
die Härte
severity
Great strictness or relentlessness in acting or judging.
Der Richter entschied mit aller Härte des Gesetzes.
The judge ruled with the full severity of the law.
hardness / severity
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severity
Great strictness or relentlessness in acting or judging.
Der Richter entschied mit aller Härte des Gesetzes.
The judge ruled with the full severity of the law.

hardness
The physical property of a material that indicates how resistant it is to being penetrated by another object.
Diamant ist bekannt für seine extreme Härte.
Diamond is known for its extreme hardness.

toughness
The personal quality of being resilient, tough, and resistant in the face of difficulties or pain.
Trotz der Verletzung zeigte die Sportlerin eine bewundernswerte Härte und spielte weiter.
Despite the injury, the athlete showed admirable toughness and kept playing.

ordeal
Colloquially, a very difficult, exhausting, or unpleasant situation.
Die Prüfung war eine echte Härte, aber ich habe sie bestanden.
The exam was a real ordeal, but I passed it.
'Die Härte' (hardness/severity) is the noun corresponding to the adjective 'hart' (hard). All meanings of the noun derive from the basic idea of 'being hard', whether with materials, in character, or in a situation.
Der Stein ist sehr hart.
The stone is very hard.
In the meaning of 'Strenge' (strictness/severity), 'Härte' (severity) is often used in formal or legal contexts. A fixed expression is 'mit aller Härte' (with full severity).
Die Polizei kündigte an, mit aller Härte gegen die Kriminalität vorzugehen.
The police announced that they would take action against crime with full severity.
When it is about the physical property, you will often find the word 'Härte' (hardness) together with materials such as 'Stahl' (steel), 'Glas' (glass), or 'Diamant' (diamond), or in technical descriptions.
Die Härte von Stahl kann durch verschiedene Verfahren erhöht werden.
The hardness of steel can be increased through various processes.
When 'Härte' (toughness) describes a character trait, the verb 'zeigen' (to show) is often used. The phrase 'Härte zeigen' means that someone is emotionally strong and resilient.
In dieser schwierigen Verhandlung musste sie Härte zeigen.
In this difficult negotiation, she had to show toughness.
The colloquial meaning is often used as an exclamation: 'Das ist die Härte!' This expresses that you find something unbelievable or outrageous.
Er hat mein Fahrrad genommen, ohne zu fragen. Das ist die Härte!
He took my bike without asking. That's outrageous!
difficulty
Eine Schwierigkeit (a difficulty) is a problem that complicates an action and must be overcome. Eine Härte (a hardship) is, by contrast, a particularly burdensome or unpleasant situation that someone has to endure. Schwierigkeit is appropriate for a solvable obstacle, while Härte is more suitable for a severe personal burden.

Die Nachtschicht ohne eine einzige Pause war eine besondere Härte für das Personal.
The night shift without a single break was a particular hardship for the staff.
Der Personalmangel war die größte Schwierigkeit bei der Nachtschicht.
The staff shortage was the biggest difficulty during the night shift.