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Roman Numeral Converter

Convert any whole number from 1 to 3999 into Roman numerals, and decode Roman numerals back into ordinary integers, instantly in your browser.

Roman numeral
MMXXIV

2,024 in Roman numerals

Quick answer

To convert a number to Roman numerals, subtract the largest possible value symbol repeatedly (M=1000, CM=900, D=500, CD=400, C=100, XC=90, L=50, XL=40, X=10, IX=9, V=5, IV=4, I=1) and append each symbol. For example, 2024 becomes MMXXIV and 1984 becomes MCMLXXXIV. To decode, add each symbol's value, subtracting when a smaller symbol precedes a larger one. Roman numerals only represent 1 through 3999.

Formula & method

The converter works in two directions. To encode an integer, it walks a fixed value table from largest to smallest — [1000=M, 900=CM, 500=D, 400=CD, 100=C, 90=XC, 50=L, 40=XL, 10=X, 9=IX, 5=V, 4=IV, 1=I] — and while the remaining number is at least the current value it appends that symbol and subtracts the value. This greedy method always yields the shortest, standard subtractive form. To decode, it scans the numeral left to right, adding each symbol's value, but when a symbol is smaller than the one after it (for example I before X), it subtracts instead, capturing subtractive pairs like IV and CM. The result is validated by re-encoding it: if re-encoding does not reproduce the exact input, the numeral is malformed (for example IIII, VV, or IC) and is rejected. Only values from 1 to 3999 are accepted, the range expressible with standard ASCII Roman numerals.

Examples

Example 1: Convert 2024 to Roman numerals
Input
Number: 2024
Result
MMXXIV
Why
2024 = 1000 (M) + 1000 (M) + 10 (X) + 10 (X) + 4 (IV), giving M M X X IV = MMXXIV.
Example 2: Convert 1984 to Roman numerals
Input
Number: 1984
Result
MCMLXXXIV
Why
1984 = 1000 (M) + 900 (CM) + 50 (L) + 10+10+10 (XXX) + 4 (IV) = MCMLXXXIV.
Example 3: Convert 49 to Roman numerals
Input
Number: 49
Result
XLIX
Why
49 = 40 (XL) + 9 (IX). Note it is XLIX, not IL — only certain subtractive pairs are allowed.
Example 4: Decode MMXXIV to a number
Input
Roman numeral: MMXXIV
Result
2024
Why
M(1000) + M(1000) + X(10) + X(10) + IV(4) = 2024. IV is read as a subtractive pair worth 4.
Example 5: Convert 3999 (the maximum)
Input
Number: 3999
Result
MMMCMXCIX
Why
3999 = 3000 (MMM) + 900 (CM) + 90 (XC) + 9 (IX) = MMMCMXCIX, the largest standard Roman numeral.

When to use this tool

  • Reading dates on buildings, monuments, book copyright pages, and movie credits that use Roman numerals.
  • Naming chapters, appendices, outline levels, or monarchs and popes (for example writing 'Louis XIV' or 'Chapter VIII').
  • Numbering Super Bowls, Olympic Games, or other events that traditionally use Roman numerals.
  • Decoding a clock face, watch dial, or sundial that shows hours in Roman numerals.
  • Teaching or learning the Roman numeral system and checking your encoding or decoding by hand.

Common mistakes

  • Writing four identical symbols in a row, such as IIII for 4 or XXXX for 40. Standard notation uses the subtractive forms IV and XL instead.
  • Using invalid subtractive pairs like IL for 49 or IC for 99. Only I before V/X, X before L/C, and C before D/M are valid, so 49 is XLIX and 99 is XCIX.
  • Trying to convert 0 or negative numbers. Classical Roman numerals have no symbol for zero and cannot express values below 1.
  • Attempting numbers above 3999. Values of 4000 and up need an overline (vinculum) notation that is not part of standard ASCII numerals.
  • Forgetting that letter order matters: VI is 6 but IV is 4. A smaller symbol after a larger one adds, while a smaller symbol before a larger one subtracts.

Frequently asked questions

What is the largest number this converter supports?

3999, written MMMCMXCIX. Standard ASCII Roman numerals top out here because 4000 and above require an overline (vinculum) over symbols to multiply them by 1000, which is not part of the basic letter set.

Is there a Roman numeral for zero?

No. The Roman system has no symbol for zero, so it can only represent whole numbers from 1 upward. The medieval scholar Bede used the word 'nulla' for zero in tables, but it was never a numeral.

Why is 4 written IV and not IIII?

Standard subtractive notation places a smaller symbol before a larger one to mean 'one less,' so IV is 5 minus 1. Writing IIII is an additive variant still seen on some clock faces, but it is non-standard and this tool returns the modern IV form.

Why can't I write 49 as IL?

Subtraction is only allowed with specific pairs: I before V or X, X before L or C, and C before D or M. Since I cannot precede L, 49 is built as 40 (XL) plus 9 (IX), giving XLIX.

Does the converter handle lowercase Roman numerals?

Yes. When decoding, lowercase letters such as 'mcmlxxxiv' are accepted and treated the same as uppercase, since case carries no meaning in Roman numerals.

How does the tool know a Roman numeral is invalid?

After decoding a numeral to a number, it re-encodes that number back to standard form and compares. If the result does not exactly match what you typed, the numeral is malformed (like IIII, VV, or XM) and the tool reports it as invalid.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

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Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.

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