verhältnis

Verhältnis is a German noun that denotes a relation between things or people, a proportion or ratio in mathematics, and the state or circumstances under which something exists. The term covers both quantitative relations and qualitative conditions, and it can refer to how elements compare, how a situation stands, or how entities stand to one another. In everyday language, it often appears in compounds such as Lebensverhältnisse (living conditions) or Arbeitsverhältnis (employment relationship).

In mathematics, Verhältnis expresses a quantitative relation between two values. It can be written as a:b or A zu B, and describes a ratio or relative size. When two ratios are equal, they form a proportion. In common math usage, "Verhältnis" is the technical term for the ratio between numbers, while "Quotient" denotes the result of division.

In general usage, "Verhältnis" also means the conditions under which something exists, or the relationship between people, organizations, or things. Phrases such as "im Verhältnis zu" (in relation to) or "das Verhältnis zwischen Angebot und Nachfrage" highlight relative comparisons. "Verhältnis stehen" expresses a connection or correspondence, and "ein gutes Verhältnis zu jemandem haben" describes a favorable personal relationship, while "Arbeitsverhältnis" or "Privatverhältnis" denote specific kinds of relations.

Notes: The term is more formal or neutral than "Beziehung" when referring to people; but in a mathematical context it is the canonical word for ratio and proportionality. The meaning is usually inferred from context, since "Verhältnis" covers many related but distinct senses.