This page is intended as a guide to deciphering Roman numeral year dates[1] as they are commonly found in the imprints of both modern and early printed books. It explains the basic principles for converting numbers from Roman to Arabic form and also describes some of the unusual features of Roman numerals that may be encountered in older books. It does not provide a history of the origin or development of Roman numerals; nor does it attempt to explain the ancient practice of numeration, or to prescribe present-day usage.

Two date conversion aids are also provided[2]. One is a simple html list of Roman and Arabic equivalencies for the years 1401-2000, which can be searched using the Find utility of any popular web browser. The other resource is a Java applet that accepts numerical input in the range of 1-4,999 and converts the input to either Roman or Arabic form. The applet is designed to be compatible with older, Java 1.0-compliant browsers, but should also run in the current generation of browsers, including Internet Explorer 5.x, on both Windows and Macintosh platforms. To successfully launch and run the calculator the browser used must be both Java- and JavaScript-enabled.

Both resources are based on the modern Roman numeral conventions described in the section "Basic Conversion Principles" that follows.

#### Basic Conversion Principles:

In general, Roman numerals can be converted mathematically by simply assigning a numerical value to each letter, according to the chart below, and calculating a total:

M=1000 | D=500 | C=100 | L=50 | X=10 | V=5 | I=1

Although the historical practice has varied, the modern convention has been to arrange the letters from left to right in order of decreasing value; the total is then calculated by adding the numerical values of all the letters in the sequence. For example, MDCLXVI = 1000 + 500 + 100 + 50 + 10 + 5 + 1 = 1666.

A well-known, but still often confusing feature of modern Roman numerals is the subtraction principle, which requires that a lower numeral appearing before a higher one[3] be subtracted from the higher value, not added to the total. For example, IX is the Roman numeral for 9 (that is, 10 - 1). In the same way XIX represents the number 19 (X + IX, or 10 + 9) rather than 21, which is written as XXI (10 + 10 + 1). Likewise the Roman numeral for the year 1995 is usually written as MCMXCV (M + CM + XC + V, or 1000 + 900 + 90 + 5). Many other similar examples can be found by browsing the accompanying conversion table, which strictly follows this subtraction convention.

Another present-day convention is the avoidance of more than three consecutive occurrences of the same letter in favor of the more succinct forms achieved by using the subtraction principle -- for example, IV for IIII (4), XL for XXXX (40), and CD for CCCC (400). An exception is the numeral M, or 1000, which is used 4 times to represent our number 4000, since the Romans had no single-letter numeral representing a higher value than M. It is now also customary not to repeat the values V, L, or D (5, 50, or 500) in the same numeral.

#### Alternative Forms:

In actual practice, neither ancient nor modern usage of Roman numerals has conformed rigidly to hard and fast rules. Even the subtraction principle, perhaps the most conspicuous feature of Roman numerals as we know them today, was applied only sporadically by the Romans themselves[4]. Indeed, the appearance of a smaller numeral before a larger one in both ancient and medieval sources will often signify multiplication rather than subtraction. For example, VM for 5,000 or VIIC for 700 (also written as V.M and VIII.C, or with M and C as superscripts).

Any number of other variant or alternative forms may also be found, especially in the imprint dates of books from earlier centuries. These forms include the use of the long versions of the numbers 400 (CCCC) or 40 (XXXX) -- these were actually the preferred forms in ancient times and still appear in 20th-century books -- as well as XXC for LXXX, IC for XCIX, VIX for XVI, or IIXX for XVIII, to mention only a few of the more obvious variant patterns. Occasionally more challenging variations may also be encountered, including instances of Roman numeral chronograms[5], which actually occur with some frequency on the title pages of early printed books. Such forms may require special efforts to decipher -- they won't appear in the conversion table, at any rate -- but in most cases their values can be calculated by applying the basic principles previously described with a little imagination.

Certain orthographic conventions observed by early printers may also give rise to unexpected forms. For example, the once wide-spread practice of using the letters "j" and "i" somewhat interchangeably[6], depending on their position within a word, can result in numeral forms such as mcdxxiij where mcdxxiii would ordinarily be expected (for Roman numerals, substitution of j for i at the terminal position is the most commonly seen instance of this practice). The values of j and i are the same in these cases, and such numbers should cause little difficulty. More problematical, however, is the practice -- actually fairly rare -- of using an upper case letter "I" in the terminal position of a numeral. For example:

**mdcxcvI**

Alternatively, a larger font size may be used in the case of a Roman numeral set in all capitals:

**MDCXCVI**

These "tall" forms of the letter I usually indicate a doubling of the letter's numerical value -- namely, two instead of one. Thus the date represented by the example above would be 1697, rather than 1696. This convention is presumably based on the occasional Roman practice (seen more frequently in Latin texts from the era of printing) of using a single tall I to represent the contraction of double i's (*ii*), especially in the genitive singular case ending of words in *-ius* or *-ium.*

#### Use of the Apostrophus:

A very common practice among early printers was to represent certain large numbers through the combination of the letters C and I with the ancient Roman apostrophus, a simple curved figure that looks something like this:

** )**

For imprint dates these composite, apostrophic forms will most often be seen where the letters M (1,000) and D (500) would normally be used. For example, the year MDLXXXVII might be represented as

where M has been replaced by the form C-I-apostrophus and D by I-apostrophus.

This use of the apostrophus (the source for our word "apostrophe," as its name and shape would suggest) is said to be based on the ancient Roman practice of representing the number 1000 by the Greek letter phi, a character that looks like this:

Subsequently the phi came to be represented by the Romans as a | enclosed within a pair of facing apostrophi (much like our parentheses in appearance) to produce: ( | ). When setting title-page dates, early printers would often imitate this variant form of 1000, which they constructed typographically by combining the so-called apostrophic C (the character C typeset upside down[7]) with a normal letter C and an I (the latter sometimes of a larger point size) in one of several different ways:

or or

Alternatively, the symbol was sometimes also represented by a character familiar to us as the mathematical symbol for infinity:

As might be expected, the Roman figure | ) represents a visual and numerical halving of ( | ), and like the numeral D, which it obviously resembles, its value is 500. It typically appears in early printed books as:

or or

#### Other Large Roman Numerals:

An obvious limitation of the Roman numeral system as we know it is that it does not permit the representation of large numbers, for which there was evidently little use in ancient times. In fact, the largest value that can be written using the conventional symbols I, V, X, L, C, D and M is the number 4,999, or MMMMCMXCIX.

The Romans themselves devised various methods for working around this limitation, although none of them was particularly effective and none continues in widespread use today. One convention adopted by the Romans for this purpose -- the use of multiplication, as in VM to represent 5,000 -- has already been mentioned. A more common method, which actually persisted well into the modern era, was to place repeatable ( ) symbols around the apostrophic numeral forms ( | ) and | ) to indicate multiplication by powers of ten. For example, ( ( | ) ) = 1,000 x 10 or 10,000 and | ) ) = 500 x 10, or 5,000. The numbers 100,000 and 50,000 were indicated by adding a third ( ) or ) outside of the second. While these values are obviously too large to be found in imprint dates, they were used in many other contexts throughout the early centuries of the era of the printing press. Several examples of this archaic practice, as well as other large numeral variants, are illustrated in the following table of Roman-Arabic equivalencies (3,000-8,000) taken from an early edition of Pietro Bongo's __Mysticae Numerorum Significationis Liber__ [8]:

Besides the use of the familiar apostrophic forms ( | ), | ), etc., note especially the unexpected substitution of ICC for | ) ) and the frequent use of the infinity symbol in place of ( | ).

The table also illustrates several different types of mathematical operations used in forming Roman numerals, including the placement of smaller numerals before larger ones to indicate either subtraction or multiplication, the use of a bar (or *vinculum*) over a number to indicate multiplication by 1,000, and the subtraction of multiple smaller numbers from a single higher one.

This confusing and seemingly haphazard mixture of the principles of addition, subtraction, and multiplication is largely explained as the result of efforts to achieve concision with an essentially additive system of numbering that produced unmanageably large numerals that were difficult to read, much less calculate with. The survival of these archaic Roman numeral conventions in early printed books, long after Arabic numbers first appeared in print in the 15th century, suggests the strong interest in the revival of classical antiquity that motivated early printers and the scholars and writers whose works they produced. It must be admitted, however, that some of the more fanciful numerals shown here seem to have been inspired less by ancient practices than by a simple interest in the arcane.

1. For an overview of the Roman calendar see the discussion of the "Development of the Modern Calendar" under the entry for Calendar in The Columbia Encyclopedia, 6th edition, ©2000. Also extremely useful for converting Roman calendar dates is Otfried Lieberknecht's Calendar Tools (JavaScript calculator). [ return ]

2. See also Edward R. Hobbs' playful Compvter Romanvs (Java applet), a true calculator which accepts Roman numerals in the range 1 - 3,999,999, validates the input, and performs basic mathematical functions -- addition, subtraction, multiplication, and division. [ return ]

3. The smaller number must be a power of ten (I, X or C) and precede a number no larger than 10 times its own value. The smaller number itself can be preceded only by a number at least 10 times greater (e.g. LXC is invalid) and it must also be larger than any numeral that follows the one from which it is being subtracted (e.g. CMD is invalid). [ return ]

4. Cappelli indicates that the Romans rarely used the subtraction principle and that the convention was equally uncommon during the Middle Ages. See his __Dizionario di abbreviature latine ed italiane__, 6th ed., Milano, 1967, p. LIV. [ return ]

5. Chronograms are sentences, phrases, inscriptions, or other brief texts that contain dates embedded within them, usually in the form of upper case Roman numerals. If upper case letters appear on the title page of a book seemingly at random, the letters may well represent a chronogram for the date of publication. The intended date can usually be deciphered by making a simple total of all of the letters' corresponding numerical values without regard for their order (the order isn't usually meaningful). For example, the phrase "I MarrIeD LuCy In CInCInnatI" would suggest that its author was married in 1856. [ return ]

6. See R.B. McKerrow, __Introduction to Bibliography for Literary Students,__ Oxford, 1927 (appendix 3) for a brief discussion. Also his fuller treatment of 16th-century practices in __The Library__, 3rd Ser., no. 1. [ return ]

7. Sometimes referred to as a "backwards C", although the term is not strictly accurate. Like modern-day rubber stamps, type used in making early books consisted of a raised printing surface (face) cast on a solid body (shank) with no reverse-side image. Consequently, it wasn't physically possible to turn type over, or backwards, to create an exact mirror image such as this:

Rather, printers would reverse the C by rotating the type 180 degrees to an upside down position:

This is the classic form of the apostrophic C, used throughout the era of the handpress and still occasionally found in printed books today. Digital technology of course makes it a simple matter to produce backwards, or mirror image letters, as can be seen in the Unicode Consortium's published standard for the apostrophic C, or ROMAN NUMERAL REVERSED ONE HUNDRED (Unicode glyph U+2183, v. 4.0 (.pdf)). [ return ]

8. Bongo's curious work on "the mystery of numbers" (or Numerorum Mysteria, as it was commonly known), was first published in two parts at Bergamo (1583-1584) and frequently reissued. The partial table reproduced here originally appeared in the 1614 edition and was scanned from a text illustration in David Smith's __Rara Arithmetica__, Boston, 1908 (see figs. 190-191). Click here to view a reproduction of the title-page of Bongo's original work (part 2, dated 1584), which bears a Roman numeral imprint date displaying several of the features under discussion. [ return ]