Roman Numeral Converter

How Roman numerals work

Roman numerals use seven letters, each with a fixed value, combined by addition. Write the symbols in descending order and add them up: MMXXVI is 1000 + 1000 + 10 + 10 + 5 + 1, or 2026. There is no positional value — an X is always ten wherever it appears, unlike the 2 in 20 and 200.

That simplicity is also the system’s limitation. Without place value there is no column to carry into, which makes multiplication and division awkward, and there is no symbol for zero because a positional system is what makes zero necessary in the first place. The Romans did have fractions, based on twelfths rather than tenths, written with their own separate symbols.

For the opposite idea, a fully positional system built from just two symbols, see the binary converter. And Rome was not alone in treating letters as numbers: Hebrew gematria and Greek isopsephy assign a value to every letter of an entire alphabet, the same idea reaching a different conclusion.

The origin notes are the conventional account rather than settled etymology.

The subtractive rules

Strict addition would make 4 into IIII and 9 into VIIII. Standard notation instead allows a smaller symbol placed before a larger one to be subtracted from it, giving IV and IX. This is the part of the system that generates almost every wrong answer, because the rule is narrower than people assume.

Only six subtractive pairs are legal. I may precede V or X. X may precede L or C. C may precede D or M. That is the complete list. V, L and D never subtract, and no symbol may skip more than one power of ten. So 99 is not IC — it is XCIX, ninety plus nine. And 999 is not IM but CMXCIX: nine hundred, ninety, nine. The converter above rejects the invalid forms and tells you which rule they break rather than silently guessing.

The repetition rules

I, X, C and M may repeat up to three times in a row. V, L and D may not repeat at all, because two of them would always be better written as the next symbol up — VV is simply X. Combined with the subtractive pairs, these rules mean every number from 1 to 3,999 has exactly one correct representation.

Converting by hand

1. Start with the largest symbol value that fits inside your number.
2. Write that symbol down and subtract its value.
3. Repeat with the remainder, always taking the largest value that fits.
4. Treat the six subtractive pairs as values in their own right — 900 and 400 and 90 and 40 and 9 and 4 — so they come out correctly without special handling.
5. Stop when the remainder reaches zero.

For 1994: the largest fitting value is 1000, leaving 994. Then 900 (CM), leaving 94. Then 90 (XC), leaving 4. Then 4 (IV), leaving 0. The result is MCMXCIV. Working the other way is a left-to-right scan: if a symbol is smaller than the one after it, subtract it, otherwise add it.

The working panel in the converter above runs this same trace live on whatever you type, in both directions.

Dates in Roman numerals

Dates are the most common reason people convert Roman numerals, and the reason is usually permanent: a wedding band, an anniversary piece, a tattoo, a cornerstone. Getting it wrong is expensive, which is why the date tab above shows a large preview before you commit.

There is no single official format. The convention is to convert each component separately and join them with a separator, most often an interpunct: 14 February 2026 becomes XIV•II•MMXXVI. Day-month-year is the more common ordering internationally and month-day-year in the United States, so the order is a choice rather than a rule — but it should match how the wearer reads it, because the numerals give no clue which is which. A date like III•IV•MMXXVI is ambiguous between 3 April and 4 March.

Two practical notes. Single-digit days and months produce very short groups, so IV•VII•MMXXV can look unbalanced next to a long year; some jewellers pad with a leading I-form, which is not standard and changes the value, so avoid it. And film and television copyright dates are traditionally set in Roman numerals, which is why the year at the end of the credits is often the hardest thing on screen to read.

Years in Roman numerals

Numbers above 3,999

Standard notation stops at 3,999, written MMMCMXCIX, because four thousand would need four Ms and M may only repeat three times. The extended system solves this with a vinculum — a horizontal line drawn above a symbol, multiplying its value by a thousand. V with a line is 5,000, X with a line is 10,000, and M with a line is a million. That takes the ceiling to 3,999,999.

The vinculum is genuinely historical rather than a modern invention, though it was never fully standardised and other conventions existed alongside it, including enclosing a numeral in a partial box. In practice the overline is rarely needed — almost nothing outside mathematics puzzles requires a Roman numeral above about 2,100 — but a converter that simply fails above 3,999 without explanation is unhelpful, so this one handles it and says what it is doing.

The converter renders overlines with the Unicode combining overline, and its copy button also offers a plain-text fallback using pipes (|V| for 5,000), because combining marks do not survive every paste target.

For developers

Converting between integers and Roman numerals is a standard programming exercise and a common interview question — leetcode ranks 10th on this very search term with its Integer to Roman problem, which is an unusual thing to see on a converter SERP and a fair indication of who is searching.

The integer-to-Roman direction is solved cleanly by greedy subtraction over an ordered value table that includes the six subtractive pairs as first-class entries. Because those pairs are in the table, no special-case logic is needed and the output is canonical by construction — the algorithm cannot emit IIII or IM. The trace table above is that algorithm running on 1994.

The Roman-to-integer direction is a single left-to-right pass: add each symbol’s value, unless it is smaller than the symbol immediately following it, in which case subtract it. It is four lines of code and it will happily accept malformed input like IIII or IM and return a plausible number, which is why a separate validation pass matters if you are accepting user input rather than trusted data.

Worth knowing for test cases: 3,999 is the largest standard value; 3,888 is the longest numeral under 4,000 at fifteen characters; 1,444 and 444 exercise multiple subtractive pairs in one value; and 1,994 is the conventional textbook example because it uses three of the six pairs.

Who uses this and why

Where Roman Numerals Are Used Today