Herzlichen Glückwunsch!

Because herzlichen is the inflected form of the adjective herzlich.

In Herzlichen Glückwunsch!, Glückwunsch is a masculine noun, and this fixed expression uses the accusative singular form. For a masculine noun in the accusative, the adjective takes -en:

• herzlicher Glückwunsch = nominative
• herzlichen Glückwunsch = accusative

So herzlichen is the grammatically correct form in this expression.

Because this is a fixed exclamation or set phrase. German often uses short expressions without a verb, especially in greetings, wishes, and polite formulas.

Compare:

• Guten Morgen!
• Gute Besserung!
• Herzlichen Glückwunsch!

English does the same thing with Congratulations! There is no verb there either, but it still works as a complete expression.

In these short formulaic expressions, German often leaves out the article.

So instead of something fuller, German simply says:

• Herzlichen Glückwunsch!

This is completely normal and idiomatic. You do not need to add einen when using it as a standalone congratulation.

Glückwunsch is a compound noun:

• Glück = luck, happiness, good fortune
• Wunsch = wish

So literally it is something like a wish of good fortune. In actual usage, though, it means congratulation.

German often forms nouns this way by combining smaller words into one compound.

Because German very often combines nouns into a single compound word.

So:

• Glück
  • Wunsch → Glückwunsch

This is extremely common in German. English sometimes writes similar ideas as two words, but German usually joins them into one.

Because the two languages package the idea differently.

In English, congratulations is the normal fixed expression. In German, the usual formula is based on the singular noun der Glückwunsch.

So even though English uses a plural-looking form, German normally says:

• Herzlichen Glückwunsch!

not a plural version.

This is one of those places where a word-for-word translation is not helpful.

A rough learner-friendly pronunciation is:

• HER-ts-li-khen GLUEK-vunsh

A few important points:

• z in German sounds like ts
• w in German sounds like English v
• sch sounds like English sh
• ü has no exact English equivalent; try saying ee while rounding your lips
• the ch in herzlichen is the soft sound heard in ich

So Glückwunsch is not pronounced with an English w sound.

You use it when congratulating someone on a positive event or achievement, for example:

• a birthday
• passing an exam
• a wedding
• a promotion
• a new baby
• winning something

It works in both speech and writing.

For birthdays, both of these are common:

• Herzlichen Glückwunsch zum Geburtstag!
• Alles Gute zum Geburtstag!

Yes. Glückwunsch! is perfectly possible and quite common.

However, it is usually:

• shorter
• more casual
• sometimes a little drier in tone

Herzlichen Glückwunsch! sounds warmer and more complete.

So if you want the safest, most standard version, use Herzlichen Glückwunsch!

Yes, very often.

Common examples:

• Herzlichen Glückwunsch zum Geburtstag! = congratulations/happy birthday
• Herzlichen Glückwunsch zur Hochzeit! = congratulations on the wedding
• Herzlichen Glückwunsch zur bestandenen Prüfung! = congratulations on passing the exam

Here:

• zum = zu dem
• zur = zu der

They introduce the occasion you are congratulating someone on.

Glückwunsch is capitalized because it is a noun, and German capitalizes all nouns.

Herzlichen is capitalized here only because it is the first word of the sentence. Adjectives in German are not normally capitalized just because they are adjectives.