Roman Numerals Converter - Convert Roman numbers (2024)

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1. What are Roman numerals?
2. Conversion of Roman numerals to Arabic numerals
3. Conversion of Arabic numerals to Roman numerals
4. Roman numerals conversion table

What are Roman numerals?

The Roman numeric system originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages due to the vast influence of Greco-Roman culture over the European civilization. In the Roman system numerals are represented by combinations of letters from the Latin alphabet, particularly: I, V, X, L, C, D, and M. Each of them corresponds to a whole positive number, as you can see in the conversion table below. Roman numbers are also in use today, even though their replacement by the more convenient Arabic numerals began as early as the 14-th century.

The Roman system is not positional, but the order of the numbers does matter. Numbers with a higher numerical value are generally written to the left of ones with a lower numerical value. However, if a number of a lower numerical value is written to the left of a number with a higher numerical value, it needs to be subtracted. This is the so-called "subtractive notation". So, IV results in 4 since we subtract I from V = 5 - 1 = 4. Similarly, XC is 90: X(10) is to the left of C(100), so we subtract 10 from 100 to get 90. Note that we do not write 40 as XXXX as it takes more space than XL. Our Roman number converter handles all of this for your convenience.

Roman numerals can be seen on clock faces, as chapter numbers in books, papers, etc., as movie sequels. They are also frequently used when writing down names of popes or monarchs, e.g. Elizabeth II, as well as generational suffixes where the same name is often shared across generations. They can also be seen on plaques with construction years on building faces and cornerstones. Due to their still fairly extensive use, the need to convert a Roman numeral to an Arabic one or vice versa: an Arabic number to a Roman number, is still quite common.

Conversion of Roman numerals to Arabic numerals

To convert a Roman numeral to an Arabic numeral, you need to sum up all roman numbers from left to right. First, make note of the current numeral you are at, then compare it to the one on its right. If it is smaller than it, then you need to subtract from the current sum (or add its negative). If it is larger, simply perform the addition.

For example, if the number is MXIV, we proceed as follows. Start with a sum of zero. Then, we read M, which from the conversion table below we know is 1000. The next number is X, which is 10. 10 < 1000 so we simply add 1000 to our sum, to get 1000. Next we read X, and compare it to I to its right. Since I is 1, we simply add 10 to the sum getting 1010. Then we read I and compare it to V to its right. 1 is smaller than 5, so we subtract 1. Our sum is now 1009. Finally, we read V and since it is the last number, we simply add it to the sum, getting the result: 1014.

Obviously, the above procedure is manual and takes a lot of time for larger Roman numbers, so we recommend using our Roman numerals converter instead.

Conversion of Arabic numerals to Roman numerals

Converting an Arabic numeral to a Roman one is a bit more complex. You start by noting the Roman numerals corresponding to 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 and ordering them in descending order (result: M, CM, D, CD, C, XC, L, XL, X, IX, V, IV, I). Begin the conversion by dividing the Arabic number by the equivalent of the first Roman numeral in this ordered list.

If the result is one or higher, write down the Roman numeral as many times as the division result. Proceed by dividing the remainder by the next number in the list. Continue in this manner until the remainder of the division is zero.

For example, to convert the number 1494 to a Roman numeral, begin by dividing 1494 by 1000. The result is 1 with a remainder of 494. Write down "M". Divide 494 by 900, the result is less than 1, proceed. Divide 494 by 500, the result is less than 1, proceed. Divide 494 by 400. The result is 1 with a remainder of 94, so write down "CD" (current result: "MCD"). Divide 94 by 100, the result is less than 1, simply proceed. Divide 94 by 90, the result is 1, so write down "XC" (current result: "MCDXC"). Dividing 4 by 50, 10, 9, 5 is less than 1, so we end up dividng 4 by 4, getting 1, writing down "IV" to get the final result: "MCDXCIV".

As you can see, even for moderately large number the conversion from an Arabic number to a Roman number can be quite laborous, so using our Arabic to Roman numeral converter will save you a lot of time.

Roman numerals conversion table