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Unit Conversions
Roman Numeral Converter — Number to Roman & Roman to Number
Two-way conversion between Arabic numbers and Roman numerals, validated and explained
Roman numerals refuse to disappear. You meet them on clock faces, in movie copyright years, on Super Bowl logos, in book chapter headings, on cornerstones, and after the names of monarchs and popes (Elizabeth II, Louis XIV). This converter goes both ways: type a whole number from 1 to 3999 to get its Roman form, or paste a Roman numeral like MCMLXXXIV to read it back as a number — with the numeral validated so you know the input is well-formed.
The modern standard uses seven letters, each a fixed value: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Numbers are built by writing symbols from largest to smallest and adding them up — so MMXX = 1000 + 1000 + 10 + 10 = 2020.
The twist is subtractive notation, which avoids four-in-a-row. Instead of writing IIII for 4, you put a smaller symbol before a larger one to subtract it: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900. That's why 1990 is MCMXC and not MDCCCC LXXXX. The greedy algorithm this tool uses walks a fixed value table — 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) — subtracting the largest chunk that fits, over and over, until nothing remains. It is exact by construction.
Worked example — 1984. 1984 ÷ 1000 → M, remainder 984. 984 has a 900 chunk → CM, remainder 84. 84 has 50 → L, remainder 34; then 10+10+10 → XXX, remainder 4; finally 4 → IV. Result: MCMLXXXIV.
The classic limit is 1 to 3999. The largest "plain" numeral is MMMCMXCIX = 3999, because writing 4000 would need MMMM (four M's in a row), which standard notation forbids. To go higher, the Romans drew an overline (vinculum) over a symbol to multiply it by 1000 — so V̄ = 5000 and X̄ = 10000 — but that bar isn't plain text, so most converters (this one included) cap cleanly at 3999. Enter a number on the left to encode, or a numeral on the right to decode, and you'll also get the full I–M reference chart.
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• Symbol values: I=1, V=5, X=10, L=50, C=100, D=500, M=1000 • Subtractive pairs: IV=4, IX=9, XL=40, XC=90, CD=400, CM=900 • Encode (greedy): repeatedly subtract the largest value M,CM,D,CD,C,XC,L,XL,X,IX,V,IV,I that fits, appending its symbol • Decode: scan left→right; if a symbol is smaller than the one after it, subtract it, otherwise add it • Range: 1 to 3999 (MMMCMXCIX); larger needs an overline/vinculum (×1000)
📰 Formula
• Symbol values: I=1, V=5, X=10, L=50, C=100, D=500, M=1000 • Subtractive pairs: IV=4, IX=9, XL=40, XC=90, CD=400, CM=900 • Encode (greedy): repeatedly subtract the largest value M,CM,D,CD,C,XC,L,XL,X,IX,V,IV,I that fits, appending its symbol • Decode: scan left→right; if a symbol is smaller than the one after it, subtract it, otherwise add it • Range: 1 to 3999 (MMMCMXCIX); larger needs an overline/vinculum (×1000)
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Writing four of the same symbol in a row (IIII, XXXX, CCCC) instead of using subtractive form (IV, XL, CD).
- Using V, L or D as the smaller, subtracted symbol — only I, X and C can be subtracted (so 95 is XCV, never VC).
- Subtracting across two place-values, e.g. writing IM for 999 instead of the correct CMXCIX.
- Trying to convert 0 or a negative number — Roman numerals have no symbol for zero and no negatives.
- Attempting numbers above 3999 in plain text, which requires an overline (vinculum) this format can't show.
💡 Tips
- Build from the left: knock off the thousands (M's) first, then hundreds, then tens, then ones.
- Memorize the six subtractive pairs (IV, IX, XL, XC, CD, CM) and the rest is just adding symbols.
- Only I, X and C are ever subtracted, and only from the next one or two larger symbols — never V, L or D.
- A valid numeral never repeats V, L or D, and never repeats I, X, C or M more than three times.
- For dates, 1900s start with MCM and 2000s start with MM — a fast way to sanity-check a year.
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❓ Frequently asked questions
How do I write a number in Roman numerals?
Break the number into thousands, hundreds, tens and ones, then write each part using I, V, X, L, C, D, M and the subtractive pairs. For example 276 = 200 (CC) + 70 (LXX) + 6 (VI) = CCLXXVI.
Why is 4 written as IV instead of IIII?
Standard Roman numerals avoid four of the same symbol in a row, so 4 uses subtractive notation: a smaller I before a larger V means 5 − 1 = 4. The same rule gives IX for 9, XL for 40 and CM for 900.
What is the largest number in Roman numerals?
In standard notation the largest is 3999 = MMMCMXCIX, because 4000 would need four M's (MMMM), which isn't allowed. Larger values use an overline (vinculum) that multiplies a symbol by 1,000, so V̄ = 5,000.
Is there a Roman numeral for zero?
No. The Roman system has no symbol for zero and no way to write negative numbers. The smallest value you can convert is 1 (I), which is why this tool only accepts 1 through 3999.
What year is MMXXIV in Roman numerals?
MMXXIV is 2024: MM = 2000, XX = 20, and IV = 4. You'll see it on 2024 movie copyrights, logos and event branding.
Which symbols can be subtracted in Roman numerals?
Only I, X and C are ever used as the subtracted (smaller) symbol, and only before the next one or two larger symbols. So 9 is IX, 40 is XL, 900 is CM — but you never write VC or IL; 95 is XCV and 49 is XLIX.
How do I convert a Roman numeral back to a number?
Read left to right and add each symbol's value, but when a smaller symbol sits before a larger one, subtract it instead. In MCMXC, the C before M is −100 (CM = 900) and the X before the final C is −10 (XC = 90), giving 1990.
What are the years 1990 and 2000 in Roman numerals?
1990 is MCMXC (M + CM + XC) and 2000 is MM. The 1900s all start with MCM and the 2000s start with MM, which makes movie and copyright years easy to read at a glance.
Why doesn't the converter accept decimals or fractions?
Roman numerals represent whole numbers only — there's no positional decimal point. The Romans expressed fractions with a separate duodecimal system (like the uncia), so this tool rounds to whole numbers and works on integers 1–3999.