Min søsters fødselsdag er den tolvte august.

Because min agrees with søster, the noun it belongs to in min søsters.

Danish uses:

• min for singular common-gender nouns
• mit for singular neuter nouns
• mine for plural nouns

So:

• min søster
• mit barn
• mine søstre

In this sentence, min refers to søster, not to fødselsdag.

Søsters is the genitive form of søster. Danish usually shows possession by adding -s directly to the noun, much like English sister's.

Examples:

• min søsters bog = my sister's book
• Peters bil = Peter's car

Unlike English, Danish normally does not use an apostrophe here. An apostrophe is mainly used when the word already ends in s, x, or z, for example Lars' bil.

Because Danish very often combines nouns into one compound word.

Fødselsdag is made from:

• fødsel = birth
• a linking s
• dag = day

So Danish writes this as one word: fødselsdag.

This is very common in Danish. English often uses separate words where Danish prefers one compound.

Because Danish main clauses usually follow the verb-second pattern.

In this sentence, the whole subject Min søsters fødselsdag counts as the first element, and then the finite verb er comes next:

• Min søsters fødselsdag = first element
• er = second element

Here that happens to look the same as English word order, but it fits a broader Danish rule.

In Danish, full dates are commonly expressed as:

den + ordinal number + month

So:

• den første maj
• den tredje juni
• den tolvte august

Here den is part of the date expression. It is roughly like the in the twelfth of August. In standard Danish, you normally keep den in this kind of phrase.

Because dates use ordinal numbers, not cardinal numbers.

• tolv = twelve
• tolvte = twelfth

When giving a date, Danish uses the ordinal form:

• den tolvte august

If written with numerals, it is usually:

• den 12. august

The period after 12 shows that it is an ordinal number.

Not in this sentence. Den tolvte august is completely normal Danish.

You can also hear:

• den tolvte i august

Both are possible, but the version without i is very common in full dates.

You do use i when the month stands alone:

• i august = in August

Because in Danish, months and days are normally written with lowercase letters unless they begin the sentence.

So Danish writes:

• august
• januar
• mandag

This is different from English, where August would be capitalized.

Yes, it is correct and natural. But another very common way to say the same thing is:

Min søster har fødselsdag den tolvte august.

Both are good, but they focus slightly differently:

• Min søsters fødselsdag er den tolvte august focuses on the birthday as a date.
• Min søster har fødselsdag den tolvte august focuses on your sister having her birthday on that date.

In everyday conversation, the har fødselsdag version is especially common.