It is the 24th (if Yo is included) letter of the Russian alphabet. It is used both in native Slavic words (and corresponds to Proto-Indo-European *k in certain positions) and in borrowed words:
as a match for the Latin ⟨c⟩ in words of Latin origin, such as цирк (circus), центр (centre),
for the German ⟨z⟩ and ⟨tz⟩, in words borrowed from German, such as цинк (Zink), плац (Platz),
⟨ци⟩ may correspond to Latin ⟨ti⟩ (before vowels), such as сцинтилляция (scintillation).
Unlike most other consonants (but like ⟨ж⟩ and ⟨ш⟩), ⟨ц⟩ never represents a palatalised consonant in Russian (except occasionally in foreign proper names with ⟨ця⟩ or ⟨цю⟩). Since /i/ after unpalatalised consonants becomes [ɨ], the combinations ⟨ци⟩ and ⟨цы⟩ are pronounced identically: [tsɨ]. A notable rule of Russian orthography is that ⟨ц⟩ is seldom followed by ⟨ы⟩, with the following exceptions:
the ending -⟨ы⟩ of the pluralnumber or the genitive case (птица nominative singular → птицы nominative plural or genitive singular),
possessive suffix -⟨ин⟩ is spelled -⟨ын⟩ after ⟨ц⟩ and only then: троицын, курицын,
the suffix is very popular in Russian last names, but spelling varies and both -⟨цын⟩ and -⟨цин⟩ are possible, Ельцин is an example,
the ending of adjectives -⟨ый⟩ (that becomes -⟨ые⟩, -⟨ым⟩, -⟨ыми⟩, -⟨ых⟩ in declension) such as куцый or бледнолицый,
conjugation of a vulgar verb сцать (сцы, сцым, сцыт, сцыте, сцышь) and its prefixed derivatives,
a few other word roots: цыган, цык- (цыкать, цыкнуть), цып- (цыплёнок, цыпки, цыпочки, цып-цып), цыц,
pre-1956 lists contain words such as цыбик, цыбуля, цыгарка, цыдулка, цыкля, цымбалы, цымес, цынга, цыновка, цынубель, цырюльня, цытварный, цыфирь, панцырь etc. (examples taken from Ya. S. Khomutov's spelling dictionary, 1927 but now all those words are spelled with -ци-),
Pinyin's ⟨ci⟩ becomes ⟨цы⟩, and ⟨qi⟩ becomes ⟨ци⟩.
Related letters and other similar characters