms

• (antonym(s) of “oblique punctuation mark”): See backslash

Derived terms

• antidiagonal
• broken diagonal
• Cantor's diagonal argument
• counterdiagonal
• diagonal argument
• diagonal calendar
• diagonal element
• diagonalization
• diagonalize
• diagonally
• diagonal mark
• diagonal matrix
• diagonal morphism
• diagonal scale
• diagonal spread
• leading diagonal
• main diagonal
• minor diagonal
• secondary diagonal
• space diagonal

Translations

something forming or resembling a diagonal line

• Bulgarian: диагонал (bg) m (diagonal)
• Dutch: diagonaal (nl)
• Finnish: diagonaali (fi), lävistäjä (fi), halkaisija (fi), viistorivi (fi), viisto (fi)
• French: diagonale (fr) f
• German: Diagonale (de) f
• Hebrew: אֲלָכְסוֹן (he) m (alakhsón)
• Irish: trasnán m
• Italian: diagonale (it)
• Kazakh: диагональ (dıyagonalʹ)
• Māori: hōkai, hauroki
• Portuguese: diagonal (pt) f
• Romanian: diagonală (ro) f
• Russian: диагона́ль (ru) f (diagonálʹ)
• Swedish: diagonal (sv)
• Ukrainian: перекутня f (perekutnja)

line or cut across a fabric

• Dutch: diagonaal (nl)

slash — see slash

geometry: diagonal line or plane

• Bengali: কর্ণ (bn) (korno)
• Bulgarian: диагонал (bg) m (diagonal)
• Catalan: diagonal (ca) f
• Czech: uhlopříčka f (only line?), diagonála f (only line?)
• Dutch: diagonaal (nl)
• Finnish: lävistäjä (fi)
• Hebrew: אלכסון (he) m (alakhson)
• Hungarian: átló (hu)
• Irish: trasnán m
• Italian: diagonale (it)
• Japanese: 斜め (ja) (naname)
• Latin: linea diagonalis f, diagonalis f, diagonus m
• Māori: hauroki
• Navajo: dinéenáago ídzoh
• Polish: diagonal (pl) m, diagonala f
• Portuguese: diagonal (pt) f
• Romanian: diagonală (ro) f
• Sanskrit: कर्ण (sa) (karṇa)
• Spanish: diagonal (es) f
• Swedish: diagonal (sv)
• Tagalog: hilis

Anagrams

• ganoidal, gonadial

Catalan

Etymology

Borrowed from Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”).

Pronunciation

• IPA^(key): (Northern, Central) [di.ə.ɣuˈnal]
• IPA^(key): (Balearic) [di.ə.ɣoˈnal]
• IPA^(key): (Valencia, Northwestern) [di.a.ɣoˈnal]

• Audio (Barcelona):

  (file)

Adjective

diagonal m or f (masculine and feminine plural diagonals)

1. diagonal

Derived terms

• diagonalment

Noun

diagonal f (plural diagonals)

1. diagonal

Crimean Tatar

Etymology

Borrowed from Russian диагональ (diagonalʹ).

Noun

diagonal

1. diagonal

Declension

Declension of diagonal

	singular	plural
nominative	diagonal	diagonallar
genitive	diagonalnıñ	diagonallarnıñ
dative	diagonalğa	diagonallarğa
accusative	diagonalnı	diagonallarnı
locative	diagonalda	diagonallarda
ablative	diagonaldan	diagonallardan

References

• “diagonal”, in Luğatçıq (in Russian)

Danish

Pronunciation

• IPA^(key): /diaɡonaːl/, [d̥iaɡ̊oˈnæːˀl]

Adjective

diagonal

1. diagonal

Inflection

Inflection of diagonal

	positive	comparative	superlative
indefinite common singular	diagonal	—	—2
indefinite neuter singular	diagonalt	—	—2
plural	diagonale	—	—2
definite attributive1	diagonale	—	—

¹ When an adjective is applied predicatively to something definite,
the corresponding "indefinite" form is used.
² The "indefinite" superlatives may not be used attributively.

Noun

diagonal c (singular definite diagonalen, plural indefinite diagonaler)

1. diagonal

Declension

Declension of diagonal

common gender	singular		plural
	indefinite	definite	indefinite	definite
nominative	diagonal	diagonalen	diagonaler	diagonalerne
genitive	diagonals	diagonalens	diagonalers	diagonalernes

References

• “diagonal” in Den Danske Ordbog

French

Etymology

Learned borrowing from Latin diagōnālis.

Pronunciation

• IPA^(key): /dja.ɡɔ.nal/

• Audio (France (Lyon)):

  (file)

Adjective

diagonal (feminine diagonale, masculine plural diagonaux, feminine plural diagonales)

1. diagonal, transverse, oblique

Derived terms

• diagonalement

Descendants

• → Polish: diagonal

Further reading

• “diagonal”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012

Galician

Etymology

Etymology tree

Proto-Indo-European *dwóh₁

▲

Proto-Indo-European *trísinflu.

Proto-Indo-European *dwísder.

Ancient Greek διά (diá)

Ancient Greek δια- (dia-)

Proto-Indo-European *ǵónu

Proto-Hellenic *gónu

Proto-Hellenic *-ía

Proto-Hellenic *gonwía

Ancient Greek γωνίᾱ (gōníā)

Proto-Indo-European *-yósder.

Ancient Greek -ιος (-ios)

Ancient Greek διαγώνιος (diagṓnios)

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin diagōnālisder.

Galician diagonal

Derived from Latin diagōnālis.

Adjective

diagonal m or f (plural diagonais)

1. diagonal

Derived terms

• diagonalmente

Further reading

• “diagonal”, in Dicionario da Real Academia Galega (in Galician), A Coruña: Royal Galician Academy, 2012–2026

German

Etymology

From Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”).

Pronunciation

• Audio (Germany (Berlin)):

  (file)

• Rhymes: -aːl

Adjective

diagonal (strong nominative masculine singular diagonaler, not comparable)

1. diagonal

Declension

Positive forms of diagonal (uncomparable)

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist diagonal	sie ist diagonal	es ist diagonal	sie sind diagonal
strong declension (without article)	nominative	diagonaler	diagonale	diagonales	diagonale
	genitive	diagonalen	diagonaler	diagonalen	diagonaler
	dative	diagonalem	diagonaler	diagonalem	diagonalen
	accusative	diagonalen	diagonale	diagonales	diagonale
weak declension (with definite article)	nominative	der diagonale	die diagonale	das diagonale	die diagonalen
	genitive	des diagonalen	der diagonalen	des diagonalen	der diagonalen
	dative	dem diagonalen	der diagonalen	dem diagonalen	den diagonalen
	accusative	den diagonalen	die diagonale	das diagonale	die diagonalen
mixed declension (with indefinite article)	nominative	ein diagonaler	eine diagonale	ein diagonales	(keine) diagonalen
	genitive	eines diagonalen	einer diagonalen	eines diagonalen	(keiner) diagonalen
	dative	einem diagonalen	einer diagonalen	einem diagonalen	(keinen) diagonalen
	accusative	einen diagonalen	eine diagonale	ein diagonales	(keine) diagonalen

Further reading

• “diagonal”, in Digitales Wörterbuch der deutschen Sprache‎^[2] (in German)
• “diagonal” in Uni Leipzig: Wortschatz-Lexikon

Polish

Pronunciation

• IPA^(key): /djaˈɡɔ.nal/
• Rhymes: -ɔnal
• Syllabification: dia‧go‧nal

Etymology 1

Etymology tree

Proto-Indo-European *dwóh₁

▲

Proto-Indo-European *trísinflu.

Proto-Indo-European *dwísder.

Ancient Greek διά (diá)

Ancient Greek δια- (dia-)

Proto-Indo-European *ǵónu

Proto-Hellenic *gónu

Proto-Hellenic *-ía

Proto-Hellenic *gonwía

Ancient Greek γωνίᾱ (gōníā)

Proto-Indo-European *-yósder.

Ancient Greek -ιος (-ios)

Ancient Greek διαγώνιος (diagṓnios)

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin diagōnālislbor.

French diagonalbor.

Polish diagonal

Borrowed from French diagonal.

Noun

diagonal m inan

1. (textiles) cavalry twill
2. (mining) diagonal mine walkway
3. (geometry) diagonal line or axis

   Synonym: diagonala

Declension

Declension of diagonal

	singular	plural
nominative	diagonal	diagonale
genitive	diagonalu	diagonali/diagonalów
dative	diagonalowi	diagonalom
accusative	diagonal	diagonale
instrumental	diagonalem	diagonalami
locative	diagonalu	diagonalach
vocative	diagonalu	diagonale

Alternative forms

• djagonal (pre-reform orthography (1936))

Etymology 2

See the etymology of the corresponding lemma form.

Noun

diagonal f

1. genitive plural of diagonala

Further reading

• “diagonal”, in Polish dictionaries at PWN‎^[3] (in Polish)
• Aleksander Zdanowicz (1861), “djagonal”, in Słownik języka polskiego, Wilno 1861
• diagonal in Narodowy Fotokorpus Języka Polskiego

Portuguese

Etymology

Etymology tree

Proto-Indo-European *dwóh₁

▲

Proto-Indo-European *trísinflu.

Proto-Indo-European *dwísder.

Ancient Greek διά (diá)

Ancient Greek δια- (dia-)

Proto-Indo-European *ǵónu

Proto-Hellenic *gónu

Proto-Hellenic *-ía

Proto-Hellenic *gonwía

Ancient Greek γωνίᾱ (gōníā)

Proto-Indo-European *-yósder.

Ancient Greek -ιος (-ios)

Ancient Greek διαγώνιος (diagṓnios)

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin diagōnālislbor.

Portuguese diagonal

Learned borrowing from Latin diagōnālis.

Pronunciation

• (Brazil) IPA^(key): /d͡ʒi.a.ɡoˈnaw/ [d͡ʒi.a.ɡoˈnaʊ̯], (faster) /d͡ʒja.ɡoˈnaw/ [d͡ʒja.ɡoˈnaʊ̯]

 

• (Portugal) IPA^(key): /di.ɐ.ɡuˈnal/ [di.ɐ.ɣuˈnaɫ], (faster) /djɐ.ɡuˈnal/ [djɐ.ɣuˈnaɫ]

• (Portugal) IPA^(key): /di.ɐ.ɡuˈnal/ [di.ɐ.ɣuˈnaɫ], (faster) /djɐ.ɡuˈnal/ [djɐ.ɣuˈnaɫ]
  • (Southern Portugal) IPA^(key): /di.ɐ.ɡuˈna.li/, (faster) /djɐ.ɡuˈna.li/

Adjective

diagonal m or f (plural diagonais)

1. (geometry) diagonal (joining two nonadjacent vertices)
2. diagonal (having a slanted or oblique direction)

Derived terms

• diagonalmente

Noun

diagonal f (plural diagonais)

1. diagonal (something arranged diagonally or obliquely)
2. (geometry) diagonal (diagonal line or plane)

Further reading

• “diagonal”, in Dicionário Aulete Digital (in Portuguese), Rio de Janeiro: Lexikon Editora Digital, 2008–2026
• “diagonal”, in Dicionário Priberam da Língua Portuguesa (in Portuguese), Lisbon: Priberam, 2008–2026

Romanian

Etymology

Etymology tree

Proto-Indo-European *dwóh₁

▲

Proto-Indo-European *trísinflu.

Proto-Indo-European *dwísder.

Ancient Greek διά (diá)

Ancient Greek δια- (dia-)

Proto-Indo-European *ǵónu

Proto-Hellenic *gónu

Proto-Hellenic *-ía

Proto-Hellenic *gonwía

Ancient Greek γωνίᾱ (gōníā)

Proto-Indo-European *-yósder.

Ancient Greek -ιος (-ios)

Ancient Greek διαγώνιος (diagṓnios)

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin diagōnālislbor.

French diagonalbor.

Romanian diagonal

Borrowed from French diagonal.

Adjective

diagonal m or n (feminine singular diagonală, masculine plural diagonali, feminine/neuter plural diagonale)

1. diagonal

Declension

Declension of diagonal

		singular			plural
		masculine	neuter	feminine	masculine	neuter	feminine
nominative- accusative	indefinite	diagonal		diagonală	diagonali	diagonale
	definite	diagonalul		diagonala	diagonalii	diagonalele
genitive- dative	indefinite	diagonal		diagonale	diagonali	diagonale
	definite	diagonalului		diagonalei	diagonalilor	diagonalelor

Spanish

Etymology

Etymology tree

Proto-Indo-European *dwóh₁

▲

Proto-Indo-European *trísinflu.

Proto-Indo-European *dwísder.

Ancient Greek διά (diá)

Ancient Greek δια- (dia-)

Proto-Indo-European *ǵónu

Proto-Hellenic *gónu

Proto-Hellenic *-ía

Proto-Hellenic *gonwía

Ancient Greek γωνίᾱ (gōníā)

Proto-Indo-European *-yósder.

Ancient Greek -ιος (-ios)

Ancient Greek διαγώνιος (diagṓnios)

Proto-Indo-European *h₂el-

Proto-Indo-European *-is

Proto-Indo-European *h₂élisder.?

Proto-Italic *-ālis

Latin -ālis

Latin diagōnālisder.

Spanish diagonal

Derived from Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”) + Latin -ālis.

Pronunciation

• IPA^(key): /djaɡoˈnal/ [d̪ja.ɣ̞oˈnal]
• Rhymes: -al
• Syllabification: dia‧go‧nal

Adjective

diagonal m or f (masculine and feminine plural diagonales)

1. diagonal

Derived terms

• diagonalmente
• leer en diagonal
• matriz diagonal

Noun

diagonal f (plural diagonales)

1. diagonal

Derived terms

• diagonal principal

Further reading

• “diagonal”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8.1, Royal Spanish Academy [Spanish: Real Academia Española], 15 December 2025

Swedish

Etymology

From Latin diagōnālis, from Ancient Greek διαγώνιος (diagṓnios, “from angle to angle”).

Adjective

diagonal (not comparable)

1. diagonal

Declension

Inflection of diagonal

Indefinite	positive	comparative	superlative1
common singular	diagonal	—	—
neuter singular	diagonalt	—	—
plural	diagonala	—	—
masculine plural2	diagonale	—	—
Definite	positive	comparative	superlative
masculine singular3	diagonale	—	—
all	diagonala	—	—

¹ The indefinite superlative forms are only used in the predicative.
² Dated or archaic.
³ Only used, optionally, to refer to things whose natural gender is masculine.

Derived terms

• diagonalt

Noun

diagonal c

1. diagonal

Declension

Declension of diagonal

		nominative	genitive
singular	indefinite	diagonal	diagonals
	definite	diagonalen	diagonalens
plural	indefinite	diagonaler	diagonalers
	definite	diagonalerna	diagonalernas

Derived terms

• diagonala