
rechnen
to calculate
To solve mathematical problems or perform calculations.
In der Grundschule lernen die Kinder lesen, schreiben und rechnen.
In elementary school, children learn to read, write, and calculate.
to calculate / to expect
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to calculate
To solve mathematical problems or perform calculations.
In der Grundschule lernen die Kinder lesen, schreiben und rechnen.
In elementary school, children learn to read, write, and calculate.

to expect
To expect something, foresee it, or firmly assume that something will happen.
Wir rechnen morgen mit starkem Schneefall.
We expect heavy snowfall tomorrow.

to pay off
To be worthwhile; to be profitable or advantageous.
Die Investition in eine neue Heizung wird sich in wenigen Jahren rechnen.
The investment in a new heating system will pay off in a few years.

to count among
To be counted as belonging to a particular group or category, or to be considered part of it.
Man rechnet ihn zu den besten Autoren seiner Generation.
He is counted among the best authors of his generation.
The verb 'rechnen' changes its meaning fundamentally depending on whether it is used on its own, reflexively, or with a preposition. Always pay attention to the words that directly follow 'rechnen' in order to understand the correct meaning.
Kannst du das im Kopf rechnen?
Can you calculate that in your head?
The expression 'rechnen mit' means 'erwarten' (to expect) or 'voraussehen' (to foresee). The preposition 'mit' always takes the dative.
Die Polizei rechnet mit vielen Demonstranten in der Stadt.
The police expect many demonstrators in the city.
The reflexive form 'sich rechnen' means that something is profitable or worthwhile. The subject of the sentence is the thing that brings the benefit.
Es rechnet sich nicht, für diese kurze Strecke ein Taxi zu nehmen.
It isn't worth taking a taxi for this short distance.
The construction 'jemanden/etwas zu etwas rechnen' means to consider someone or something part of a group. The preposition 'zu' requires the dative here.
Man rechnet dieses Restaurant zu den besten der Stadt.
This restaurant is counted among the best in the city.
to expect
Erwarten and mit etwas rechnen both refer to a future event. Erwarten sounds more like a specific assumption or expectation, while mit etwas rechnen emphasizes planning for a possible development. Use rechnen mit when you take this possibility into practical consideration.

Wir rechnen morgen mit starkem Regen und nehmen einen Schirm mit.
We are expecting heavy rain tomorrow, so we are taking an umbrella.
Wir erwarten morgen starken Regen und bleiben deshalb zu Hause.
We expect heavy rain tomorrow, so we are staying home.