Roman numerals are a numeral system of ancient Rome based on letters of the alphabet, which are combined to signify the sum of their values. The first ten Roman numerals are:

I, II, III, IV, V, VI, VII, VIII, IX, X

The Roman numeral system is decimal but not directly positional and does not include a zero. It is a cousin of the Etruscan numerals , and the letters derive from earlier non-alphabetical symbols; over time the Romans came to identify the symbols with letters of their Latin alphabet . The system was modified slightly during the Middle Ages to produce the system used today.

Roman numerals are commonly used in numbered lists (such as the outline format of an article), clock faces, pages preceding the main body of a book, chord triads in music analysis, the numbering of movie publication dates, months of the year, successive political leaders or children with identical names, and the numbering of annual events.

For arithmetic involving Roman numerals, see Roman arithmetic and Roman abacus.

Roman numerals are based on seven symbols: a stroke (identified with the letter I) for a unit, a chevron (identified with the letter V) for a five, a cross-stroke (identified with the letter X) for a ten, a C (identified as an abbreviation of Centum) for a hundred, etc.:

Symbols are iterated to produce multiples of the decimal (1, 10, 100, 1000) values, with V, L, D substituted for a multiple of five, and the iteration continuing: I "1", II "2", III "3", V "5", VI "6", VII "7", etc., and the same for other bases: X "10", XX "20", XXX "30", L "50", LXXX "80"; CC "200", DCC "700", etc. At the fourth iteration, a subtractive principle may be employed, with the base placed before the higher base: IIII or IV "4", VIIII or IX "9", XXXX or XL "40", LXXXX or XC "90", CCCC or CD "400", DCCCC or CM "900".

The Romans only used what we now call capital (upper case) letters. In the Middle Ages, minuscule (lower case) letters were developed, and these are commonly used for Roman numerals: i, ii, iii, iv, etc. Also in medieval use was the substitution of j for a final i to end numbers, such as iij for 3 or vij for 7. This was not a separate letter, but merely a swash variant of i. It is used today, especially in medical prescriptions , to prevent tampering with the numbers after they are written.

For large numbers (4000 and above), a bar can be placed above a base numeral, or parentheses placed around it, to indicate multiplication by 1000, although the Romans themselves often just wrote out the "M"s:

• V or (V) for five thousand
• X or (X) for ten thousand
• L or (L) for fifty thousand
• C or (C) for one hundred thousand
• D or (D) for five hundred thousand
• M or (M) for one million

The parentheses are more versatile; (II) is synonymous with MM, but *II is not found.

The basic multiples of Roman numerals thus follow a pattern:

	×1	×2	×3	×4	×5	×6	×7	×8	×9
Ones	I	II	III	IV	V	VI	VII	VIII	IX
Tens	X	XX	XXX	XL	L	LX	LXX	LXXX	XC
Hundreds	C	CC	CCC	CD	D	DC	DCC	DCCC	CM
Thousands	M	MM	MMM	IV	V	VI	VII	VIII	IX
Ten thousands	X	XX	XXX	XL	L	LX	LXX	LXXX	XC
Hundred thousands	C	CC	CCC	CD	D	DC	DCC	DCCC	CM

A practical way to write a Roman number is to consider the modern Arabic numeral system, and separately convert the thousands, hundreds, tens, and ones as given in the chart above. So, for instance, 1234 may be thought of as "one thousand and two hundreds and three tens and four", obtaining M (one thousand) + CC (two hundreds) + XXX (thirty) + IV (four), for MCCXXXIV. Thus eleven is XI (ten and one), 32 is XXXII (thirty and two) and 2009 is MMIX (two thousand and nine). Note that the subtractive principle is not extended beyond the chart, and VL is not used for 45, which can only be forty (XL) and five (V), or XLV.