gradient

See also: Gradient and gradiënt

English

Etymology

From Latin gradiēns, present participle of gradior (“to step, to walk”).

Pronunciation

• IPA^(key): /ˈɡɹeɪdiənt/

• Audio (US):

  (file)

• Rhymes: -eɪdiənt

Noun

gradient (plural gradients)

1. A slope or incline.
2. A rate of inclination or declination of a slope.
   • 1950 November, H. P. White, “The Furka-Oberalp Railway”, in Railway Magazine, page 767:

     Just beyond that station the first step is encountered and the rack resorted to, taking the line on a gradient of 1 in 9 over a steeply inclined bridge and through a spiral tunnel.

3. (calculus, of a function) The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.
4. (sciences) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
5. (calculus) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ
6. A gradual change in color; a color gradient; gradation.

Synonyms

• (slope): hill, incline, ramp, slope, grade
• (calculus, ratio of rates of change): slope (of a line), angular coefficient

Coordinate terms

• (calculus, differential operator): curl, divergence, viscid, viscous

Derived terms

• gradient descent
• gradient post
• gradient wind
• pressure gradient
• pressure gradient force
• ruling gradient
• supergradient
• temperature gradient

 

Translations

slope or incline

• Bulgarian: склон (bg) (sklon)
• Czech: sklon (cs) m, svah (cs) m
• Dutch: richtingscoëfficiënt m
• Finnish: rinne (fi), pengerrys (fi)
• French: pente (fr) f
• German: Steigung (de) f, Gefälle (de) n, Neigung (de) f
• Hindi: ढाल (hi) f (ḍhāl)
• Indonesian: tanjakan (id)
• Irish: grádán m
• Macedonian: на́клон m (náklon), стр́мнина f (stŕmnina)
• Maltese: pendil m, mejla f
• Maori: panaunga, tāwhatinga
• Norwegian:

  Bokmål: stigning m or f

  Nynorsk: stigning f

• Polish: zbocze (pl) n
• Scottish Gaelic: àrdachadh m
• Serbo-Croatian: nagib (sh) m
• Spanish: gradiente (es) f
• Swedish: lutning (sv) c

rate of inclination or declination of a slope

• Bulgarian: наклон (bg) m (naklon)
• Catalan: gradient m
• Czech: sklon (cs) m
• Dutch: verhang (nl)
• Finnish: kaltevuus (fi)
• French: pente (fr)
• German: Steigung (de) f, Gefälle (de) n, Neigung (de) f
• Hindi: प्रवणता (hi) (pravaṇtā)
• Indonesian: gradien (id), kemiringan (id)
• Irish: grádán m
• Macedonian: на́клон m (náklon)
• Maltese: pendil m
• Norwegian:

  Bokmål: stigning m or f

  Nynorsk: stigning f

• Portuguese: gradiente (pt) m
• Scottish Gaelic: àrdachadh m
• Serbo-Croatian: gradijent (sh) m
• Spanish: gradiente (es) f
• Swedish: lutning (sv) c

in calculus

• Armenian: գրադիենտ (hy) (gradient)
• Bulgarian: градиент m (gradient)
• Czech: sklon (cs) m
• Dutch: gradiënt (nl) m
• Finnish: gradientti (fi)
• French: gradient (fr) m
• German: Gradient (de) m
• Greek: εφαπτομένη (el) f (efaptoméni), συντελεστής διεύθυνσης m (syntelestís diéfthynsis)
• Hindi: प्रवणता (hi) (pravaṇtā)
• Hungarian: hradiens
• Indonesian: gradien (id)
• Irish: grádán m
• Italian: gradiente (it) m
• Portuguese: gradiente (pt) m
• Russian: градие́нт (ru) m (gradijént)
• Serbo-Croatian: gradijent (sh) m

in physics

• Armenian: գրադիենտ (hy) (gradient)
• Bulgarian: градиент m (gradient)
• Catalan: gradient m
• Dutch: gradiënt (nl) m
• Finnish: gradientti (fi)
• French: gradient (fr) m
• German: Gradient (de) m
• Hindi: प्रवणता (hi) (pravaṇtā)
• Italian: gradiente (it) m
• Portuguese: gradiente (pt) m
• Russian: градие́нт (ru) m (gradijént)
• Serbo-Croatian: gradijent (sh) m
• Spanish: gradiente (es) m

in vector algebra

• Armenian: գրադիենտ (hy) (gradient)
• Bulgarian: градиент m (gradient)
• Dutch: gradiënt (nl) m
• Finnish: gradientti (fi)
• French: gradient (fr) m
• German: Gradient (de) m
• Italian: gradiente (it) m
• Polish: gradient (pl) m
• Russian: градие́нт (ru) m (gradijént)
• Serbo-Croatian: gradijent (sh) m
• Swedish: gradient (sv) c

change in color

• Finnish: liukuväri
• French: dégradé (fr) m
• Indonesian: gradasi (id)
• Polish: gradient (pl) m
• Portuguese: gradiente (pt) m, degradê (pt) m
• Swedish: färggradient c

Adjective

gradient (not comparable)

1. Moving by steps; walking.
   • 1648, John Wilkins, Mathematical Magick:

     movable and Gradient Automata

2. Rising or descending by regular degrees of inclination.

   the gradient line of a railroad

3. Adapted for walking, as the feet of certain birds.

Anagrams

• atreding, derating, e-trading, gantried, red giant, redating, treading

French

Pronunciation

• Audio:

  (file)

Noun

gradient m (plural gradients)

1. gradient

Further reading

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

Norwegian Bokmål

Etymology

From English gradient, from Latin gradiens.

Noun

gradient m (definite singular gradienten, indefinite plural gradienter, definite plural gradientene)

1. a gradient

References

• “gradient” in The Bokmål Dictionary.
• “gradient” in Det Norske Akademis ordbok (NAOB).

Norwegian Nynorsk

Etymology

From English gradient, from Latin gradiens.

Noun

gradient m (definite singular gradienten, indefinite plural gradientar, definite plural gradientane)

1. a gradient

References

• “gradient” in The Nynorsk Dictionary.

Polish

Etymology

Borrowed from English gradient, from Latin gradiēns.

Pronunciation

• IPA^(key): /ˈɡra.djɛnt/

• Audio:

  (file)

• Rhymes: -adjɛnt
• Syllabification: gra‧dient

Noun

gradient m inan

1. (mathematical analysis) gradient (differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar)
2. gradient (change in color)

Declension

Declension of gradient

	singular	plural
nominative	gradient	gradienty
genitive	gradientu	gradientów
dative	gradientowi	gradientom
accusative	gradient	gradienty
instrumental	gradientem	gradientami
locative	gradiencie	gradientach
vocative	gradiencie	gradienty

Derived terms

adjective

• gradientowy

 

noun phrase

• gradient geotermiczny

 

Further reading

• gradient in Polish dictionaries at PWN

Romanian

Etymology

Borrowed from French gradient.

Noun

gradient m (plural gradienți)

1. gradient

Declension

Declension of gradient

	singular		plural
	indefinite articulation	definite articulation	indefinite articulation	definite articulation
nominative/accusative	(un) gradient	gradientul	(niște) gradienți	gradienții
genitive/dative	(unui) gradient	gradientului	(unor) gradienți	gradienților
vocative	gradientule		gradienților

Slovak

Pronunciation

• IPA^(key): [ˈɡraɟi̯ent]

Noun

gradient m inan (genitive singular gradientu, nominative plural gradienty, genitive plural gradientov, declension pattern of dub)

1. gradient

Declension

Declension of gradient

	singular	plural
nominative	gradient	gradienty
genitive	gradientu	gradientov
dative	gradientu	gradientom
accusative	gradient	gradienty
locative	gradiente	gradientoch
instrumental	gradientom	gradientmi

Further reading

• “gradient”, in Slovníkový portál Jazykovedného ústavu Ľ. Štúra SAV [Dictionary portal of the Ľ. Štúr Institute of Linguistics, Slovak Academy of Science] (in Slovak), https://slovnik.juls.savba.sk, 2024

Swedish

Noun

gradient c

1. (mathematical analysis) gradient; a vector operator

Declension

Declension of gradient

		nominative	genitive
singular	indefinite	gradient	gradients
	definite	gradienten	gradientens
plural	indefinite	gradienter	gradienters
	definite	gradienterna	gradienternas

Anagrams

• indraget, tragedin