
in Erwägung ziehen
to consider
To seriously consider something as a possibility or think about doing something.
Wir ziehen in Erwägung, nächstes Jahr ein Haus zu kaufen.
We are considering buying a house next year.
consideration
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to consider
To seriously consider something as a possibility or think about doing something.
Wir ziehen in Erwägung, nächstes Jahr ein Haus zu kaufen.
We are considering buying a house next year.

consideration
The process of thinking about and weighing different options, reasons, or consequences before a decision is made.
Nach reiflicher Erwägung aller Fakten lehnte sie das Angebot ab.
After careful consideration of all the facts, she turned down the offer.

consideration
A single thought, aspect, or reason that factors into deliberation. It is often used in the plural.
Wirtschaftliche Erwägungen spielten bei der Standortwahl die größte Rolle.
Economic considerations played the biggest role in the choice of location.
'Die Erwägung' (consideration) comes from the verb 'erwägen' (to consider). This verb contains the stem 'wägen', which means 'weigh'. So an 'Erwägung' is figuratively the weighing of reasons and possibilities, just as one compares weights on a scale.
Man muss die Vor- und Nachteile sorgfältig erwägen.
You have to carefully consider the pros and cons.
The word 'Erwägung' (consideration) belongs to formal language. You often find it in business, legal, or academic texts.
Aus finanziellen Erwägungen wurde das Projekt gestoppt.
The project was stopped for financial considerations.
The most common use is the fixed expression 'etwas in Erwägung ziehen' (to consider something). What you are considering can be a noun in the accusative or a subordinate clause, often an infinitive clause with 'zu'.
Ich ziehe einen Jobwechsel ernsthaft in Erwägung.
I am seriously considering changing jobs.
In the meaning of 'process of thinking', the word is often used in the fixed combination 'nach reiflicher Erwägung' (after careful consideration). This means 'after having thought about it long and thoroughly'.
Nach reiflicher Erwägung hat er sich für den anderen Kandidaten entschieden.
After careful consideration, he decided in favor of the other candidate.
When 'Erwägung' (consideration) means a single reason, it is often used in the plural with an adjective. Typical combinations are 'wirtschaftliche Erwägungen' (economic considerations), 'persönliche Erwägungen' (personal considerations), or 'strategische Erwägungen' (strategic considerations).
Bei der Entscheidung spielten vor allem persönliche Erwägungen eine Rolle.
Personal considerations played the main role in the decision.
consideration / thought
Both words can refer to thinking things over before a decision. Überlegung is more general and common in everyday language, while Erwägung sounds more formal and places greater emphasis on weighing several options, reasons, or consequences. Use Überlegung in normal conversation and Erwägung in more formal contexts.

Nach sorgfältiger Erwägung aller Folgen nahm die Leitung das Angebot an.
After carefully considering all the consequences, the management accepted the offer.
Nach kurzer Überlegung nahm Jonas das Angebot an.
After giving it some thought, Jonas accepted the offer.