How to Convert Roman Numerals (Rules & Examples)
Learn how to read and write Roman numerals with the seven base symbols, subtractive notation rules, worked examples for dates, and tips for avoiding mistakes.
Roman numerals appear on clock faces, in movie credits, on building cornerstones, at the Super Bowl, in book chapter headings, and across legal and academic documents. Despite being over 2,000 years old, they remain a common numbering system for formal and decorative contexts.
This guide covers the seven base symbols, the rules for combining them, subtractive notation, and step-by-step methods for converting between Roman numerals and standard (Arabic) numbers. For instant conversions, try our Free Roman Numeral Converter.
The Seven Base Symbols
The Roman numeral system uses exactly seven letters, each representing a fixed value:
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
Every Roman numeral is formed by combining these seven symbols according to specific rules. There’s no symbol for zero—the Romans had no concept of zero as a number.
The Two Core Rules
Rule 1: Additive Notation (Larger Before Smaller = Add)
When a symbol with a larger or equal value appears before a smaller or equal one, you add the values together. Read left to right and keep adding.
- VI = 5 + 1 = 6
- XV = 10 + 5 = 15
- LXII = 50 + 10 + 1 + 1 = 62
- MDCLXVI = 1000 + 500 + 100 + 50 + 10 + 5 + 1 = 1,666
Rule 2: Subtractive Notation (Smaller Before Larger = Subtract)
When a symbol with a smaller value appears directly before one with a larger value, you subtract the smaller from the larger. This keeps numerals compact and avoids writing four identical symbols in a row.
- IV = 5 - 1 = 4 (instead of IIII)
- IX = 10 - 1 = 9 (instead of VIIII)
- XL = 50 - 10 = 40 (instead of XXXX)
- XC = 100 - 10 = 90
- CD = 500 - 100 = 400
- CM = 1000 - 100 = 900
Only six subtractive combinations are valid:
| Combination | Value |
|---|---|
| IV | 4 |
| IX | 9 |
| XL | 40 |
| XC | 90 |
| CD | 400 |
| CM | 900 |
Why only these six? The rule is that you can only subtract a power of 10 (I, X, C), and only from the next two larger symbols. I subtracts from V and X. X subtracts from L and C. C subtracts from D and M. You can’t write IL for 49 or IC for 99—those aren’t valid.
The Repetition Rule
No symbol can appear more than three times consecutively. That’s why we use IV instead of IIII, XL instead of XXXX, and CD instead of CCCC.
- III = 3 (valid, three repetitions)
- IIII = not standard (use IV = 4 instead)
- XXX = 30 (valid)
- XXXX = not standard (use XL = 40 instead)
Exception on clock faces: Many traditional clocks display 4 as IIII rather than IV. This is a centuries-old stylistic convention, not a mathematical rule. The most common explanation is visual balance—IIII on the left side of the dial mirrors VIII on the right. You will see this on the Big Ben clock tower, Rolex watches, and countless church clocks.
How to Convert Arabic Numbers to Roman Numerals
Break the number into thousands, hundreds, tens, and ones, then convert each group.
Example: Convert 1,994 to Roman numerals.
| Place Value | Number | Roman |
|---|---|---|
| Thousands | 1,000 | M |
| Hundreds | 900 | CM |
| Tens | 90 | XC |
| Ones | 4 | IV |
Combine: MCMXCIV
Example: Convert 2,024 to Roman numerals.
| Place Value | Number | Roman |
|---|---|---|
| Thousands | 2,000 | MM |
| Hundreds | 0 | (nothing) |
| Tens | 20 | XX |
| Ones | 4 | IV |
Combine: MMXXIV
Example: Convert 3,888 to Roman numerals. This is the longest standard Roman numeral under 4,000.
| Place Value | Number | Roman |
|---|---|---|
| Thousands | 3,000 | MMM |
| Hundreds | 800 | DCCC |
| Tens | 80 | LXXX |
| Ones | 8 | VIII |
Combine: MMMDCCCLXXXVIII (15 characters!)
How to Convert Roman Numerals to Arabic Numbers
Scan left to right. If the current symbol is smaller than the next one, subtract it. Otherwise, add it.
Example: Convert MCMXLIV to a number.
- M = 1,000 (M > C, so add) → running total: 1,000
- C = 100 (C < M, so subtract) → running total: 900
- M = 1,000 (added to the subtracted C) → running total: 1,900
- X = 10 (X < L, so subtract) → running total: 1,890
- L = 50 (added to the subtracted X) → running total: 1,940
- I = 1 (I < V, so subtract) → running total: 1,939
- V = 5 (added to the subtracted I) → running total: 1,944
Result: 1,944
An easier way: identify the subtractive pairs first (CM, XL, IV), replace them with their values, then add everything.
- M = 1,000
- CM = 900
- XL = 40
- IV = 4
- Total: 1,000 + 900 + 40 + 4 = 1,944
Roman Numerals in Everyday Life
Super Bowl numbering: The NFL has used Roman numerals for the Super Bowl since Super Bowl V (1971). Super Bowl LIX was the 59th edition. The only exception was Super Bowl 50, which used Arabic numerals because “L” looked awkward in the logo design.
Movie and TV credits: Copyright years at the end of films are traditionally shown in Roman numerals. A film copyrighted in 2024 displays MMXXIV. This convention dates back to early Hollywood and was partly used to make the production year less obvious to audiences.
Building cornerstones: The year a building was constructed or a monument was dedicated is often carved in Roman numerals on the cornerstone. The US Supreme Court building shows MCMXXXV (1935).
Monarchs and popes: Henry VIII, Louis XIV, Pope Benedict XVI, Queen Elizabeth II. Ordinal numbering of rulers and religious leaders uses Roman numerals to distinguish between people who share the same name.
Outlines and lists: Academic papers, legal documents, and formal outlines use Roman numerals for top-level headings (I, II, III) and lowercase Roman numerals for sub-lists (i, ii, iii).
Common Mistakes
Writing IL for 49: The correct form is XLIX (XL + IX = 40 + 9). You can’t skip levels in subtractive notation—I only subtracts from V and X.
Writing IC for 99: The correct form is XCIX (XC + IX = 90 + 9).
Using IIII in formal contexts: While clocks get a pass, writing IIII in documents or academic work isn’t considered correct. Use IV.
Exceeding three repetitions: CCCC is wrong. Use CD (400). XXXX is wrong. Use XL (40).
Numbers above 3,999: Standard Roman numerals max out at MMMCMXCIX (3,999). For larger numbers, the Romans used a bar notation (vinculum) where a line above a numeral multiplies its value by 1,000. For example, V with a bar = 5,000. This notation is rarely used today.
Skip the Math
Our Roman Numeral Converter converts in both directions instantly. Type a number or a Roman numeral and get the result with a full breakdown of how the conversion works.
Frequently Asked Questions
Why is 4 written as IV and not IIII?
Subtractive notation keeps Roman numerals compact and avoids four consecutive identical symbols. IV (5 minus 1) is shorter than IIII and follows the standard rules established during the Roman Empire. However, IIII was actually common in ancient Rome and still appears on clock faces today as a stylistic tradition. In formal writing and modern usage, IV is always the correct form.
What is the largest number you can write in standard Roman numerals?
The largest standard Roman numeral is MMMCMXCIX, which equals 3,999. Since M (1,000) is the largest base symbol and you can only repeat it three times, 3,000 is the maximum for the thousands place. Add CM (900), XC (90), and IX (9) for the largest value in each remaining position. To represent numbers 4,000 and above, you need the vinculum (overline) notation, where a bar above a symbol multiplies its value by 1,000.
How do I read the year on a building or movie in Roman numerals?
Break the numeral into recognizable chunks. Look for subtractive pairs first: CM (900), CD (400), XC (90), XL (40), IX (9), IV (4). Then add up all the groups. For example, MCMLXVIII: M (1,000) + CM (900) + LX (60) + VIII (8) = 1,968.
Did the Romans have a symbol for zero?
No. The Roman numeral system doesn’t have a representation for zero. The concept of zero as a number was developed in India around the 5th century and later transmitted to Europe through Arabic mathematicians. This absence of zero is one reason Roman numerals were eventually replaced by the Hindu-Arabic numeral system (0-9) for mathematics and commerce—performing arithmetic without zero is extremely cumbersome.
Why do some clocks use IIII instead of IV?
Several theories exist. The most popular is visual symmetry: IIII on the left side of the clock (at the 4 position) balances VIII on the right side (at the 8 position). Another theory is that IV was associated with IVPITER (Jupiter), the king of the Roman gods, and using it on a common timepiece was considered disrespectful. A third explanation is simply tradition—early clockmakers used IIII and the convention stuck. Whatever the reason, IIII on clocks is universally accepted even though IV is the standard everywhere else.
Related Calculators
Related Articles
- How to Fix Line Breaks from PDF Copy-Paste
Fix unwanted line breaks when copying text from PDFs. Learn why PDFs add breaks, how to remove them, and techniques for cleaning up formatted text quickly.
- How to Calculate Body Fat Percentage (Navy Method)
Learn the U.S. Navy body fat formula with step-by-step examples, body fat category charts, measurement tips, and comparisons to DEXA, calipers, and other methods.
- How to Calculate Daily Calories for Your Goals
Learn the Mifflin-St Jeor equation, activity multipliers, and how to set calorie targets for weight loss, maintenance, or muscle gain. Includes worked examples.
- How to Calculate Ideal Weight (4 Formulas Compared)
Compare the Devine, Robinson, Miller, and Hamwi ideal weight formulas with worked examples. Learn why ideal weight varies and what these numbers actually mean.
Share this article
Have suggestions for this article?