investigation / determination
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investigation
The official examination of a matter, especially by authorities such as the police or the public prosecutor's office, in order to find facts or responsible persons. Often used in the plural.
Die Polizei hat die Ermittlungen in dem Fall aufgenommen.
The police have opened the investigation into the case.
determination / calculation
The determination or calculation of a value, quantity, or result.
Die Ermittlung des genauen Bedarfs ist der erste Schritt der Planung.
Determining the exact need is the first step in planning.
'Die Ermittlung' (the investigation/determination) comes from the verb 'ermitteln' (to determine/investigate). If you know the verb, you also understand the noun: it is about finding out or determining something.
Die Polizei ermittelt den Täter.
The police are investigating the perpetrator.
The context makes the meaning clear: if it is about the police, a crime, or a case, it means an investigation. If it is about numbers, data, or costs, it means a calculation.
Die Ermittlung im Fall des Diebstahls dauert an.
The investigation in the theft case is ongoing.
In the meaning 'police investigation', the plural 'die Ermittlungen' (the investigations) is almost always used. The singular is very rare in this context.
Die Staatsanwaltschaft hat die Ermittlungen eingestellt.
The public prosecutor's office has closed the investigation.
In connection with police investigations, 'Ermittlungen' (investigations) is often combined with the verbs 'aufnehmen' (to open/resume), 'einleiten' (to initiate), 'führen' (to conduct), or 'einstellen' (to close/discontinue).
Nach dem Hinweis eines Zeugen wurden die Ermittlungen wieder aufgenommen.
After a witness's tip, the investigation was resumed.
In the meaning 'calculation', a genitive or 'von' + dative often follows in order to specify exactly what is being calculated or determined.
Die Ermittlung des richtigen Preises ist sehr komplex.
Determining the right price is very complex.
investigation / examination
Untersuchung and Ermittlung can both refer to an official process of clarification. An Untersuchung is the broader examination process and can deal comprehensively with causes or procedures. An Ermittlung typically involves the police or public prosecutor's office specifically seeking reliable facts and those responsible.
Die Staatsanwaltschaft begann Ermittlungen, um die Verantwortlichen für den vermuteten Betrug zu finden.
The public prosecutor's office began an investigation to find those responsible for the suspected fraud.
Die Behörde begann eine umfassende Untersuchung der Abläufe nach dem Betrugsverdacht.
The authorities began a comprehensive investigation into the procedures after the suspicion of fraud.
