How to Read Roman Numerals
The first step in learning how to read Roman numerals is to familiarize yourself with the Arabic value represented by each letter -- which can be seen in the following chart:
Arabic Value of Roman Numerals| 1 | 5 | 10 | 50 | 100 | 500 | 1000 |
|---|---|---|---|---|---|---|
| I | V | X | L | C | D | M |
The next step in learning how to read Roman numerals is to become aware of how the placement of numerals impacts the translated value. In that regard, there are two rules you need to be aware of when attempting to translate the numerals into values:
- If a letter representing an equal or greater value is placed directly in front of a letter representing an equal or smaller value, the two values are simply added together. For example, "XX" would translate to "20" and "XI" would translate to "11".
- If a letter representing a smaller value is placed directly in front of a letter representing a larger value, the smaller value is subtracted from the larger value. For example, "IX" would translate to "9" and "IV" would translate to "4".
The following conversion chart shows how you would read the Roman numeral "MMMCDLXII" -- which includes instances of both addition and subtraction:
How to Read the Roman Numeral "MMMCDLXII"| Place
Value | Roman
Numerals | Addition or Subtraction | Arabic
Numerals |
|---|---|---|---|
| 1000s | MMM | 1000 + 1000 + 1000 | 3000 |
| 100s | CD | 500 - 100 | 400 |
| 10s | LX | 50 + 10 | 60 |
| 1s | II | 1 + 1 | 2 |
| Totals | MMMCDLXII | = | 3462 |
Notice that in the 100s line, "CD" indicates a subtraction because "C" (100) is less than the "D" (500) it precedes. The above is how the Roman Numeral Converter shows its work.
How to Write Roman Numerals
In addition to the rules you have learned for reading Roman numerals, there are a few more rules you need to know when writing Roman numerals.
- A letter cannot be repeated more than 3 times in succession, and only powers of 10 can be repeated. In other words, "CCCC" is invalid, and "VVV" is invalid (5 is not a power of 10). The correct way to write 400, would be "CD" (500 - 100 = 400), and the correct way to write 15 would be "XV" (10 + 5 = 15).
- Only powers of 10 (1, 10, 100) can be subtracted from a larger value. Therefore you could not write 5 as "VX" (10 - 5 = 5) because 5 is not a power of 10.
- Only a single smaller value may precede a larger value. This means you could not write 3 as "IIV" (5 - 1 - 1 = 3) because "II" is placing 2 smaller values in front of a larger value.
- In the case of a smaller value being subtracted from a larger value, the larger value cannot be more than 10 times the smaller value. In other words, you cannot write 999 as "IM" (1000 - 1 = 999) because "M" is more than 10 times greater than "I". Instead you would write 999 as "CMXCIX" [(1000 - 100) + (100 - 10) + (10 - 1)]. Aren't you glad we use Arabic numbers?
- To write numerals greater than 3999 (without breaking any rules), you would need to place a line above the appropriate letters to indicate the value is a thousand times greater. For example, a "V" with a line above it would indicate 5000 (5 * 1000). Note that the Roman numeral converter does not accommodate numbers or numerals greater than 3999 (MMMCMXCIX).
With the above rules in mind, here is how you would write the Roman numeral for the Arabic number 2345:
Writing the Roman numeral for "2345"| Digit | Place
Value | Addition or Subtraction | Roman
Numerals |
|---|---|---|---|
| 2 | 2000 | 1000 + 1000 | MM |
| 3 | 300 | 100 + 100 + 100 | CCC |
| 4 | 40 | 50 - 10 | XL |
| 5 | 5 | 5 | V |
| Totals | 2345 | = | MMCCCXLV |
The above is how the Roman Numeral Converter shows its work.