# Roman numerals

The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. The system used in antiquity was slightly modified in the Middle Ages to produce the system we use today.

It is based on certain letters which are given values as numerals:

I or i for one,
V or v for five,
X or x for ten,
L or l for fifty,
C or c for one hundred (the initial of centum),
D or d for five hundred, derived from halving the 1,000 Phi glyph (see below)
M or m for one thousand (the initial of mille), originally represented by the Greek letter Φ (Phi).

Roman numerals are commonly used today in numbered lists (in outline format), clockfaces, pages preceding the main body of a book, and the numbering of movie sequels.

 Contents

## Zero

In general, the number zero did not have its own Roman numeral, but the concept of zero as a number was well known by all medieval computists (responsible for calculating the date of Easter). They included zero (via the Latin word nullae meaning nothing) as one of nineteen epacts, or the age of the moon on March 22. The first three epacts were nullae, xi, and xxii (written in minuscule or lower case). The first known computist to use zero was Dionysius Exiguus in 525, but the concept of zero was no doubt well known earlier. Only one instance of a Roman numeral for zero is known. About 725, Bede or one of his colleagues used the letter N, the initial of nullae, in a table of epacts, all written in Roman numerals.

A notation for the value zero is quite distinct from the role of the digit zero in a positional notation system. The lack of a zero digit prevented Roman numerals from developing into a positional notation, and led to their gradual replacement by Arabic numerals in the early second millennium.

## IIII or IV?

The notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent "four". The subtractive notation (which uses IV instead of IIII) has become universally used only in modern times. For example, Forme of Cury, a manuscript from 1390, uses IX for "nine", but IIII for "four". Another document in the same manuscript, from 1381, uses IV and IX. A third document in the same manuscript uses both IIII and IV, and IX. Constructions such as IIX for "eight" have also been discovered. In many cases, there seems to have been a certain reluctance in the use of the less intuitive subtractive notation. Its use increased the complexity of performing Roman arithmetic, without conveying the benefits of a full positional notation system.

Some rules regarding Roman numerals state that a symbol representing 10x may not precede any symbol larger than 10x+1. For example, one should represent the number "ninety-nine" as XCIX, not IC. However, these rules are not universally followed.

## Calendars and clocks

Clock faces that are labelled using Roman numerals conventionally show IIII for 4 o'clock and IX for 9 o'clock, using the subtractive principle in one case and not in the other. There are several suggested explanations for this:

• The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not.
• IV is the first two letters of IVPITER, the supreme god of the Romans, and therefore not appropriate to use.
• The number of symbols on the clock totals twenty Is, four Vs, and four Xs; so clock makers need only a single mould with five I's, a V, and an X in order to make the correct number of numerals for the clocks. The alternative uses seventeen Is, five Vs, and four Xs, possibly requiring several different moulds.
• The I symbol would be the only symbol in the first 4 hours of the clock, the V symbol would only appear in the next 4 hours, and the X symbol only in the last 4 hours. This would add to the clock's radial symmetry.
• IV is difficult to read upside down and on an angle, particularly at that location on the clock.
• A particular Roman ruler had a clock manufactured incorrectly (with IIII) and others started making their clocks that way in order not to offend him.
• Louis XIV, king of France, preferred IIII over IV, ordered his clockmakers to produce clocks with IIII and not IV, and thus it has remained.

## Year in Roman numerals

In seventeenth century Europe, using Roman numerals for the year of publication for books was standard; there were many other places it was used as well. Publishers attempted to make the number easier to read by those more accustomed to Arabic positional numerals. On British title pages, there were often spaces between the groups of digits: M DCC LXI is one example. This may have come from the French, who separated the groups of digits with periods, as: M.DCC.LXV. or M. DCC. LXV. Notice the period at the end of the sequence; many foreign countries did this for roman numerals in general, but not necessarily Britain.

These practices faded from general use before the start of the twentieth century, though the cornerstones of major buildings still occasionally use them. Roman numerals are today still used on building faces for dates: 2005 can be represented as MMV.

The film industry has used them perhaps since its inception to denote the year a film was made, so that it could be redistributed later, either locally or to a foreign country, without making it immediately clear to viewers what the actual date was. This became more useful when films were broadcast on television to partially conceal the age of films. From this came the policy of the broadcasting industry, including the BBC, to use them to denote the year in which a television program was made (the Australian Broadcasting Corporation has largely stopped this practice but still occasionally lapses).

## Other modern usage by English-speaking peoples

Roman numerals remained in common use until about the 14th century, when they were replaced by Arabic numerals (thought to have been introduced to Europe from al-Andalus, by way of Arab traders and arithmetic treatises, around the 11th century). The use of Roman numerals today is mostly restricted to ordinal numbers, such as volumes or chapters in a book or the numbers identifying monarchs (e.g. Elizabeth II).

Sometimes the numerals are written using lower-case letters (thus: i, ii, iii, iv, etc.), particularly if numbering paragraphs or sections within chapters, or for the pagination of the front matter of a book.

Undergraduate degrees at British universities are generally graded using I, IIi, IIii, III for first, upper second, lower second and third class respectively.

Modern English usage also employs Roman numerals in many books (especially anthologies), movies (e.g., Star Wars), sporting events (e.g., the Super Bowl), and historic events (e.g.: World War I, World War II ). The common unifying theme seems to be stories or events that are episodic or annual in nature, with the use of classical numbering suggesting importance or timelessness.

In music theory a scale degrees or diatonic functions are often identified by Roman numerals (as in chord symbols) as follows:

 Roman numeral I II III IV V VI VII Scale degree tonic supertonic mediant subdominant dominant submediant leading tone/subtonic

## Modern non English speaking usage

The above uses are customary for English-speaking countries. Although many of them are also maintained in other countries, those countries have some additional uses for them which are unknown in English-speaking regions.

The French and the Spanish use capital roman numerals to denote centuries, e.g., 'XVIII' refers to the eighteenth century, so as to not confuse the first two digits of the century with the first two digits of most, if not all, of the years in the century. The Italians do not, instead referring to the digits in the years, e.g., quattrocento is their name for the fifteenth century. Some scholars in English-speaking countries prefer the French method, among them Lyon Sprague de Camp.

In Germany, Poland, and Russia, roman numerals were used in a method of recording the date. Just as an old clock recorded the hour by roman numerals while minutes were measured in arabic numerals, in this system, the month was in roman numerals while the day was in arabic numerals, e.g. 14-VI-1789 was June the fourteenth, 1789. It is by this method that dates are inscribed on the walls of the Kremlin, for example. This method has the advantage that days and months are not confused in rapid note-taking, and that any range of dates or months could be expressed in a mixture of arabic and roman numerals with no confusion, e.g., V-VIII is May to August, while 1-V-31-VIII is May first to August thirty-first.

But as the French use capital roman numerals to refer to the quarters of the year , e.g., 'III' is the third quarter , and which has apparently become standard in some European standards organization, (but which in American business is 'Q3'), the aforementioned method of recording the date has had to switch to minuscule roman numerals, e.g., 4-viii-1961. (Later still, the ISO specified that dates should be given in all arabic numerals, which can lead to confusion.)

Romanian uses Roman numerals for floor numbers.

## Alternate forms

In the Middle Ages, Latin writers used a horizontal line above a particular numeral to represent one thousand times that numeral, and additional vertical lines on both sides of the numeral to denote one hundred times the number, as in these examples:

$\mathrm{\bar{I}}$ for one thousand
$\mathrm{\bar{V}}$ for five thousand
$\mathrm{\bar{|I|}}$ for one hundred thousand
$\mathrm{\bar{|V|}}$ for five hundred thousand

The same overline was also used with a different meaning, to clarify that the characters were numerals.

Sometimes 500, usually D, was written as I followed by an apostrophus, resembling a backwards C (Ɔ), while 1,000, usually M, was written as CIƆ. This is believed to be a system of encasing numbers to denote thousands (imagine the Cs as parentheses). This system has its origins from Etruscan numeral usage. The D and M symbols to represent 500 and 1,000 were most likely derived from and CIƆ, respectively.

An extra Ɔ denoted 500, and multiple extra Ɔs are used to denote 5,000, 50,000, etc. For example:

Base Number: 1 extra Ɔ: 2 extra Ɔs: 3 extra Ɔs: CIƆ = 1,000 CCIƆƆ = 10,000 CCCIƆƆƆ = 100,000 IƆ = 500 CIƆƆ = 1,500 CCIƆƆƆ = 10,500 CCCIƆƆƆƆ = 100,500 IƆƆ = 5,000 CCIƆƆƆƆ = 15,000 CCCIƆƆƆƆƆ = 105,000 IƆƆƆ = 50,000 CCCIƆƆƆƆƆƆ = 150,000

Sometimes CIƆ was reduced to an infinity symbol ($\infty$) for denoting 1,000. John Wallis is often credited for introducing this symbol to represent infinity, and one conjecture is that he based it off of this usage, since 1,000 was hyperbolically used to represent very large numbers.

In medieval times, before the letter j emerged as a distinct letter, a series of letters i in Roman numerals was commonly ended with a flourish; hence they actually looked like ij, iij, iiij, etc. This practice is now merely an antiquarian's note; it is never used. (It did, however, lead to the Dutch diphthong IJ.)

## Table of Roman numerals

The "modern" Roman numerals, post-Victorian era, are shown below:

Roman Alternative Arabic Notes
none none 0 There was no need for a zero.
I 1
II ⅠⅠ (or Ⅱ) 2
III ⅠⅠⅠ (or Ⅲ) 3
IV ⅠⅤ (or Ⅳ) 4 IIII (ⅠⅠⅠⅠ) is still used on clock and card faces.
V 5
VI ⅤⅠ (or Ⅵ) 6
VII ⅤⅠⅠ (or Ⅶ) 7
VIII ⅤⅠⅠⅠ (or Ⅷ) 8
IX ⅠⅩ (or Ⅸ) 9
X 10
XI ⅩⅠ (or Ⅺ) 11
XII ⅩⅠⅠ (or Ⅻ) 12
XIII ⅩⅠⅠⅠ 13
XIV ⅩⅠⅤ 14
XV ⅩⅤ 15
XIX ⅩⅠⅩ 19
XX ⅩⅩ 20
XXX ⅩⅩⅩ 30
XL ⅩⅬ 40
L 50
LX ⅬⅩ 60
LXX ⅬⅩⅩ 70 The abbreviation for the Septuagint
LXXX ⅬⅩⅩⅩ 80
XC ⅩⅭ 90
C 100 This is the origin of using the slang term "C-bill" or "C-note" for "\$100 bill".
CC ⅭⅭ 200
CD ⅭⅮ 400
D 500 Derived from I Ↄ, or half of the alternative symbol for 1000, see above.
DCLXVI ⅮⅭⅬⅩⅤⅠ 666 Using every basic symbol but M once gives the beast number.
CM ⅭⅯ 900
M 1000
MCMXLV ⅯⅭⅯⅩⅬⅤ 1945
MCMXCIX ⅯⅭⅯⅩⅭⅠⅩ 1999 There are no short cuts, so the I can only precede V or X. IMM (ⅠⅯⅯ) or MIM (ⅯⅠⅯ) is therefore invalid.
MM ⅯⅯ 2000
MMM ⅯⅯⅯ 3000
ⅠↃↃ 5000 I followed by two reversed C, an adapted Chalcidic sign

An accurate way to write large numbers in Roman numerals is to handle first the thousands, then hundreds, then tens, then units.
Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is VIII.
Put it together: MCMLXXXVIII (ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ).

The "shortcut method" for large numbers such as 1998 is not recommended, but still used by some:
1998
Two thousand is MM (ⅯⅯ), so subtract two (II [ⅠⅠ]) and you have 1998
MIIM (ⅯⅠⅠⅯ) or alternatively IIMM (ⅠⅠⅯⅯ).

Unicode has a number of characters specifically designated as Roman numerals, as part of the Number Forms range from U+2160 to U+2183. For example, MCMLXXXVIII could alternatively be written as ⅯⅭⅯⅬⅩⅩⅩⅤⅠⅠⅠ. This range includes both upper- and lowercase numerals, as well as pre-combined glyphs for numbers up to 12 (Ⅻ or XII), mainly intended for the clock faces for compatibility with non–West-European languages. The pre-combined glyphs should only be used to represent the individual numbers where the use of individual glyphs is not wanted, and not to replace compounded numbers. Similarily precombined glyphs for 5000 and 10000 exist.

The Unicode characters are present only for compatibility with other character standards which provide these characters; for ordinary uses, the regular Latin letters are preferred. Displaying these characters requires a user agent that can handle Unicode and a font that contains appropriate glyphs for them.

## Games

After the Renaissance, the Roman system could also be used to write chronograms. It was common to put in the first page of a book some phrase, so that when adding the I, V, X, L, C, D, M present in the phrase, the reader would obtain a number, usually the year of publication. The phrase was often (but not always) in Latin, as chronograms can be rendered in any language that utilises the Roman alphabet.