skill / dexterity
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dexterity
The ability to carry something out precisely, quickly, and skillfully, especially with the hands.
Ein Uhrmacher braucht eine ruhige Hand und große Geschicklichkeit.
A watchmaker needs a steady hand and great dexterity.
skill / tact
The ability to handle difficult or delicate situations cleverly and diplomatically.
Sie hat die Verhandlungen mit großer diplomatischer Geschicklichkeit geführt.
She conducted the negotiations with great diplomatic skill.
'Geschicklichkeit' (skill/dexterity) is the noun corresponding to the adjective 'geschickt' (skillful). The suffix '-keit' turns adjectives into nouns that describe a quality or ability.
Er ist sehr geschickt, deshalb bewundere ich seine Geschicklichkeit.
He is very skillful, which is why I admire his dexterity.
The context tells you whether manual or social ability is meant. If it is about hands, tools, or sports, manual ability is meant. With negotiations, conversations, or conflicts, social cleverness is meant.
Das Falten der kleinen Papierfiguren erfordert viel Geschicklichkeit.
Folding the small paper figures requires a lot of dexterity.
In connection with manual skills, the word is often used with verbs such as 'erfordern' (to require), 'beweisen' (to demonstrate), or 'trainieren' (to train). Typical adjectives are 'handwerklich' (craft/manual) or 'motorisch' (motor).
Ein Chirurg muss große Geschicklichkeit beweisen.
A surgeon must demonstrate great dexterity.
When it is about social competence, typical combinations are 'diplomatische Geschicklichkeit' (diplomatic skill) or 'taktische Geschicklichkeit' (tactical skill). You can master a situation 'mit Geschicklichkeit' (with skill).
Dank seiner diplomatischen Geschicklichkeit konnte ein Kompromiss gefunden werden.
Thanks to his diplomatic skill, a compromise was found.
ability
Fähigkeit generally means that someone is able to accomplish something. Geschicklichkeit emphasizes skillful execution: either precise and quick work with the hands or clever handling of a difficult situation. Use Fähigkeit for the ability itself, and Geschicklichkeit when the focus is on skilled execution.
Er bewies große Geschicklichkeit, als er die schwierige Aufgabe unter Zeitdruck löste.
He demonstrated great skill when he solved the difficult task under time pressure.
Er hat die Fähigkeit, schwierige Aufgaben auch unter Zeitdruck zu lösen.
He has the ability to solve difficult tasks even under time pressure.
