Roman Numeral History

The Beginnings

Roman Numerals, as we know them, was the standard numbering system and method of Arithmetic in Ancient Rome and Europe until about 900 AD, when the Arabic Numbering System, which was originated by the Hindu's, came into use. The concept of zero did not exist in Europe until after the late 900's AD; thus, there was no Roman Numeral symbol for 0 (zero). The concept of negative numbers was not yet around either. (My wife would have done better with her checkbook then.) If you think adding or subtracting in Roman Numerals is time consuming, awkward and clumsy; try multiplication or long division! (It is worse than binary, octal or HEX!) HP and TI were not around to bring out the calculators to do that sort of thing. Only seven numeral characters (septal?) were used and when a numeral was over barred (in the later years of the use of Roman Numerals), it represented the base character value, multiplied by a thousand. This convention is really no longer used in the formal sense of Roman Numerals, as Roman Numerals are seldom utilized for values beyond 4999. It is mentioned here for information only and is not used in our calculator. Roman Numerals, as a recognized number representation, was the standard, and as far as we know, the only number system used by the Roman empire and other ancient European civilizations until the Arabic system was introduced. Roman numerals were used primarily for counting, mainly taxation, as the ancients had little use for, or understanding of, "calculation" or arithmetic as we know it today. We might assign the name of "tallying" to the most frequent use of the system. With some effort, you can do regular addition and subtraction and even multiplication with Roman Numerals. Both the Roman Numeral and later Arabic Number systems are "Base 10" (though only 1 thru 9). Zero came later, about 1000AD, the best we can determin. Long division? Well that was your everyday Roman problem, more like calculation. Bring your lunch because it is an all day job. The Romans were world leaders prior to the fall of Rome. They were not only active in trade and commerce, they were dominant. Though the Chinese had a useful and superior math system, the Romans were either unaware of it or unimpressed by it. From the time of learning to write, Roman scholars needed a way to indicate numbers and devised the set of characters now known as Roman Numerals. Though extremely awkward and cumbersome, the system they developed lasted many centuries, and still sees some limited, but specialized, use today.

In usage, Roman Numerals traditionally indicate the order of rulers, church leaders or ships that share the same name (such as the Queen Elizabeth II). They are used for family offspring of the same name, often II instead of Jr., and III for the third. Roman Numerals are also often still used in the publishing and media industries for copyright dates, in construction for time capsules and on cornerstones, and in the life and death of society, on headstones when the family of the deceased wishes to create an impression of classical dignity, or in many cases, the illusion of such. More recently, they were used to indicate the anniversary of SuperBowl games. The Roman numbering system also lives on in our languages, which still use Latin word roots to express numerical ideas. A few examples include unit, unilateral, duo, triple, quadricep, septuagenarian, decade, milliliter. In fact, the entire metric system is a pretty good example of our retaining the entire concept.

The big differences between Roman and Arabic numerals (the ones we use today) are that Romans didn't have a symbol for zero, and that numeral placement within a number can sometimes indicate subtraction rather than addition. It is obvious to the most casual computer programmer, that digital electronics would have never been invented if left to the Romans. Binary could not exist. These are the characters that are used in Roman numerals, and the values they represent. M=1000, D=500, C=100, L=50, X=10, V=5, and I=1. There is a more detailed explanation below the calculator. Using the strict rules of Roman Numerals, the largest number that can be represented is 4,999.

Roman Numeral Bi-Directional Calculator Our JavaScript Calculator has a limitation of the accuracy of your browser, usually 18 digits. The calculator will handle conversions from that number size to Roman Numerals, but the display would be as long as your desk. we suggest that you limit your decimal entry to 5 digits. The generally accepted maximum for display of a Roman Numeral is 4,999. We are not restricting you to that, but in the strictest acceptance of the guidlines of Roman Numerals, that is the cap. Enter a number (pick a number, any number, such as 26) or a Roman Numeral (such as XXVI, as in SuperBowl), and click the Convert button. You may clear the result field by clicking on Clear Result. You may also click on Convert another time and the result should be your initial entry.

The Basics

I	The easiest way to note down a number is to make that many marks - little (actually, capital I's) I's. Thus I means 1, II means 2, III means 3. However, four strokes seemed like too many, and according to strict Roman numeral rules it is....
V	So the friends, Romans and countrymen selected the symbol for 5, V. Placing I in front of the V, or placing any smaller number in front of any larger number, indicates subtraction. Thus, IV indicates 4. After V, a sequential series of additions of 1, represented by I; VI is 6, VII is 7, and VIII is 8. A lot of people ask ‘Why is the number 4 on a clock face depicted as IIII and not as IV?’ It is an exception; that is a fairly good possibility. There is no certain answer to this question but there are several theories, some better than others. One common suggestion is that around the circle of the clock face, the IIII balances the VIII which is in its mirror image symmetrical place holder, that is if a mirror was placed vertically between the XII and VI, the VIII and IIII would reflect on to each other. There are problems with this theory (as with all theories), the V does not balance the VII, nor the I the XI. Another reasonable explanation might be that IV has three strokes and is more likely to be confused with the neighboring III, as both are at unfamiliar angles to the reader. But neither really offers an adequate explanation of why the normal rules of Roman numerals have been broken. The practice of using IIII rather than IV on clock faces, although common, is not universal. The well known clock, known universally as Big Ben, at the Palace of Westminster in London has gothic style Roman numerals around its face and the 4 is depicted as IV. Other examples of an IV on a clock face are rare in England, but the clock in the South Transept of Norwich Cathedral is one. Others are found in Spain. San Sebastian in northern Spain has at least two clocks, one on the cathedral and one on another church, which both have clear plain Roman numerals on the dial and which use IV for the 4. The Romans used the subtraction rule, but not always. Doorway numbers at the Colosseum in Rome (c.80AD) show 40 as XL but 44 as XLIIII rather than XLIV. My personal theory is one of lack of universal practice (TANS) and perhaps, illiterate craftsmen. You could even say 'It was a bad day'. After all, the Internet had not evolved yet and they could not seek information on it.
X	X is 10. Hold it, in my books, 9 comes before 10. What about 9? Does it follow the Roman Numeral subtraction rule? It does. IX suggests subtract I from X, leaving 9. (carry the naught, knit 1, pearl 2...) Numbers in the teens, twenties and thirties follow the same rules and pattern as the units; the multiples rule applies meaning with X's indicating the number of tens. Those tens are cumlative. So XXXI is 31, and XXIV is 24. OK, I am seeing the light here. XXX is a problem and will never be on this site.
L	L represents 50. Based on previous examples, it can be easily determined tha 40 is XL. The equivalent of 10 subtracted from 50, or extra large in men's pants. Following the evolving pattern, 60, 70, and 80 are LX, LXX and LXXX.
C	C is the representation for centum, the Latin word for 100. In slang in the US, a "C Note" is a one hundred dollar bill. A Roman centurion was a highly respected leader of men, a Green Beret of his time; he led 100 men when going in battle. We still use this in words like "century", "centurian" and "cent." The normal Roman Numeral subtraction rule suggests that 90 is written as XC. Like the X's and L's, the C's are placed to preceed numbers to indicate how many hundreds there are; CCCLXIX is 369.
D	D is the representation for 500. As you can probably determine, CD is 400. (It also stands for $14.99 when you go to buy one.) Following our guidlines, CDXLVIII is 448. (See why we switched systems? Romanary or Romadecimal would just not have cut it in computers. Would Septal have worked?)
M	M is the representation for 1,000. In our society today, the M character is seen often because Roman numerals are very frequently used to indicate special dates. Most every movie has in the credits a Roman Numeral indicating the year made.
_	Though outside the area of the strict, original Roman Numeral rules, a generally accepted current practice concerning larger numbers is that they were indicated by putting a horizontal bar above the Roman Numeral characters, which indicated the value of the character should be multiplied by 1,000. All characters except the I are eligible. (Three bars in a row wins the jackpot.) Hence an X with a bar over the top of it, indicates 10,000. Although, this usage is no longer current, because the largest numbers usually expressed in the Roman system are dates, as discussed above, it is still valid, in all but the strictest of Roman Numeral rules.

Summary

In summary, a letter repeated once, twice, or three times, repeats its value that many times (XXX = 30, CC = 200, etc.). One or more letters placed after another letter of greater value increases the greater value by the amount of the smaller (VI = 6, LXX = 70, MCC = 1200, etc.). A letter placed before another letter of greater value decreases the greater value by the amount of the smaller (IV = 4, XC = 90, CM = 900, etc.). And stretching the strict and formal Roman Numeral rules, a bar placed on top of a letter or string of letters increases the numeral's value by 1,000 times (XV = 15, XV = 15,000, MM = 1,000,000). There is no 0 and there are no negative numbers.