What is a Roman Numeral?
A Roman numeral is a system for expressing numbers that originated in the Roman Empire. It is still used in certain cases today, such as on clocks or watch faces, book chapters, and for numbering large events such as the Olympics and the Superbowl.
Roman Numerals were widely used long after the fall of the Roman Empire up until Arabic numerals started to replace them around the 14th century. Arabic numerals (0, 1, 2, 3...) are the numerals that we are most accustomed to using today worldwide.
The 7 Basic Roman Numerals
| Roman Numeral | I | V | X | L | C | D | M |
|---|---|---|---|---|---|---|---|
| Arabic Number | 1 | 5 | 10 | 50 | 100 | 500 | 1,000 |
How to Read and Write Roman Numerals
Although there are only 7 Roman numerals used in the modern day, there are various rules for writing them that enable us to express a wide range of numbers. Notice that there is no zero symbol for Roman numerals.
- Addition: Consecutive Roman numerals have their values added in cases where the numerals are equivalent, or the numeral directly to the left is larger than that on the right.
- III = 3
- VI = 6
- MCL = 1150
- Subtraction: When a numeral that has a smaller value is followed by one with a larger value, the smaller numeral is subtracted from the larger one.
- IV = 5 - 1 = 4
- XIV = 10 + (5 - 1) = 14
- CD = 500 - 100 = 400
- No Repetition for V, L, D: The numerals V (5), L (50), and D (500) are never repeated. They also cannot be written before a larger symbol, so they cannot be subtracted. For example, VX does not exist (15 is written as XV).
- Maximum of 3 Consecutive Numerals: Only up to 3 consecutive identical numerals can be written (e.g., III, XXX, MMM). Therefore, IIII or XXXX do not exist (they are written as IV and XL respectively).
- Subtraction Limits: The numeral I can only be subtracted from V or X. The numeral X can only be subtracted from L or C. The numeral C can only be subtracted from D or M.
Writing Large Numbers (The Vinculum)
As Roman numerals get larger, they get more difficult to read and write. Because no numeral can be repeated more than 3 times, the largest standard numeral is MMMCMXCIX (3,999). To write numbers larger than 3,999, the Romans developed the vinculum.
A vinculum is an overline drawn above a Roman numeral. It indicates that the numeral it is written above is multiplied by 1,000. For example, a V with a line over it equals 5,000.
| Roman Numeral (with Vinculum) | V̅ | X̅ | L̅ | C̅ | D̅ | M̅ |
|---|---|---|---|---|---|---|
| Arabic Number | 5,000 | 10,000 | 50,000 | 100,000 | 500,000 | 1,000,000 |
How to Convert Between Roman and Arabic Numerals
Arabic to Roman
To convert Arabic numerals to Roman numerals, break the number up into its components by place value. Let's convert 768:
- Break it up: 768 = 700 + 60 + 8
- Convert 700: DCC
- Convert 60: LX
- Convert 8: VIII
- Combine from left to right: DCCLXVIII
Roman to Arabic
To convert Roman numerals to Arabic numerals, break the string down into known values and sum them. Let's convert MMMCCLXXVIII:
- MMM = 3000
- CC = 200
- LXX = 70
- VIII = 8
- Total: 3000 + 200 + 70 + 8 = 3278
Dates in Roman Numeral Form
There are a few different ways that Roman numerals are written in date form. One way is to convert each component (the day, month, and year) to Roman numerals independently. For example, when using the YYYY/MM/DD format, the date March 4th, 2026, is written as MMXXVI / III / IV.
Another way to represent dates is to use a mix of Arabic and Roman numerals. In this case, the month is typically written using Roman numerals while the day and year are written using Arabic numerals. For example, 3/4/2026 may be written as III/4/2026.