Können vs. dürfen
The German modal verbs können and dürfen are often both translated as can in English, which can be confusing. However, they have distinct meanings: können relates to ability or possibility, while dürfen relates to permission.
Können
A1The word können primarily expresses an ability, a skill, or a possibility. It answers the question Am I able to do this? or Is it possible for this to happen?. In colloquial German, it is also frequently used to ask for permission, much like can is used in English.
Ich kann sehr gut schwimmen.
(I can swim very well.)
Er kann fließend Japanisch sprechen.
(He can speak fluent Japanese.)
Es kann heute Nachmittag regnen.
(It can rain this afternoon.)
Wir können später darüber reden.
(We can talk about it later.)
Kannst du mir bitte helfen?
(Can you please help me?)
Dürfen
A2The word dürfen expresses permission or allowance. It is used to ask if something is permitted or to state that something is allowed. Its negated form, nicht dürfen, means that something is forbidden.
Darf ich hier parken?
(May I park here?)
Du darfst das letzte Stück Kuchen haben.
(You may have the last piece of cake.)
Kinder dürfen diesen Film nicht sehen.
(Children are not allowed to watch this movie.)
In diesem Bereich dürfen Hunde ohne Leine laufen.
(In this area, dogs are allowed to run without a leash.)
Man darf während der Prüfung nicht sprechen.
(One is not allowed to speak during the exam.)
Summary
In short, the core difference is ability versus permission. Use können when you are talking about being physically or mentally able to do something, or if something is possible. Use dürfen when you are talking about having permission or being allowed to do something. A good mental shortcut is to think of können as to be able to and dürfen as to be allowed to.