There is not, and never has been, an "official", "binding", or universally accepted standard for Roman numerals. Usage in ancient Rome varied greatly and remained somewhat inconsistent in medieval times and later. The "rules" of the system as it is now applied have been established only by general usage over the centuries.
Roman numerals are essentially a decimal or "base 10" number system. Powers of ten – thousands, hundreds, tens and units – are written separately, from left to right, in that order. Different symbols are used for each power of ten, but a common pattern is used for each of them.
The underlying form of this pattern employs the symbols I and V (representing 1 and 5) as simple tally marks, to build the numbers from 1 to 9. Each marker for 1 (I) adds a unit value up to 5 (V), and is then added to (V) to make the numbers from 6 to 9. Finally the unit symbol for the next power completes a "finger count" sequence:
- I, II, III, IIII, V, VI, VII, VIII, VIIII, X.
At some early time the Romans started to use the abbreviated forms IV ("one less than 5") and IX ("one less than 10") for IIII and VIIII, a convention that has been widely, although not universally, used ever since.[a] This convention is called "subtractive" notation,as opposed to the purely "additive" notation of IIII and VIIII. Thus the numbers from 1 to 10 are generally written as
- I, II, III, IV, V, VI, VII, VIII, IX, X.
The multiples of 10, from 10 to 100, are written according to the same pattern, with X, L, and C taking the place of I, V, and X
- X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C.
Note that 40 is usually written XL ("10 less than 50") rather than XXXX, and 90 as XC ("10 less than 100") rather than LXXXX.
Similarly, the multiples of 100, 100 to 1000, are written as
- C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M.
where CD is to be read as "100 less than 500" (that is, 400), and CM as "100 less than 1000" (that is, 900).
Since the system has no standard symbols for 5,000 and 10,000, the only multiples of 1000 that can be represented in subtractive notation are 1,000, 2,000 and 3,000:
- M, MM, MMM.
A number containing several decimal places is represented, as in the Arabic system, by writing its power-of-ten parts — thousands, hundreds, tens and units — in sequence, from left to right, in descending order of value. For example:
- 39 = 30 + 9 = XXX + IX = XXXIX.
- 246 = 200 + 40 + 6 = CC + XL + VI = CCXLVI.
- 789 = 700 + 80 + 9 = DCC + LXXX + IX = DCCLXXXIX.
- 2421 = 2000 + 400 + 20 + 1 = MM + CD + XX +I = MMCDXXI.
Any missing place (represented by a zero in the Arabic equivalent) is omitted, as in Latin (and English) speech:
- 160 = 100 + 60 = C + LX = CLX ("one hundred and sixty").
- 207 = 200 + 7 = CC + VII = CCVII ("two hundred and seven").
- 1009 = 1,000 + 9 = M + IX = MIX ("A thousand and nine")
- 1066 = 1,000 + 60 + 6 = M + LX + VI = MLXVI ("a thousand and sixty six").
Roman numerals for large numbers are nowadays seen mainly in the form of year numbers, as in these examples:
The largest number that can be represented in this notation is 3,999 (MMMCMXCIX).[b]
Use of additive notation
While subtractive notation for multiples of 4 (IV, XL, CD) has been prevalent since Roman times, additive notation (IIII, XXXX, and CCCC continued to be used, including in compound numbers like XXIIII, LXXIIII, and CCCCLXXXX. The additive forms for 9, 90, and 900 (VIIII,LXXXX, and DCCCC,) have also been used, although less frequently.
The two conventions could be mixed in the same document or inscription, even in the same numeral. On the numbered gates to the colosseum, for instance, IIII is systematically used instead of IV, but subtractive notation is used for other digits; so that gate 44 is labelled XLIIII. Isaac Asimov speculates that the use of "IV", as the initial letters of "IVPITER" (the classical Latin spelling of the name of the Roman god Jupiter) may have been felt to have been impious in this context.
Modern clock faces that use Roman numerals still usually employ IIII for four o'clock but IX for nine o'clock, a practice that goes back to very early clocks such as the Wells Cathedral clock of the late 14th century. However, this is far from universal: for example, the clock on the Palace of Westminster tower, "Big Ben", uses a subtractive IV for 4 o'clock.
An inscription on Admiralty Arch
, London. The number is 1910, for which MCMX
would be more usual.
Several monumental inscriptions created in the early 20th century use variant forms for "1900" (usually written MCM). These vary from MDCCCCX - a classical use of additive notation for MCMX (1910), as seen on Admiralty Arch, London, to the more unusual, if not unique MDCDIII for MCMIII (1903),[c] on the north entrance to the Saint Louis Art Museum .
While the subtractive and additive notations seem to have been used interchangibly through history, some other Roman numerals have been occasionally observed that do not fit either system. Some of these variants do not seem to have been used outside specific contexts, and may have been regarded as errors even by contemporaries.
- IIXX was how people associated with the XXII Roman Legion used to write their number. The practice may have been due to a common way to say "twenty-second" in Latin, namely duo et vice(n)sima (literally "two and twentieth") rather than the "regular" vice(n)sima secunda ("twentieth second")..
Epitaph of centurion
Marcus Caelius, showing "XIIX
- Likewise, XIIX was used by officers of the XVIII Roman Legion to write their number. The notation appears prominently on the cenotaph of their senior centurion Marcus Caelius (~45 BC – 9 AD). There does not seem to be a linguistic explanation for this use, although it is one stroke shorter than XVIII.
- On the other hand, "irregular" subtractives like IIIXX for 17 and IIXX for 18 were occasionally used in more modern times. A possible explanation is that the word for 18 in Latin was duodeviginti, literally "two from twenty". Similarly, the word for 19 was undeviginti ("one from twenty"). These ways of saying 18 and 19 have been attributed to influence from the Etruscans, who would say "three from twenty" for 17, "two from twenty" for 18, and "one from twenty" for 19. Apparently, at least one ancient stonecutter mistakenly thought that the IIXX of "22nd Legion" stood for 18, and "corrected" it to XVIII. However, the explanation does not seem to apply to IIIXX, since the Latin word for 17 was septendecim ("seven ten"), and for "17th" was septimus decimus ("seventh tenth").
- Likewise, 98 and 99 are occasionally rendered as IIC and IC instead of XCVIII and XCIX, perhaps reflecting the Latin words duodecentum and undecentum ("two/one from a hundred") for those numbers.
- Sometimes 5 and 50 have been written IIIII and XXXXX instead of V and L; and there are instances such as IIIIII and XXXXXX rather than VI or LX.
Padlock used on the north gate
of the Irish town of Athlone
. "1613" in the date is rendered XVIXIII
, (literally "16, 13") instead of MDCXIII
- There is at least one example (see illustration) of a year number written as two Roman numerals corresponding to the spoken English "sixteen thirteen", or XVI-XIII for 1613. This, and other non-standard numerals other than those described above — such as VXL for 45, instead of the standard XLV — may be due to error rather than being genuine variant usage.
- Not all combinations of symbols used in Roman numerals are intended to be taken numerically. For example "XXX" and "XL" have other connotations besides their values as Roman numerals, while "IXL" more often than not means "I excel", and is in any case not an unambiguous Roman numeral.