rau
rough
Describing a surface that is uneven, coarse, and not smooth.
Nach der Arbeit im Garten hatte er raue Hände.
After working in the garden, he had rough hands.

rough
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rough
Describing a surface that is uneven, coarse, and not smooth.
Nach der Arbeit im Garten hatte er raue Hände.
After working in the garden, he had rough hands.

You can recognize the exact meaning of 'rau' (rough) from the noun it describes. A 'raue Hand' (rough hand) is uneven, a 'raues Klima' (harsh climate) is inhospitable, and a 'raue Stimme' (hoarse voice) is hoarse.
Die raue Oberfläche des Steins fühlte sich interessant an.
The rough surface of the stone felt interesting.
In its literal meaning, 'rau' (rough) often describes surfaces. Typical combinations are 'raue Hände' (rough hands), 'raue Haut' (rough skin), 'raues Holz' (rough wood), or 'rauer Stoff' (rough fabric).
Für diese Arbeit brauchst du Handschuhe, sonst bekommst du raue Hände.
You need gloves for this work, otherwise you'll get rough hands.
In connection with nature, 'rau' (harsh) describes inhospitable and stormy conditions. Common phrases are 'ein raues Klima' (a harsh climate), 'eine raue See' (a rough sea), or 'ein rauer Wind' (a harsh wind).
Die Seefahrer kämpften gegen die raue See.
The sailors fought against the rough sea.
When a voice is 'rau' (hoarse), it sounds hoarse or scratchy. The reason for it is often mentioned, for example 'vom Schreien' (from shouting), 'vom Singen' (from singing), or 'durch eine Erkältung' (because of a cold).
Seine Stimme ist von der Erkältung noch immer ganz rau.
His voice is still completely hoarse from the cold.
The expression 'raue Schale, weicher Kern' (rough shell, soft core) describes a person who seems crude or unfriendly on the outside but actually has a good character.
Lass dich von seiner Art nicht täuschen. Er hat eine raue Schale, aber einen weichen Kern.
Don't be fooled by his manner. He has a rough exterior but a soft heart.
The phrase 'in rauen Mengen' means 'a great deal' or 'in large quantities'. It is a fixed combination and is often used for things like food, drinks, or other consumer goods.
Auf der Party gab es Essen und Trinken in rauen Mengen.
At the party, there was food and drink in large quantities.
fine
'fein' and 'rau' form a clear contrast when talking about surfaces or material. 'fein' describes something very small, thin, or delicate, for example 'feiner Sand' (fine sand) or 'feines Mehl' (fine flour). 'rau' describes a surface that is uneven, coarse, or not smooth. So the difference is: 'fein' tends to feel soft, small, or smooth; 'rau' tends to feel scratchy or coarse.

Nach der Renovierung war die Wand noch rau und musste geschliffen werden.
After the renovation, the wall was still rough and had to be sanded.
Für den Kuchen braucht man sehr feinen Zucker.
You need very fine sugar for the cake.