Roman numerals converter

What are Roman numerals?

Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers throughout Europe well into the late Middle Ages. Instead of using positional digits like the decimal system, Roman numerals combine seven letters from the Latin alphabet, each standing for a fixed value.

The seven symbols are I (1), V (5), X (10), L (50), C (100), D (500), and M (1000). By arranging and combining these letters according to a small set of rules, you can write any whole number from 1 to 3999.

Roman numerals are still used today for clock faces, book chapters, movie sequels, the names of monarchs and popes, and the year of copyright on films and buildings.

How does the calculator work?

This converter works in two directions. Choose Roman from number to turn a regular integer into a Roman numeral, or Number from Roman to turn a Roman numeral back into an integer.

• In number-to-Roman mode, enter any whole number between 1 and 3999. The calculator builds the numeral by repeatedly subtracting the largest possible value and appending the matching symbols.
• In Roman-to-number mode, type a numeral using the letters I, V, X, L, C, D, and M (upper or lower case). The calculator reads the symbols from left to right, adding each value and subtracting whenever a smaller symbol comes before a larger one. Only valid, canonical numerals are accepted.

The conversion rules

To build a Roman numeral, the values are taken from largest to smallest:

A symbol placed before a larger symbol is subtracted; otherwise values are added. The six subtractive pairs are:

To read a numeral, sum the values of its symbols, subtracting any symbol whose value is smaller than the one that follows it.

Worked examples

Example 1: 2024 → MMXXIV

Break 2024 into parts: $2000 + 20 + 4$. This gives $MM + XX + IV$, so $2024 = MMXXIV$.

Example 2: 4 → IV

Four is written with the subtractive pair $IV$ (one before five), so $4 = IV$.

Example 3: 49 → XLIX

Split 49 into $40 + 9$. Forty is $XL$ and nine is $IX$, so $49 = XLIX$.

Example 4: 1994 → MCMXCIV

Break 1994 into $1000 + 900 + 90 + 4$. This gives $M + CM + XC + IV$, so $1994 = MCMXCIV$.

Example 5: XIV → 14

Reading $XIV$: ten plus (five minus one) is $10 + 4 = 14$.

Practical notes

• The classic Roman system has no symbol for zero and no way to write negative numbers, which is why the range is limited to 1–3999.
• Numbers above 3999 historically used a bar over a symbol (a vinculum) to multiply its value by 1000, but this calculator uses only the standard seven letters.
• Always write numerals in canonical form: for example, four is $IV$, not $IIII$, and nine is $IX$, not $VIIII$.

If you are exploring how other numeral systems represent values, see the binary to decimal converter and the binary converter.