Numerale.
The words that count.

German numerals split into three jobs. Cardinal numbers count → eins, zwei, drei, and they almost never change form. Ordinal numbers put things in order → erste, zweite, dritte, and they behave exactly like adjectives, with all the endings that come with that. A third group, words like viele, einige, and beide, count without giving an exact number, and they follow the same endings as the ordinals.

Cardinal numbers: counting without endings

The numbers from 0 to 12 are individual words, learned one by one.

0	1	2	3	4	5	6	7	8	9	10	11	12
null	eins	zwei	drei	vier	fünf	sechs	sieben	acht	neun	zehn	elf	zwölf

From 13 to 19, every number is built the same way: the unit plus -zehn. drei + -zehn = dreizehn (13), sechs + -zehn = sechzehn (16, the -s of sechs drops), sieben + -zehn = siebzehn (17, the -en of sieben drops).

The tens follow -zig, with two spelling exceptions at the start of the sequence.

20	30	40	50	60	70	80	90
zwanzig	dreißig	vierzig	fünfzig	sechzig	siebzig	achtzig	neunzig

zwanzig (20) and dreißig (30) don't follow the regular -zig pattern exactly, and sechzig and siebzig trim a letter from sechs and sieben before adding -zig. Everything else in that row is fully regular.

Numbers between the tens stack the unit first, then und (and), then the ten. einundzwanzig (21) is, word for word, "one-and-twenty." vierunddreißig is 34, neunundneunzig is 99. Every two-digit number in German follows this pattern, with no exceptions.

Whatever the size of the number, cardinal numbers almost never take an ending. hundert Bücher, tausend Euro → hundert and tausend stay exactly as they are, no matter what they're counting and in almost every case.

eins or ein? Same word, two jobs

There's one cardinal number that breaks the "never changes" rule in everyday use → eins. When eins stands alone, counting up or telling the time, it stays eins. The moment it stands directly before a noun, it becomes ein- and declines exactly like the indefinite article. There's also a rarer, formal exception: without an article, in the genitive, zwei and drei take an ending too → zweier Teilnehmer, dreier Tore.

Use	Example	Form
Counting	eins, zwei, drei...	Stays eins
Telling time	Es ist eins. (It's one o'clock.)	Stays eins
Before a masculine noun, Akkusativ	Ich habeeinenBruder.	einen
Before a feminine noun, Nominativ	Das isteineLampe.	eine
Before a neuter noun, Nominativ	Das isteinBuch.	ein

eins only ever appears on its own. The instant a noun follows, the ending kicks in and eins turns into ein-, following exactly the pattern of the indefinite article.

The full ein- / eine- / einen- table, side by side with kein: ein, eine, kein. The indefinite articles.

Ordinal numbers: now they're adjectives

Ordinal numbers answer "which one in the order": first, second, third. The formation rule is simple: from 2 to 19, add -te to the cardinal number. From 20 upward, add -ste. A handful of small numbers are irregular.

Cardinal	Ordinal	English
eins	erste	1st (irregular)
zwei	zweite	2nd
drei	dritte	3rd (irregular)
vier	vierte	4th
sieben	siebte	7th (drops -en)
acht	achte	8th (only adds -e, already ends in -t)
zwanzig	zwanzigste	20th (-ste begins here)
einundzwanzig	einundzwanzigste	21st

Once an ordinal number is formed, it stops behaving like a number and starts behaving like an adjective. Position decides if it needs an ending, and which one, exactly like any other adjective.

• derersteTag (the first day, Nominativ, weak ending after the definite article)
• denzweitenStock (the second floor, Akkusativ)

Dates use the Dativ. am (a fusion of an + dem) is followed by the ordinal number with the Dativ ending -en.

amdrittenMai (on the third of May)

The full adjective ending system that ordinal numbers plug into: Adjektive. How they describe nouns.

Counting without a number

A last group of words counts without naming an exact number. In the table below they appear without sentence context, so they stay gray. The moment they land in a sentence and carry a case, they pick up the matching color → yellow for Nominativ, green for Akkusativ, and so on.

Word	Meaning
viele	many
wenige	few
einige	some
mehrere	several
einpaar	a couple of
alle	all
beide	both

These words follow the same adjective endings as the ordinals above. vieleschöneTage (many nice days): both viele and schöne carry the plural ending -e. beide is the one to watch: it almost always points at two specific things already mentioned, so anything describing the noun after it takes the weak ending that normally follows a definite article, as in diebeidenjungenBrüder (the two young brothers).