krank
sick
Suffering from an illness; not physically or mentally healthy.
Er kann heute nicht zur Arbeit kommen, er ist krank.
He can't come to work today; he's sick.

sick
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sick
Suffering from an illness; not physically or mentally healthy.
Er kann heute nicht zur Arbeit kommen, er ist krank.
He can't come to work today; he's sick.

'Krank' (sick) is the base word for many important nouns such as 'die Krankheit' (illness) or 'das Krankenhaus' (hospital). If you understand 'krank' (sick), you can more easily work out these related words.
Wegen einer schweren Krankheit musste er operiert werden.
Because of a serious illness, he had to have surgery.
When someone cannot go to work or school because of illness, German uses the fixed expression 'sich krankmelden' (to call in sick). The verb 'krankmelden' is used reflexively here.
Ich fühle mich nicht gut, ich glaube, ich melde mich für heute krank.
I don't feel well; I think I'll call in sick for today.
The verb 'kranken' is always used with the preposition 'an' and the dative. It metaphorically describes a fundamental problem or deficiency in a system or organization, not a person.
Viele Unternehmen kranken an einer veralteten Organisationsstruktur.
Many companies suffer from an outdated organizational structure.
In colloquial use, 'krank' (sick) can express a negative judgment and then means 'verrückt' (crazy), 'gestört' (disturbed), or 'moralisch seltsam' (morally strange). It often refers to ideas or behavior.
Er kontrolliert ständig ihr Handy, das ist doch krank.
He constantly checks her phone; that's just sick.
In youth slang, 'krank' (sick) often has a positive meaning and expresses that something is extremely good, impressive, or unbelievable. Tone of voice and context make the difference from the negative meaning clear.
Hast du das Tor gesehen? Das war einfach nur krank!
Did you see that goal? That was just sick!
good
'gut' and 'krank' are opposites when talking about someone's physical or emotional state. 'gut' is often used in sentences like 'Mir geht es gut' (I'm doing well), meaning that you feel well. 'krank' means that someone is not healthy and has, for example, pain, a fever, or another illness. So the contrast is not 'good behavior' versus 'sick', but 'feeling well' versus 'being sick'. In questions about how someone is doing, 'gut' is very natural; for an illness, 'krank' is more precise.

Sofia bleibt heute zu Hause, weil sie krank ist.
Sofia is staying home today because she is sick.
Nach ein paar Tagen Ruhe geht es meinem Vater wieder gut.
After a few days of rest, my father is doing well again.