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.
Many numbers include hundreds, units and tens. The Roman numeral system being basically decimal, each "place" 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.
As each 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:
- 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 a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval and modern times.
- Inscriptions dating from the Roman period not infrequently use "additive" forms such as IIII and VIIII for "4" and "9" instead of IV and IX. There are even instances of both forms appearing within the same document or inscription. On the numbered gates to the colosseum, for instance, IV seems to have been systematically avoided in favour of IIII, although other "subtractives", such as IX and XL are used.
- 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.
- While in standard usage subtractive notation is limited to use of "adjacent" numerals, so that 98 and 99 (for example) are written XCVIII and XCIX, forms such as IIC and IC are not unknown, perhaps originally from the Latin duodecentum and undecentum (one/two less than a hundred).
An inscription on Admiralty Arch
, London. The number is 1910, for which MCMX
would be more usual.
- Sometimes V and L are not used, with instances such as IIIIII and XXXXXX rather than VI or LX.
- At the beginning 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.