勾配|こうばいkoubai[0]heiban (flat)

1. nounslope; incline; gradient; grade; pitch
   屋根やねの勾配こうばいをどうするか決きめるのはとても重要じゅうようです。↗

   It is very important to decide what to do about the slope of the roof.
2. noun, mathslope (of a linear function)
3. noun, math, physicsgradient (vector calculus)

• Synonym傾斜けいしゃNeutralRefers to tilting or leaning, and figuratively to a drift in ideas, as in 「右翼に傾斜」; 「勾配」specifically measures how steep a slope is.
• Synonym傾きかたむきNeutralNative word of wide use: the tilt and its degree, but also tendencies or trends, and in math the slope of a line.
• RelatedスロープNeutralLoanword for a ramp or sloped walkway, e.g. a wheelchair 「スロープ」; it stresses a passable slope rather than its steepness.
• Related坂さかCasualColloquial word for a sloping road as a place, also figuratively an age milestone as in 「五十の坂」; it names the spot, not the grade.
• Related斜面しゃめんNeutralPoints to the sloping ground or surface itself; 「勾配」expresses the degree of tilt instead.
• Related傾斜角けいしゃかくWrittenWritten term for the angle of inclination; 「勾配」is more often given as a ratio or percentage.
• Related傾斜度けいしゃどWrittenWritten, technical term for the degree of incline; close in sense to 「勾配」but used less often.
• Related傾斜面けいしゃめんWrittenWritten term for an inclined plane, as in physics; it names the surface and does not express how steep it is.
• Related法面のりめんWrittenSpecialist written term for a steeply sloped part of land, especially a slope formed by cut-and-fill construction work.
• Antonym平坦へいたんNeutralAntonym: flat, even ground with no rises or falls — the opposite of land that has a 「勾配」.

Use 「勾配」 for how steep a slope is, as in 「急勾配の坂」 or 「屋根の勾配」. For the state of tilting, use 「傾斜」; for a sloped path or ramp, choose 「スロープ」 or the colloquial 「坂」. 「傾き」 is a broad native word; 「斜面」 and 「傾斜面」 name the surface itself; 「傾斜角」, 「傾斜度」 and 「法面」 are written technical terms; the opposite is 「平坦」.

Usage comparisons are AI-assisted and cross-checked by multiple models; for study reference only

1. 地形ちけい等とうにおける水平面すいへいめんに対たいする傾斜けいしゃの程度ていど。
2. スカラー場じょうに対たいして定義ていぎされ、場ばの各かく方向ほうこうへの変化率へんかりつを記述きじゅつする偏微分へんびぶんベクトル場じょう。xyz空間くうかんではgrad,F=∇F=((∂F)/(∂x),(∂F)/(∂y),(∂F)/(∂z))。