
böse
angry
To be annoyed or angry with someone.
Ich bin böse auf dich, weil du mein Geheimnis verraten hast.
I'm angry with you because you revealed my secret.
angry / evil / bad
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angry
To be annoyed or angry with someone.
Ich bin böse auf dich, weil du mein Geheimnis verraten hast.
I'm angry with you because you revealed my secret.

evil
Morally bad, malicious, or guided by bad intentions.
In dem Film kämpft der Held gegen einen bösen Zauberer.
In the film, the hero fights against an evil wizard.

bad / nasty
Serious, unpleasant, or severe. Often used for injuries, illnesses, or surprises.
Er hat sich beim Skifahren eine böse Verletzung zugezogen.
He suffered a nasty injury while skiing.

naughty
Badly behaved or disobedient. Used mainly in connection with children's behavior.
Wenn du dein Gemüse nicht isst, kommt der böse Wolf.
If you don't eat your vegetables, the big bad wolf will come.
The meaning of 'böse' (angry/evil/bad) depends heavily on the context. In connection with a person, often with 'auf' (at/with) or in the dative, it means 'angry'. Before nouns like 'Hexe' (witch) or 'Plan' (plan), it means 'morally bad'. Before nouns like 'Verletzung' (injury) or 'Überraschung' (surprise), it means 'serious' or 'severe'.
Sei mir nicht böse, dass ich zu spät bin.
Don't be angry with me for being late.
To express that you are angry with someone, there are two common constructions. You can say 'böse auf jemanden sein' (to be angry with someone), with the preposition 'auf' and the accusative, or 'jemandem böse sein' (to be angry with someone), with the person in the dative.
Bist du immer noch böse auf mich?
Are you still angry with me?
In the meaning 'moralisch schlecht' (morally bad), 'böse' (evil) is often used for characters in stories or for bad intentions. Typical combinations are 'der böse Wolf' (the big bad wolf), 'eine böse Hexe' (an evil witch), 'böse Mächte' (evil powers), or 'böse Absichten' (evil intentions).
In vielen Märchen kämpft das Gute gegen das Böse.
In many fairy tales, good fights against evil.
To describe something as 'schlimm' (bad/serious) or 'heftig' (severe/intense), 'böse' (bad/nasty) is often combined with negative events or conditions. Common phrases are 'eine böse Überraschung erleben' (to be in for a nasty surprise), 'eine böse Ahnung haben' (to have a bad feeling), or 'ein böser Sturz' (a bad fall).
Als er die Rechnung sah, erlebte er eine böse Überraschung.
When he saw the bill, he was in for a nasty surprise.
The meaning 'unartig' (naughty) is used almost exclusively when speaking to or about children. It is a typical wording in parenting or in children's stories.
Sei kein böses Kind und iss dein Gemüse auf!
Don't be a naughty child, and finish your vegetables!
heavy / difficult
When talking about injuries, schwer and böse can both express a high degree of severity. Schwer describes the severity in a more objective and neutral way. Böse sounds more evaluative and often more alarming, emphasizing how severe or unpleasant the injury is; schwer is therefore usually more suitable for a neutral statement.

Beim Sturz zog sie sich eine böse Verletzung am Knie zu.
She suffered a nasty knee injury in the fall.
Der Arzt stellte eine schwere Verletzung am Knie fest.
The doctor diagnosed a serious knee injury.