sich verrechnen
to miscalculate
To make a mistake when calculating, so that the result is wrong.
Entschuldigung, ich habe mich verrechnet, die Summe ist 15 Euro, nicht 14.
Sorry, I miscalculated; the total is 15 euros, not 14.

to miscalculate / offset
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to miscalculate
To make a mistake when calculating, so that the result is wrong.
Entschuldigung, ich habe mich verrechnet, die Summe ist 15 Euro, nicht 14.
Sorry, I miscalculated; the total is 15 euros, not 14.

'Verrechnen' is an inseparable verb. The prefix 'ver-' always remains attached to the stem 'rechnen' (to calculate). It often indicates that something is done incorrectly ('sich verrechnen', to miscalculate) or that a transaction is completed.
Ich glaube, der Kassierer hat sich verrechnet.
I think the cashier miscalculated.
In the meaning 'einen Rechenfehler machen' (to make a calculation error), the verb must always be used reflexively: 'sich verrechnen' (to miscalculate). The subject of the sentence is the person who makes the mistake.
Pass auf, dass du dich bei der Addition nicht verrechnest.
Be careful not to miscalculate during the addition.
When amounts are offset against each other, the structure 'etwas (accusative) mit etwas (dative) verrechnen' is used. This is typical in financial or business contexts.
Das Pfand für die Flaschen können wir direkt mit Ihrem Einkauf verrechnen.
We can offset the deposit for the bottles directly against your purchase.
The meaning 'etwas in Rechnung stellen' (to invoice something / to charge for something) is mainly common in Austria and southern Germany. In other parts of Germany, people would more likely say 'berechnen' or 'in Rechnung stellen'.
Der Elektriker hat mir für die Anfahrt 50 Euro verrechnet.
The electrician charged me 50 euros for the trip.
to calculate / to expect
'rechnen' and 'sich verrechnen' can easily be confused because both have to do with numbers and results. 'rechnen' simply means solving a mathematical problem or calculating something. The result can be right or wrong. 'sich verrechnen', on the other hand, means making a mistake when calculating. The word is reflexive: you say 'ich habe mich verrechnet' (I miscalculated). If you only mean the activity, use 'rechnen'. If you mean the mistake, use 'sich verrechnen'.

Bei der Rechnung hat sich Tom verrechnet und zehn Euro zu wenig bezahlt.
Tom miscalculated the bill and paid ten euros too little.
Im Kopf rechne ich kurz aus, wie viel der Einkauf kostet.
I quickly calculate in my head how much the shopping costs.