Roman Numerals — Definition, Formula & Examples
Roman numerals are a number system from ancient Rome that uses letters to represent values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1,000. You combine these letters following specific rules to write any number.
Roman numerals constitute a non-positional numeral system in which fixed symbols (I, V, X, L, C, D, M) carry constant values regardless of their position. The total value of a Roman numeral is determined by summing symbol values when symbols appear in descending order, and by subtracting a smaller symbol's value when it immediately precedes a larger one. Only I, X, and C may be used as subtractive prefixes, and no symbol may be repeated more than three times consecutively.
How It Works
Read a Roman numeral from left to right. If a symbol is equal to or larger than the one after it, add its value. If a symbol is smaller than the one after it, subtract its value instead. For example, in XIV the X (10) comes before I (1), so you add them, but the I (1) comes before V (5), so you subtract: 10 + (5 − 1) = 14. When writing Roman numerals, place larger values first and use subtractive pairs (like IV for 4 or IX for 9) instead of repeating a symbol four times. The subtractive pairs you need to know are: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, and CM = 900.
Worked Example
Problem: Convert 276 to Roman numerals.
Step 1: Break the number into its place values.
Step 2: Convert 200. Since C = 100, write two C's.
Step 3: Convert 70. L = 50 and X = 10, so 70 = 50 + 10 + 10.
Step 4: Convert 6. V = 5 and I = 1, so 6 = 5 + 1.
Step 5: Combine all parts from left to right.
Answer: 276 = CCLXXVI
Another Example
This example works in reverse (Roman to decimal) and includes three subtractive pairs (CM, XL, IV), which is the trickiest part of reading Roman numerals.
Problem: Convert MCMXLIV to a regular number.
Step 1: Read left to right and identify subtractive pairs. M = 1,000. Then C comes before M, forming the subtractive pair CM = 900.
Step 2: Next, X comes before L, forming the subtractive pair XL = 40.
Step 3: Finally, I comes before V, forming the subtractive pair IV = 4.
Step 4: Add all the values together.
Answer: MCMXLIV = 1,944
Visualization
Why It Matters
Roman numerals appear in elementary and middle school math curricula as a way to explore different number systems and build number sense. Outside school, you will see them on clock faces, in movie copyright dates, for Super Bowl numbering, and in outlines for essays and reports. Understanding Roman numerals also prepares students for studying number bases and positional systems in later courses.
Common Mistakes
Mistake: Writing IIII instead of IV for 4 (or XXXX for 40)
Correction: Use subtractive notation: IV = 4, XL = 40, CD = 400. A symbol should not be repeated more than three times in a row.
Mistake: Using invalid subtractive pairs like IC for 99 or VL for 45
Correction: Only I can precede V or X, only X can precede L or C, and only C can precede D or M. Write 99 as XCIX and 45 as XLV.
Mistake: Adding values when you should subtract
Correction: Always compare each symbol to the one that follows it. If the current symbol is smaller than the next, subtract it. For example, in IX the I is smaller than X, so IX = 10 − 1 = 9, not 10 + 1 = 11.
Check Your Understanding
Write 549 in Roman numerals.
Hint: Break it into 500 + 40 + 9 and convert each part separately.
Answer: DXLIX (500 + 40 + 9)
What number does CDLXXIII represent?
Hint: Look for the subtractive pair first: C before D.
Answer: 473 (CD = 400, LXX = 70, III = 3)
Is the Roman numeral VX valid? Why or why not?
Hint: Think about which symbols are allowed in subtractive pairs.
Answer: No. V cannot be used as a subtractive prefix. Only I, X, and C can appear before a larger symbol.