Roman numerals is a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical 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.
Roman numerals are commonly used today in numbered lists (in outline format), clockfaces, pages preceding the main body of a book, chord triads in music analysis, the numbering of movie publication dates, successive political leaders or children with identical names, and the numbering of some sport events, such as the Olympic Games or the Super Bowl.
For arithmetics involving Roman numerals, see Roman arithmetic and Roman abacus.
Symbols
There are seven basic Roman numerals.
| Symbol
|
Value
|
| I
|
1 (one) ()
|
| V
|
5 (five) ()
|
| X
|
10 (ten) ()
|
| L
|
50 (fifty) ()
|
| C
|
100 (one hundred) ()
|
| D
|
500 (five hundred) ()
|
| M
|
1000 (one thousand) ()
|
Multiple symbols may be combined to produce numbers in between these values, subject to certain rules on repetition. In cases where it may be shorter, it is sometimes allowable to place a smaller, subtractive, symbol before a larger value, so that, for example, one may write IV or iv for four, rather than iiii. Again, for the numbers not assigned a specific symbol, the above given symbols are combined:
- II or ii for two
- III or iii for three. The final character is sometimes “j” instead of “i”, often in medical prescriptions.
- IV, iv, IIII, or iiii for four
- VI or vi for six
- VII or vii for seven
- VIII or viii for eight
- IX or ix for nine
- XXXII or xxxii for thirty two
- XLV or xlv for forty five
For large numbers (4000 and above), a bar is placed above a base numeral to indicate multiplication by 1000:
- for five thousand
- for ten thousand
- for fifty thousand
- for one hundred thousand
- for five hundred thousand
- for one million
For very large numbers, there is no standard format, although sometimes a double bar or underline is used to indicate multiplication by 1,000,000. That means an underlined X (X) is ten million.
Origins
Although the Roman numerals are now written with letters of the Roman alphabet, they were originally separate symbols. The Etruscans, for example, used I Λ X 8 ⊕ for I V X L C M.
They appear to derive from notches on tally sticks, such as those used by Italian and Dalmatian shepherds into the 19th century. Thus, the I descends from a notch scored across the stick. Every fifth notch was double cut (i.e. , , , , etc.), and every tenth was cross cut (X), much like European tally marks today. This produced a positional system: Eight on a counting stick was eight tallies, IIIIΛIII, but this could be abbreviated ΛIII (or VIII), as the existence of a Λ implies four prior notches. Likewise, number four on the stick was the I-notch that could be felt just before the cut of the V, so it could be written as either IIII or IV. Thus the system was neither additive nor subtractive in its conception, but ordinal. When the tallies were later transferred to writing, the marks were easily identified with the existing Roman letters I, V, X.
(A folk etymology has it that the V represented a hand, and that the X was made by placing two Vs on top of each other, one inverted.)
The tenth V or X along the stick received an extra stroke. Thus 50 was written variously as N, И, K, Ψ, , etc., but perhaps most often as a chicken-track shape like a superimposed V and I - . This had flattened to (an inverted T) by the time of Augustus, and soon thereafter became identified with the graphically similar letter L. Likewise, 100 was variously Ж, , , H, or as any of the symbols for 50 above plus an extra stroke. The form Ж (that is, a superimposed X and I) came to predominate, was written variously as >I< or , was then shortened to or C, with C finally winning out because, as a letter, it stood for (Latin for “hundred”).
The hundredth V or X was marked with a box or circle. Thus 500 was like a superposed on a or (that is, like a Þ with a cross bar), becoming a struck-through D or a Ð by the time of Augustus, under the graphic influence of the letter D. It was later identified the letter D, perhaps as an abbreviation of “half-thousand”. Meanwhile, 1000 was a circled X: , , ⊕, and by Augustinian times was partially identified with the Greek letter Φ. It then evolved along several independent routes. Some variants, such as Ψ and CD (more accurately a reversed D adjacent to a regular D), were historical dead ends (although one folk etymology later identified D for 500 as half of Φ for 1000 because of this CD variant), while two variants of survive to this day. One, , led to the convention of using parentheses to indicate multiplication by 1000 (later extended to double parentheses as in , , etc.); in the other, became and , eventually changing to M under the influence of the word (”thousand”).
Zero
In general, the number zero did not have its own Roman numeral, but a primitive form (nulla) was known by medieval computists (responsible for calculating the date of Easter). They included zero (via the Latin word meaning “none”) 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. 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 may have prevented Roman numerals from being developed into a positional notation, and led to their gradual replacement by Hindu-Arabic numerals in the early second millennium. On the other hand, it may have been the lack of positional notation that prevented the Romans from developing a zero.
Fractions
Even though the Romans used a decimal system for whole numbers, reflecting Latin, they used a duodecimal system for fractions, because the divisibility of twelve (12 = 3×4) makes it easier to handle the common fractions of 1/3 and 1/4 than in a system based on ten (10 = 2×5). On coins, many of which had values that were duodecimal fractions of the unit , they used a notational system similar to that of whole numbers, but based on twelfths and one halves rather than units and fives. A dot • indicated an (one twelfth, the source of the English words inch and ounce), and dots were added together up to five twelfths. Then one half (six twelfths) was notated using the letter S for (”half”). Dots were added to S for the fractions from seven to eleven twelfths, just as tallies were added to V for whole numbers from six to nine. Each of these fractions had its own name, which was also the name used for the corresponding coin:
| Fraction
|
Roman Numeral
|
Name
|
| 1/12
|
•
|
|
| 2/12 = 1/6
|
••
|
|
| 3/12 = 1/4
|
•••
|
|
| 4/12 = 1/3
|
••••
|
|
| 5/12
|
•••••
|
|
| 6/12 = 1/2
|
S
|
|
| 7/12
|
S•
|
|
| 8/12 = 2/3
|
S••
|
|
| 9/12 = 3/4
|
S•••
|
or
|
| 10/12 = 5/6
|
S••••
|
or
|
| 11/12
|
S•••••
|
|
| 12/12 = 1
|
I
|
|
The names mean “ounce”, “sixth”, “quarter”, “third”, “five-ounce” (quinquae unciae > quincunx), “half”, “seven-ounce” (septem unciae > septunx), “twice” (twice a third), “less a quarter” (de-quadrans > dodrans) or “ninth ounce” (nona uncia > nonuncium), “less a sixth” (de-sextans > dextans) or “ten ounces” (decem unciae > decunx), “less an ounce” (de-uncia > deunx), and “unit”. The arrangement of the dots was variable and not necessarily linear. Five dots arranged like :·: (as on dice faces ) are known as a quincunx from the name of the Roman fraction/coin. The Latin words sextans and quadrans are the source of the English words sextant and quadrant.
Other Roman fractions include:
- 1/8 (from sesqui- + uncia, i.e. 1 uncias), represented by a sequence of the symbols for the semuncia and the uncia.
- 1/24 (from semi- + uncia, i.e. of an uncia), represented by several variant glyphs deriving from the shape of Greek letter sigma , one variant resembling the pound sign without the horizontal line(s) and another resembling Cyrillic letter .
- 1/36 (”two sextulas”) or , represented by a sequence of two reversed S.
- 1/48 , represented by a reversed C.
- 1/72 (1/6 of an uncia), represented by a reversed S.
- 1/144 (”half a sextula”), represented by a reversed S crossed by a horizontal line.
- 1/288 , represented by a symbol resembling Cyrillic letter .
- 1/1728 , represented by a symbol resembling closing guillemets ».
IIII vs. IV
The notation of Roman numerals has varied through the centuries. Originally, it was common to use IIII to represent four, because IV represented the Roman god Jupiter, whose Latin name, IVPITER, begins with IV. 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 IIII, IV, and IX. Constructions such as IIIII for five, IIX for eight or VV for 10 have also been discovered. Subtractive notation arose from regular Latin usage: the number 18 was or “two from twenty”; the number 19 was or “one from twenty”. The use of subtractive notation increased the complexity of performing Roman arithmetic, without conveying the benefits of a full positional notation system.
Likewise, on some buildings it is possible to see MDCCCCX, for example, representing 1910 instead of MCMX – notably Admiralty Arch in London. The Leader Building in Cleveland, Ohio, at the corner of Superior Avenue and E.6th Street, is marked MDCCCCXII, representing 1912. Another notable example is on Harvard Medical School’s Gordon Hall, which reads MDCCCCIIII for 1904.
Another likely tale is that the low literacy rate made it difficult for some to do subtraction, where the IIII notation could simply be counted.
Calendars and clocks
Clock faces that are labeled using Roman numerals conventionally show IIII for four o’clock and IX for nine o’clock, using the subtractive principle in one case and not the other. There are many suggested explanations for this, several of which may be true:
- The four-character form IIII creates a visual symmetry with the VIII on the other side, which IV would not.
- With IIII, the number of symbols on the clock totals twenty I’s, four V’s, and four X’s, so clock makers need only a single mold with a V, five I’s, and an X in order to make the correct number of numerals for their clocks: VIIIIIX. This is cast four times for each clock and the twelve required numerals are separated:
- V IIII IX
- VI II IIX
- VII III X
- VIII I IX
- The IIX and one of the IX’s are rotated 180° to form XI and XII. The alternative with IV uses seventeen I’s, five V’s, and four X’s, possibly requiring the clock maker to have several different molds.
- IIII was the preferred way for the ancient Romans to write four, since they to a large extent avoided subtraction.
- As noted above, it has been suggested that since IV is the first two letters of IVPITER (Jupiter), the main god of the Romans, it was not appropriate to use.
- Only the I symbol would be seen in the first four hours of the clock, the V symbol would only appear in the next four hours, and the X symbol only in the last four 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.
- 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.W.I. Milham, Time & Timekeepers (New York: Macmillan, 1947) p. 196
Chemistry
As it relates to the nomenclature of inorganic compounds, only IV should be used. For example MnO2 should be named manganese (IV) oxide; manganese (IIII) oxide is unacceptable.
Modern usage
The Roman number system is generally regarded as obsolete in modern usage, but is still seen in certain institutions to this day.
Below are a few examples of its current use.
- The year and/or credits given at the end of a television show or film.
- Some faces of clocks and timepieces show hours in Roman numerals.
- Names of monarchies are still displayed in Roman numerals, e.g. George VI.
- Postmarks often display Roman numerals.
- Books (particularly older ones) are dated in Roman numerals, and display preliminary pages in Roman numbers. Volume numbers on spines can also be in Roman numerals.
There are many other places as well.
XCIX vs. IC?
Rules regarding Roman numerals often state that a symbol representing 10x may not precede any symbol larger than 10x+1. For example, C cannot be preceded by I or V, only by X (or, of course, by a symbol representing a value equal to or larger than C). Thus, one should represent the number ninety-nine as XCIX, not as the “shortcut” IC. However, these rules are not universally followed.
This problem manifested in such questions as why 1990 was not written as MXM instead of the universal usage MCMXC, or why 1999 was not written simply IMM or MIM as opposed to the universal MCMXCIX.
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 LX I (relating to 1000 700 60 1 or 1761) is one example. This may have come from the French, who separated the groups of digits with periods, as: M.DCC.LXI. or M. DCC. LXI. Notice the period at the end of the sequence; many countries did this for Roman numerals in general, but not necessarily Britain. (Periods were also common on each side of numerals in running text, as in “commonet .iij. viros illos”.)
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: 2007 can be represented as MMVII. They are also sometimes used in the credits of movies and television program