Roman Numerals Converter
Convert any whole number from 1 to 3999 into its Roman numeral, or translate a Roman numeral back into an Arabic number. Just pick the direction, type your value, and get the result instantly.
Convert to and from Roman Numerals
Roman Numerals Formula
Where:
- \(n\) — the Arabic number to convert (whole number from 1 to 3999)
- \(v\) — one of the thirteen symbol values of the standard system (1000, 900, 500, 400, …, 1)
- \(r_i\) — the \(i\)-th letter of the Roman numeral, read left to right
- \(\mathrm{val}\) — the value of a letter: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000
The first rule builds the numeral greedily, always taking the largest possible symbol; the second reads a numeral back by adding each letter's value, except when a smaller letter precedes a larger one, in which case it is subtracted (the subtractive pairs IV, IX, XL, XC, CD, CM).
Roman Numerals – Calculation Example
Example: convert the number 2024 to a Roman numeral (the default direction and value of the calculator).
\[ 2024 = 1000 + 1000 + 24 \to \mathrm{MM}, \qquad 24 = 10 + 10 + 4 \to \mathrm{XX} + \mathrm{IV} \]
Result: 2024 = MMXXIV
Reading it back with the subtractive rule confirms it: \(M + M + X + X + IV = 1000 + 1000 + 10 + 10 + 4 = 2024\).
How to Use the Calculator
- Open the Conversion direction dropdown and choose Number → Roman numeral or Roman numeral → Number. The input field switches automatically.
- For Number → Roman numeral, enter a whole number between 1 and 3999 in the Number field.
- For the reverse direction, type the numeral in the Roman numeral field using the letters I, V, X, L, C, D, M. Upper or lower case both work —
mmxxivandMMXXIVare the same. - Read the answer in the Your Results panel: either the Roman numeral or the Arabic number. If the input is out of range or not a valid numeral, an error message tells you exactly what to fix.
What Are Roman Numerals?
Roman numerals are the number notation of ancient Rome, built from seven capital letters: I, V, X, L, C, D and M. The system has no zero and no place value — a numeral is simply the sum of its letters, so VI is 5 + 1 = 6. Despite its age, it is still used everywhere today: clock faces, book chapters and volume numbers, film sequels and credits, monarchs and popes (Elizabeth II), Super Bowl numbering, and cornerstone dates on buildings.
The one non-obvious rule is subtractive notation: when a smaller letter stands directly before a larger one, it is subtracted rather than added. That gives exactly six allowed pairs — IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900 — and it is what keeps numerals compact. Without it, 1944 would be MDCCCCXXXXIIII; with it, the numeral is the much shorter MCMXLIV.
A correct, canonical numeral is always written from the largest value down to the smallest, with each subtractive pair kept together. When you convert a number with this calculator, the result always follows that canonical form; when you type a numeral in, it is validated against the same strict rules, so an entry like IIII or VV is rejected rather than silently misread.
Symbol Reference Table
| Symbol | Value | Symbol | Value |
|---|---|---|---|
| I | 1 | C | 100 |
| V | 5 | D | 500 |
| X | 10 | M | 1000 |
| L | 50 | — | — |
The subtractive pairs and their values:
- IV = 4, IX = 9
- XL = 40, XC = 90
- CD = 400, CM = 900
Assumptions, Limits and Practical Tips
The calculator covers the standard range 1 to 3999, which is the range expressible with the seven basic letters under the canonical rules. Numbers of 4000 and above historically required an overline (vinculum) that multiplies a symbol by 1000 — that notation is not supported here. There is also no zero: the concept simply did not exist in the Roman system.
Validation is strict on purpose. Forms that appear on old inscriptions or clock faces — such as IIII for 4, or repeated subtractions like IXIX — are not canonical and will produce an error message rather than a wrong number. If you get one, check the letters and their order: values must decrease left to right, and only the six subtractive pairs may "go backwards".
A quick sanity check for long numerals: M repeats at most three times (MMM = 3000 is the ceiling), and the total length of a well-formed numeral never exceeds 15 characters (MMMDCCCLXXXVIII = 3888). If your input looks far longer than that, something is off.
If you need conversions between modern notations and units instead — minutes to hours, metric prefixes, or temperature scales — try our Time Converter, the Metric Prefix Converter or the Fahrenheit to Celsius converter.
Frequently Asked Questions
How do I convert a number to Roman numerals by hand?
Break the number into thousands, hundreds, tens and ones, then convert each digit separately and concatenate. Write 1987 as 1000 + 900 + 80 + 7. Look up each part: 1000 = M, 900 = CM, 80 = LXXX, 7 = VII. The result is MCMLXXXVII. Each decimal digit uses its own group of letters (M/D/C for hundreds, C/L/X for tens, X/V/I for ones), so the digits never interfere with each other.
Why does the converter stop at 3999?
With only the seven letters I, V, X, L, C, D and M, the canonical rules allow M to repeat at most three times, so MMM = 3000 is the ceiling. To write 4000 and beyond, the Romans used a vinculum — an overline multiplying a symbol by 1000 — but that notation isn't supported here. If you need numbers above 3999, split them: 5000 could be written as V with an overline.
Why do some clocks show IIII instead of IV for 4?
That's a tradition, not an error. Clockmakers have used IIII on clock faces for centuries, possibly for visual balance with the VIII opposite it, or due to a legend that a clockmaker was fined for using IV to insult a king. Historically, IIII was also a common additive form on inscriptions. This calculator follows the modern canonical rules, so it always outputs IV and rejects IIII as input.
Can I write 1999 as MIM or 999 as IM?
No. The subtractive rule only allows six specific pairs: IV, IX, XL, XC, CD and CM. Only I, X and C may be subtracted, and only from a letter at most two steps larger — I subtracts from V or X, but never from M. So 1999 must be MCMXCIX (1000 + 900 + 90 + 9), and IM or MIM are invalid forms that the converter rejects.
How do I quickly read a long Roman numeral without converting every letter?
Scan left to right and keep a running total: add each letter's value, but if a letter is smaller than the one right after it, subtract it instead. Take MMXXIV: M + M + X + X are all added (2020), then I is smaller than V, so it counts as −1, and V adds 5, giving 2024. If the letters mostly decrease left to right, you can often just group and sum: MMCDL = 2000 + 400 + 50 = 2450.
What was the longest valid Roman numeral?
3888, written MMMDCCCLXXXVIII — 15 characters. It's the longest because every position uses the maximum number of repeated letters: three M's, one D, three C's, one L, three X's, one V and three I's. No other number in the range 1–3999 needs more symbols, which makes numeral length a quick sanity check: anything longer than 15 characters is definitely invalid.
Do lowercase roman numerals mean the same thing?
Yes — case doesn't change the value. Lowercase roman numerals are common in specific contexts: page numbering in book prefaces, sublist items in outlines, and chord scale degrees in music theory (i, iv, V7). MMXXIV and mmxxiv both equal 2024, and this converter accepts either. Just don't mix unrelated characters, spaces or punctuation inside the numeral.