Roman numeral reference examples
Worked examples across the supported range, illustrating additive and subtractive notation.
| Number | Roman numeral |
|---|---|
| 1 | I |
| 4 | IV |
| 9 | IX |
| 40 | XL |
| 90 | XC |
| 400 | CD |
| 900 | CM |
| 1994 | MCMXCIV |
| 2024 | MMXXIV |
| 3999 | MMMCMXCIX |
- This calculator validates Roman-numeral input strictly against the standard subtractive form and will reject non-standard variants such as IIII, VX, IC or XM.
- The supported range is 1 to 3,999 (MMMCMXCIX) — the practical limit of the standard notation without historical extensions such as an overline to multiply by 1,000.
- Modern typesetting sometimes uses the dedicated Unicode Roman numeral characters (for example Ⅳ, Ⅸ) rather than ordinary Latin letters; this calculator works with standard Latin letters (IV, IX).
What are Roman numerals?
Roman numerals are a numeral system that originated in ancient Rome, using combinations of seven letters — I (1), V (5), X (10), L (50), C (100), D (500) and M (1,000) — to represent numbers. Values are built by combining these symbols additively (placing a smaller or equal symbol after a larger one adds it, as in VI = 6) and subtractively (placing a smaller symbol immediately before a larger one subtracts it, as in IV = 4). The now-standard subtractive convention — IV rather than IIII, IX rather than VIIII — became the settled norm relatively gradually; ancient Roman inscriptions were often inconsistent, and additive forms like IIII still appear traditionally on some clock faces today.
The system has no symbol for zero and no standard mechanism for negative numbers, and the basic letter combinations only reach 3,999 (MMMCMXCIX) without extending the notation — historically, a horizontal bar (vinculum) over a numeral was sometimes used to multiply its value by 1,000 for larger figures. Because that extension is not part of the widely recognized modern convention, this calculator, like most standard Roman numeral tools, supports whole numbers from 1 to 3,999 and enforces the standard subtractive form strictly.
How to use this Roman numeral converter
- Choose a direction: "Number to Roman numeral" or "Roman numeral to number."
- In number-to-Roman mode, enter any whole number from 1 to 3,999.
- In Roman-to-number mode, enter a Roman numeral using standard subtractive notation, such as MMXXIV.
- Read the converted result. If the Roman numeral you entered uses a non-standard form (such as IIII or IC), the calculator will not return a result — re-check it against the standard notation rules.
The rules behind Roman numeral notation
Standard Roman numeral notation follows a small set of fixed rules rather than a single arithmetic formula: each letter has a fixed value, symbols are read left to right and summed, and a smaller-value symbol placed immediately before a larger one is subtracted rather than added.
Common mistakes
- Writing invalid Roman forms — IIII instead of IV, VX instead of XV, IC instead of XCIX, or XM instead of CMXC — all of which this calculator's strict validation rejects.
- Repeating a symbol more times than the standard notation allows, such as XXXX instead of XL or DD instead of M; the rules permit at most three consecutive I/X/C/M and only one V/L/D.
- Expecting a Roman numeral for zero or a negative number — the system has no symbol for zero and cannot represent negative values.
- Trying to convert a number above 3,999 or below 1 — the standard notation this calculator implements tops out at MMMCMXCIX (3,999) and has no representation below I (1).
よくある質問
What is the highest number you can write in standard Roman numerals?
3,999, written MMMCMXCIX. Standard subtractive notation allows at most three consecutive M symbols, so 4,000 and above require historical extensions (such as a bar over a numeral to multiply it by 1,000) that are not part of the widely recognized modern convention — which is why this calculator supports 1 to 3,999.
Why is 4 written as IV and not IIII?
IV uses the subtractive convention (5 − 1 = 4), which became the settled modern standard for Roman numeral notation, replacing the older additive form IIII. Ancient Roman usage was actually inconsistent between the two, and IIII still appears by tradition on some clock faces, but IV is the form recognized as standard today and the one this calculator produces and requires.
How do you convert MCMXCIV to a number?
Reading left to right: M (1,000) + CM (900, since C before M subtracts) + XC (90, since X before C subtracts) + IV (4, since I before V subtracts) = 1,994. MCMXCIV is the standard Roman numeral for 1994.
Can Roman numerals represent zero?
No. The Roman numeral system, as used by the ancient Romans and in the modern standard convention, has no symbol for zero and no standard way to represent negative numbers. This calculator only accepts whole numbers from 1 to 3,999.
Why did my Roman numeral input get rejected?
The calculator validates input strictly against standard subtractive notation. Common rejected forms include repeating a symbol too many times (IIII, XXXX), placing a smaller symbol before one that's too much larger (IC, XM), or using an invalid subtractive pair (VX). Re-check the numeral against the standard rules — for example, use IV, IX, XL, XC, CD and CM for 4, 9, 40, 90, 400 and 900.
参考文献
- Ifrah G. The Universal History of Numbers: From Prehistory to the Invention of the Computer. John Wiley & Sons, 2000.
- Cajori F. A History of Mathematical Notations. Open Court Publishing, 1928 (reprinted Dover, 1993) — historical treatment of Roman numeral notation.
- Encyclopaedia Britannica. "Roman numerals."
- Unicode Consortium. The Unicode Standard, Number Forms block (Roman numeral symbols, U+2160–U+2188).