agreement / consensus
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agreement
A formal or informal arrangement or contract between two or more parties in which agreement has been reached on certain points.
Die beiden Länder trafen eine Übereinkunft über die gemeinsamen Grenzschutzmaßnahmen.
The two countries reached an agreement on joint border protection measures.
The noun is derived from the verb 'übereinkommen', which means 'sich einigen' (to reach an agreement). It is composed of 'über', 'ein', and 'kommen'. The ending '-kunft' is an old form related to 'kommen' (to come), as also seen in 'Ankunft' (arrival) or 'Zukunft' (future).
Nach langer Diskussion sind sie endlich übereingekommen.
After a long discussion, they finally reached an agreement.
'Übereinkunft' (agreement) is a rather formal word. It is often found in written language, especially in contracts, political reports, or business correspondence.
Die offizielle Übereinkunft wurde von beiden Parteien unterzeichnet.
The official agreement was signed by both parties.
This noun is often combined with the verbs 'treffen' (to make/reach) or 'erzielen' (to achieve/reach). The phrase 'zu einer Übereinkunft kommen' or 'gelangen' (to come to/reach an agreement) is also very common.
Die Verhandlungspartner konnten eine friedliche Übereinkunft erzielen.
The negotiating parties were able to reach a peaceful agreement.
To name the topic of the agreement, you use the preposition 'über' followed by the accusative.
Sie trafen eine Übereinkunft über die Aufteilung der Kosten.
They reached an agreement on the division of the costs.
comparison / settlement
'der Vergleich' and 'die Übereinkunft' can both refer to a form of agreement. 'die Übereinkunft' is an arrangement or mutual agreement between several sides. It can be formal, but also simpler and more everyday. In this meaning, 'der Vergleich' is more specific: it usually means a legal settlement, especially when a dispute is meant to be ended. If you want to say generally that people have agreed on something, 'Übereinkunft' fits better. If it is about a legal dispute, 'Vergleich' is more precise.
Hast du die Übereinkunft mit deinem Lernpartner schon schriftlich festgehalten?
Have you already put the agreement with your study partner in writing?
Der Vergleich zwischen der Firma und dem Kunden wird morgen unterschrieben.
The settlement between the company and the customer will be signed tomorrow.