calculation
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calculation
The process by which a result or value is determined through mathematical operations; a calculation.
Die genaue Berechnung der Kosten dauert noch einige Tage.
The exact calculation of the costs will still take a few days.
'Die Berechnung' (the calculation) is the noun related to the verb 'berechnen' (to calculate). The ending '-ung' turns the action of calculating into a feminine noun.
Er hat die Berechnung noch einmal überprüft.
He checked the calculation again.
The meaning depends strongly on the context. If it is about numbers and formulas, it is a calculation. If it is about human behavior, it often describes a selfish intention. In a business context, it can also mean issuing a charge or invoice.
Die Berechnung des Gewinns war kompliziert.
The calculation of the profit was complicated.
In the mathematical sense, 'Berechnung' (calculation) is often used with prepositions such as 'laut' (according to), 'nach' (according to), or 'gemäß' (in accordance with) to refer to the result. Typical verbs are 'anstellen' (to make/carry out) or 'durchführen' (to perform/carry out).
Laut meiner Berechnung sollten wir genug Geld haben.
According to my calculation, we should have enough money.
In relation to human behavior, 'Berechnung' (calculation) has a strongly negative connotation. It describes an action aimed only at one's own advantage. The phrase 'aus reiner Berechnung' (out of pure calculation) is very typical here.
Er heiratete sie nicht aus Liebe, sondern aus reiner Berechnung.
He married her not out of love, but out of pure calculation.
This meaning is specific to business dealings. It describes the act of charging someone for something. It is often combined with 'von' (of) + type of cost.
Die Berechnung von Versandkosten erfolgt am Ende des Bestellvorgangs.
The charging of shipping costs takes place at the end of the ordering process.
bill / calculation
'die Rechnung' and 'die Berechnung' can be very similar in a mathematical sense. Both can mean that you use numbers to find a result. 'Rechnung' is the more everyday word, especially at school or for simple problems. 'Berechnung' sounds more precise and fits well when a result is determined carefully or using a method. The words can be confused because 'Rechnung' also means a bill or invoice. In a restaurant, you ask for 'die Rechnung' (the bill), not 'die Berechnung'.
Du hast die Berechnung für die Heizkosten noch einmal geprüft.
You checked the calculation for the heating costs again.
Bei dieser Rechnung hat Tom eine Null vergessen.
Tom forgot a zero in this calculation.