
der Betrag
amount
A specific sum of money.
Bitte überweisen Sie den offenen Betrag bis Ende des Monats.
Please transfer the outstanding amount by the end of the month.
amount / absolute value
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amount
A specific sum of money.
Bitte überweisen Sie den offenen Betrag bis Ende des Monats.
Please transfer the outstanding amount by the end of the month.

absolute value
In mathematics, the absolute value of a number, meaning its distance from zero on the number line, always without a sign.
Der Betrag von -15 ist 15.
The absolute value of -15 is 15.
The noun 'der Betrag' (amount) is derived from the verb 'betragen', which means 'to amount to a certain sum'. A 'Betrag' is therefore what something or an invoice amounts to.
Die Reparaturkosten betragen insgesamt 250 Euro.
The repair costs amount to 250 euros in total.
In a financial context, 'Betrag' (amount) is often used with verbs such as 'überweisen' (to transfer), 'bezahlen' (to pay), 'einzahlen' (to deposit), or 'abbuchen' (to debit). Combinations with adjectives such as 'offen' (outstanding), 'fällig' (due), or 'gering' (small/low) are also common.
Der fällige Betrag wird automatisch von Ihrem Konto abgebucht.
The due amount will be automatically debited from your account.
To name an exact sum of money, the formal phrase 'ein Betrag in Höhe von' (an amount of) followed by the dative is often used. This is typical for invoices, offers, and formal letters.
Wir stellen Ihnen einen Betrag in Höhe von 500 Euro in Rechnung.
We will invoice you for an amount of 500 euros.
You can recognize the mathematical meaning from the context. When numbers, calculations, vectors, or negative values are being discussed, it refers to the absolute value without a sign.
In der Physik ist der Betrag einer Geschwindigkeit immer positiv.
In physics, the magnitude of a velocity is always positive.
value
In mathematical statements, Wert and Betrag can both describe a number, but they do not mean exactly the same thing. The value can include the sign, whereas the absolute value indicates only the distance from zero, without a sign. For the number itself, Wert is appropriate; for its unsigned magnitude, Betrag is appropriate.

Der Betrag der Zahl ist sieben, weil das Vorzeichen nicht mitgerechnet wird.
The absolute value of the number is seven because the sign is not included.
Der Wert der Zahl ist in dieser Rechnung minus sieben.
The value of the number is negative seven in this calculation.