
ausrechnen
to calculate
To determine a result through arithmetic or calculation.
Kannst du mir schnell ausrechnen, wie viel wir für die Tickets bezahlen müssen?
Can you quickly calculate for me how much we have to pay for the tickets?
to calculate
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to calculate
To determine a result through arithmetic or calculation.
Kannst du mir schnell ausrechnen, wie viel wir für die Tickets bezahlen müssen?
Can you quickly calculate for me how much we have to pay for the tickets?

to reckon
To assess one's chances or the probability of a particular success or outcome.
Bei so starker Konkurrenz rechnete er sich nur geringe Chancen auf den Sieg aus.
With such strong competition, he reckoned he had only a small chance of winning.
'Ausrechnen' (to calculate) is a separable verb. In a main clause, the prefix 'aus' moves to the end. In a subordinate clause or infinitive with 'zu', the verb stays together.
Er rechnet die Gesamtkosten für die Reise aus.
He calculates the total cost of the trip.
The two meanings are easy to distinguish: the reflexive form 'sich etwas ausrechnen' always means to assess one's chances. Without 'sich', it refers to a mathematical calculation.
Ich rechne mir gute Chancen für den Job aus.
I reckon I have a good chance of getting the job.
When calculating, 'ausrechnen' (to calculate) can either take an accusative object or be used with a subordinate clause, often with 'wie viel' (how much), 'was' (what), or 'ob' (whether).
Ich rechne schnell den Rabatt aus.
I'll quickly calculate the discount.
When assessing one's chances, you use the reflexive structure 'sich (dative) etwas (accusative) ausrechnen'. The reflexive pronoun in the dative is crucial here.
Die Mannschaft rechnet sich gute Chancen auf den Sieg aus.
The team reckons it has a good chance of winning.
to calculate / charge
Both verbs refer to determining a numerical result. In everyday language, ausrechnen is the usual form for a specific calculation, whereas berechnen sounds somewhat more formal and emphasizes the calculation or method more strongly. ausrechnen is usually appropriate for a simple exercise, while berechnen is often used in factual texts.

Der Schüler rechnet die Fläche des Rechtecks im Heft aus.
The student calculates the area of the rectangle in his notebook.
Die Ingenieurin berechnet die genaue Fläche des Grundstücks.
The engineer calculates the exact area of the property.