Roman Numeral Converter

Roman numerals appeared about 500 years before our era. The Romans partly borrowed them from the Etruscans. Nevertheless, Roman numerals are still used for several purposes in modern life. In many or most schools, it is still part of the regular curriculum to teach Roman numerals.

Official documents and historical items such as gravestones often combine conventional Arabic numerals with Roman numerals.

Legal codes and laws use Roman numerals to designate major sections of the law, such as articles or amendments, to minimize confusion when identifying those specific sections.

You're probably familiar with plays (like Shakespeare's) that use Roman numerals for Act numbering. Similarly, movie titles employ Roman numerals such as ROCKY I, II, III... or STAR WARS, Chapter IV: A NEW HOPE.

You'll find the same convention in most books for chapters. In a more modern change, in an index or appendix, you'll see lower case Roman numerals (vi, iii, x…) to identify subsections, even though the Romans themselves did not have "lower case" lettering.

Using This Calculator

This calculator can perform calculations in both directions, either from Roman numerals to Arabic numerals or Arabic numbers to Roman numerals. Suppose you see a date on movie copyright, for example, MCMXLIV or MCMXXXVII. In that case, you can enter that into the text box, and it will instantly produce the conversion.

This calculator is very convenient. Drop your number in the text box, click the "Calculate" button, or hit your Return key and convert it to the opposite system. It will accept either Roman or Arabic format without making you click switches or change pages.

Daily Life

The Romans used numbering mostly for calculating money values. The largest single value that can be expressed in common Roman numerals is 3,999. That is an impractically large number of sheep to trade, apples to sell, or figs to buy. It would be represented as MMMCMXCIX, being 3,000 (MMM), 900 (CM), 90 (XC), and 9 (IX).

Generally, they didn't need larger numbers. However, there was a way to represent larger numbers by using an "overbar" (occasionally called an "overline"), which multiplies the numbers beneath it by 1,000.

Since C = 100, then C̅ would equal 100,000, and thus X̅ would equal 10,000, L̅= 50,000, D̅ would be 500,000, and M̅ would equal 1,000,000.

Similarly, M̅M̅M̅ would be 3,000,000, D̅C̅C̅C̅, would be 800,000, and C̅M̅XII would be 900,000 + 10 + 2 or 900,012.

It is possible to write even bigger numbers by following other conventions that developed after the fall of the Roman Empire. In practice, the ancient Romans did not use these numbers. But for example, 3,999,999,999 could be written using double bars (1,000 × 1,000), like this: M̿M̿M̿C̿M̿X̿C̿I̿X̿C̅M̅X̅C̅I̅X̅CMXCIX.

The creators of the calculator also recognize that you cannot enter the  ̅ character on most keyboards. To enter C̅ you need to type _C (underscore + C). Similarly, M̅M̅M̅ would be _M_M_M.

Limitations

This Roman numeral calculator cannot handle fractions. The Romans had a duodecimal system based on the number 12. It was more convenient for buying and selling as it allowed you to divide the amounts by 2, 3, 4, and 6.

Roman money was also denominated in fractions of 12 to make buying and selling easier. Nowadays, we use the duodecimal system for our timekeeping system.

At the same time, in the ten-based decimal system, we can divide ten only by 2 and 5.

The Romans had a representation for our modern "zero," which was N for the word "nulla" or nihil. Still, it was only used alone to indicate "nothing" and not combined with other symbols.

Reading Roman numerals without a converter

1. Seven letters of the Latin alphabet are used to denote numbers:

• I = 1 (it is an ancient Etruscan sign for 1)
• V = 5 (V is the upper half of the sign X or 10)
• X = 10 (it is an antique Etruscan sign for 10)
• L = 50 (initially, the Etruscan sign 𐌣 was used for it, which then transformed into ↆ then ⊥ and finally L)
• C = 100 (C is the first letter of the Latin word "centum" or "one hundred")
• D = 500 (D represents the half of the sign ↀ (1000); because in earlier versions, 1000 was designated as ↀ or Greek letter Φ phi);
• M = 1,000 (M is the first letter of the word "mille" or "thousand")

2. Natural numbers are written by repeating the digits.

XXX (10+10+10) = 30

3. Thousands and hundreds are written first, then tens and ones. XXV (10+10+5) = 25

4. If a big number precedes a smaller one, they are added (the addition principle), and if a smaller number precedes a bigger one, then a smaller one is subtracted from a bigger one (the subtraction principle).

• VI (5+1) = 6
• IV (5-1) = 4
• LX (50+10) = 60
• XL (50-10) = 40
• CX (100 +10) = 110
• XC (100-10) = 90

MDCCCXII (1000+500+100+100+100+10+1+1) = 1,812

5. Digits V, L, D may not be repeated in a row; digits I, X, C, M may be repeated but not more than three times in a row.

• VIII (5+1+1+1) = 8
• LXXX (50+10+10+10) = 80
• DCCC (500+100+100+100) = 800
• MMMD (1,000+1,000+1,000+500) = 3,500

6. A repetition of the same digit more than 3 times is prohibited. So, the number 40 is written in contemporary Latin notation as XL and not as XXXX.

7. The dash above a number increases its value by a factor of 1,000:

• V = 5 and V̅ = 5,000
• X = 10 and X̅= 10,000
• L = 50 and L̅= 50,000
• C = 100 and C̅= 100,000
• D = 500 and D̅= 500,000
• M = 1,000 and M̅= 1,000,000

8. Different designations of the same number are possible. For example, the number 80 can be represented as LXXX (50+10+10+10) and as XXC (100-20).

Other Uses

You'll often see draught marks in Roman numerals near the bow and stern of ships. These indicate how far the lowest point of the ship is below the water's surface. Some water bodies, harbors, canals, and docking facilities limit the depth of vessels. Roman numerals are straight lines in the range needed for this purpose, making them easy to paint and maintain. The marine industry is slowly switching to metric markings, and U.S.-based ships often use "feet."

Rocket ships use them (Titan I-III, Saturn I, IB, V, Delta II-IV, etc.). Probably going to the Moon to wander around and collect rocks in a Saturn 5 wasn't as cool as in a Saturn V, the largest and most powerful rocket ever launched!

You even find Roman numerals on fancy wristwatches and famous clocks. One of them is the 13.5-ton "Big Ben," named after the largest of its five bells.

Notably, this clock uses IV for the number "4", whereas many others use IIII. Famous author Isaac Asimov once mentioned a theory that I and V were the first two letters in the name of their God Jupiter (IVPITER). Using those two letters may have been seen as blasphemous or impious.

The Romans did not design their numerals for performing mathematics; they existed for record keeping. The Romans performed addition and subtraction calculations using the Roman Abacus tool, then wrote down the total.

The Roman Abacus was useless for dividing, but "multiplication" could be accomplished (slowly) by adding multiple times.

The use of Roman numerals is nowadays more aesthetic than functional. Seeing Roman numerals, you involuntarily realize the importance of information and its historical significance at all times. Understanding such figures is a sign of education and good manners.