Roman numeric system
Basic decimal pattern
The original pattern for Roman numerals used the symbols I, V, and X (1, 5, and 10) as simple tally marks. Each marker for 1 (I) added a unit value up to 5 (V), and was then added to (V) to make the numbers from 6 to 9:
- I, II, III, IIII, V, VI, VII, VIII, VIIII, X.
The numerals for 4 (IIII) and 9 (VIIII) proved problematic (among other things, they are easily confused with III and VIII), and are generally replaced with IV (one less than 5) and IX (one less than 10). This feature of Roman numerals is called subtractive notation.
The numbers from 1 to 10 (including subtractive notation for 4 and 9) are expressed in Roman numerals as follows:
- I, II, III, IV, V, VI, VII, VIII, IX, X.
The system being basically decimal, tens and hundreds follow the same pattern:
Thus 10 to 100 (counting in tens, with X taking the place of I, L taking the place of V and C taking the place of X):
- X, XX, XXX, XL, L, LX, LXX, LXXX, XC, C.
Note that 40 (XL) and 90 (XC) follow the same subtractive pattern as 4 and 9.
Similarly, 100 to 1000 (counting in hundreds):
- C, CC, CCC, CD, D, DC, DCC, DCCC, CM, M.
Again - 400 (CD) and 900 (CM) follow the standard subtractive pattern.
In the absence of a standard symbols for 5,000 and 10,000 the pattern breaks down at this point - in modern usage M is repeated up to three times. The Romans had several different methods for indicating larger numbers, but for practical purposes Roman Numerals for numbers larger than 3,000 are seldom if ever used nowadays, and this suffices.
- M, MM, MMM.
Many numbers include hundreds, units and tens. The Roman numeral system being basically decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example:
- 39 = "Thirty nine" (XXX+IX) = XXXIX.
- 246 = "Two hundred and forty six" (CC+XL+VI) = CCXLVI.
- 421 = "Four hundred and twenty one" (CD+XX+I) = CDXXI.
As each power of ten (or "place") has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin (and English) speech, thus:
- 160 = "One hundred and sixty" (C+LX) = CLX
- 207 = "Two hundred and seven" (CC+VII) = CCVII
- 1066 = "A thousand and sixty six" (M+LX+VI) = MLXVI.
Roman numerals for large numbers are nowadays seen mainly in the form of year numbers (other uses are detailed later in this article), as in these examples:
The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms highly problematic
- "Classical" inscriptions (those dating dating from the Roman period) not infrequently use IIII for "4" instead of IV. Other "additive" forms, such as VIIII for IX, are also sometimes seen, although they are rarer. On the numbered gates to the colosseum, for instance, IV is systematically avoided in favour of IIII, but other "subtractives" apply, so that gate 44 is labelled XLIIII and gate 49 has XLIX.
An inscription on Admiralty Arch
, London. The number is 1910, for which MCMX
would be more usual.
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
- Clock faces that use Roman numerals normally show 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, Big Ben, uses a "normal" IV.
- XIIX or IIXX are sometimes used for "18" instead of XVIII. The Latin word for "eighteen" is often rendered as the equivalent of "two less than twenty" (duodeviginti) which may be the source of this usage.
- The standard forms for 98 and 99 are XCVIII and XCIX, as described in the "decimal pattern" section above, but these are occasionally rendered as IIC and IC, perhaps originally from the Latin duodecentum and undecentum (two/one less than a hundred).
- Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX.
- Most non-standard numerals other than those described above - such as VXL for 45, instead of the standard XLV are modern and may be due to error rather than being genuine variant usage. In the early years of the 20th century, different representations of 900 (conventionally CM) appeared in several inscribed dates. For instance, 1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, while on the north entrance to the Saint Louis Art Museum, 1903 is inscribed as MDCDIII rather than MCMIII.