
noch
still / yet
Indicates that a state or action continues up to a certain point in time.
Die Kinder schlafen noch.
The children are still sleeping.
still / yet / another
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still / yet
Indicates that a state or action continues up to a certain point in time.
Die Kinder schlafen noch.
The children are still sleeping.

another / more
Refers to an additional quantity, person, thing, or action.
Möchtest du noch ein Stück Kuchen?
Would you like another piece of cake?

still / yet
Indicates that something will happen or can happen at a later point in time.
Ich rufe dich heute Abend noch an.
I'll call you later this evening.

even
Intensifies a comparison and means that a quality is present to a greater degree.
Die zweite Aufgabe war noch schwieriger als die erste.
The second task was even more difficult than the first.

again
One more time; again.
Könnten Sie die Frage bitte noch einmal wiederholen?
Could you please repeat the question again?

only ... left
Indicates that only a limited remainder of a quantity, amount of time, or possibility is available.
Wir haben nur noch zehn Minuten Zeit.
We only have ten minutes left.

never yet
At no point up to the present.
Ich bin noch nie mit einem Heißluftballon geflogen.
I have never flown in a hot-air balloon.

just barely
Indicates that something succeeds only narrowly or that a limit is almost exceeded.
Wir haben den letzten Zug gerade noch erreicht.
We just managed to catch the last train.

still
Refers to an earlier period when a state existed that has since ended.
Damals war das Dorf noch sehr klein.
Back then, the village was still very small.

what was ... again?
Used in a question when the speaker wants to recall information that was already known.
Wie hieß deine neue Kollegin noch?
What was your new colleague's name again?

however ...
Indicates that a statement applies regardless of how strongly a quality is expressed.
Auch ein noch so sorgfältiger Plan kann scheitern.
Even the most careful plan can fail.
'Noch' (still / yet) usually appears directly before the part it modifies: before a verb part, a quantity expression, an adjective, or a fixed expression. Depending on its position, it can therefore express time, addition, emphasis, or limitation.
Sie möchte noch ein Glas Wasser.
She would like another glass of water.
With a state or action, 'noch' (still / yet) often appears together with a time expression or a point in time. It indicates that something continues to apply up to that point and has not yet ended.
Um Mitternacht war das Büro noch geöffnet.
At midnight, the office was still open.
Before a quantity expression or noun, 'noch' (another / more) shows that something is added to an amount that is already present. It can also appear before an additional action.
Für den Salat brauchen wir noch zwei Tomaten.
We need two more tomatoes for the salad.
In combination with a future or time expression, 'noch' (still / yet) can announce an action that will take place by then or at a later point. The verb often appears with expressions such as 'heute' (today), 'später' (later), or 'diese Woche' (this week).
Ich muss heute noch einen wichtigen Brief abschicken.
I still have to send an important letter today.
Before a comparative adjective, 'noch' (even) intensifies the comparison. It is particularly common before forms ending in '-er' or before intensifying comparative expressions.
Im Winter wird es hier noch kälter als im Herbst.
In winter, it gets even colder here than in autumn.
In 'noch einmal' (again), 'noch' (again) appears before 'einmal' (once) and indicates a repetition. The expression can be used for a request, an instruction, or a repeated action.
Lies den letzten Absatz bitte noch einmal langsam vor.
Please read the last paragraph aloud slowly once again.
In 'nur noch' (only ... left), 'noch' (left) forms a fixed limitation together with 'nur' (only): A quantity, amount of time, or possibility is still available, but only to a limited extent. Numbers or time expressions often follow.
Im Kühlschrank ist nur noch ein Joghurt.
There is only one yogurt left in the refrigerator.
In 'noch nie' (never yet), 'noch' (yet) appears before 'nie' (never) and relates the statement to the entire period up to the present moment. The expression is often used with the present perfect.
Sie hat noch nie bei einem Marathon zugesehen.
She has never watched a marathon before.
In 'gerade noch' (just barely), 'noch' (barely) intensifies the meaning of 'gerade' (just): Something succeeds with very little room to spare or remains narrowly within a limit. The expression often appears with verbs of reaching, managing, or passing.
Mit dem letzten Tropfen konnten wir den Topf gerade noch füllen.
With the last drop, we just managed to fill the pot.
With a past-time expression such as 'damals' (back then) or 'früher' (formerly), 'noch' (still) refers to a state that existed at that earlier time. The wider context often makes it clear that the situation has since changed.
Als ich dort studierte, gab es noch keine direkte Zugverbindung.
When I studied there, there was still no direct train connection.
In a question, 'noch' (again) appears after the question word when the speaker wants to briefly bring already known information back to mind. This makes the question sound like a reminder of an earlier conversation.
Wie war der Name des Restaurants noch, in dem wir waren?
What was the name of the restaurant we went to again?
In 'noch so' (however ...), 'noch' (however) appears before an adjective and shows that the statement applies even when the quality is present to a very high degree. It is often followed by a noun and a general statement about that person or thing.
Ein noch so kleiner Fehler kann das Ergebnis verändern.
Even the smallest mistake can change the result.
more
Mehr and noch can express an additional amount. Mehr mainly emphasizes the larger amount, while noch refers to another portion or addition to what is already present. Use mehr when the amount is important and noch when something is to be added.

Möchtest du noch Suppe in deiner Schüssel?
Would you like some more soup in your bowl?
Möchtest du mehr Suppe in deiner Schüssel?
Would you like more soup in your bowl?