Roman Numeral Converter

Roman numerals use seven letters to represent values: I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). Numbers are formed by combining these letters according to additive and subtractive rules. The additive system means MMMDCCCLXXXVIII = 3000 + 800 + 80 + 8 = 3888. The subtractive system means that a smaller value before a larger value is subtracted: IV = 5-1 = 4, IX = 10-1 = 9, XL = 50-10 = 40, XC = 100-10 = 90, CD = 500-100 = 400, CM = 1000-100 = 900.



The conversion from Arabic numbers works through a greedy algorithm: find the largest Roman numeral value that fits into the remaining number, append that symbol, subtract its value, and repeat. The lookup table includes both the seven base symbols and the six subtractive combinations in decreasing value order: 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).



For decoding Roman numerals, the algorithm scans left to right comparing each letter's value to the next. If the current letter is less than the next letter, subtract it; otherwise add it.

1. Historical Document Interpretation
Legal documents, historical records, monuments, clock faces, and architectural inscriptions use Roman numerals extensively. Converting these to Arabic numbers helps researchers, historians, and curious readers interpret dates, chapter numbering, and numerical references in older texts and inscriptions.



2. Formal Document and Legal Writing
Roman numerals are conventionally used for certain formal purposes: book chapters (Chapter III), movie sequels (Rocky IV), legal sub-paragraphs (Article IV, Section ii), preliminary page numbering in books, and Super Bowl editions (Super Bowl LVIII). Writers and legal professionals use converters to confirm correct numerals for these contexts.



3. Learning Number Systems
Students learning the history of mathematics and number systems study Roman numerals as a contrasting example to the Hindu-Arabic positional numeral system. The converter helps students understand both encoding and the mathematical concepts behind additive vs. positional value systems.



4. Architecture and Design
Architects, designers, and artists incorporating Roman numerals in their work (building facades, memorial stones, artwork, typography) use converters to ensure accurate numeral representation for years, edition numbers, or numerical inscriptions.



5. Tattoo and Artistic Use
Roman numeral tattoos representing birth years, significant dates, or meaningful numbers are extremely popular. Converters ensure the tattoo artist and client have the correct numeral sequence before permanent commitment.

• Standard form vs. non-standard: The standard form uses the minimum number of symbols. IIII is non-standard (clocks sometimes use it); IV is standard for 4. VIIII is non-standard for 9; IX is correct. The converter produces standard form.



• Roman numerals max out at 3,999: Standard Roman numerals represent values from 1 to 3,999 (MMMCMXCIX). Numbers above 3,999 require extended notation (a bar over a letter multiplies it by 1,000) which is not commonly used in modern contexts.



• Zero has no Roman numeral: The Romans used "nulla" (nothing) for the concept of zero, but the numeral system doesn't include a symbol for zero. This is one reason the Hindu-Arabic system (with positional notation and zero) replaced Roman numerals for calculation.



• Years in Roman numerals: To write a year in Roman numerals, convert the year as a regular number. 2025 = MMXXV (2000 + 20 + 5).