Roman numeral converter

The rules that make a Roman numeral valid

A Roman numeral is written from the largest values to the smallest. The symbols I, X, C and M may repeat at most three times in a row, while V, L and D never repeat, because VV would simply be X, LL would be C and DD would be M.

Subtraction is allowed only in six specific pairs: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). In each pair the smaller symbol stands directly before the larger one, and what is subtracted is always a one, a ten or a hundred.

It helps to notice that every decimal place follows exactly the same pattern, only the letters change:

• Ones 1-9: I, II, III, IV, V, VI, VII, VIII, IX
• Tens 10-90: X, XX, XXX, XL, L, LX, LXX, LXXX, XC
• Hundreds 100-900: C, CC, CCC, CD, D, DC, DCC, DCCC, CM
• Thousands 1000-3000: M, MM, MMM

How to read years like MCMXCIV and MMXXVI

Read the numeral from left to right and, for each symbol, look at the next one. If the next one is larger, the two form a subtractive pair. If not, simply add the symbol.

MCMXCIV splits into M + CM + XC + IV. That is 1000 + 900 + 90 + 4 = 1994. Such a long form is typical for 20th-century years, because 1900 alone already takes three symbols, MCM.

MMXXVI is much simpler: MM = 2000, XX = 20, VI = 6, making 2026. There are no subtractive pairs here, since in VI the smaller symbol comes after the larger one. A few more examples: MCMXVIII = 1918 and MCMLXXXIV = 1984.

From a number to a Roman numeral, place by place

To convert, split the number into thousands, hundreds, tens and ones, then write each part using the pattern above. 1987 = 1000 + 900 + 80 + 7, giving M + CM + LXXX + VII = MCMLXXXVII.

A Roman numeral can be very long even for a modest number. 1888 is MDCCCLXXXVIII, 13 symbols. Within 1-3999 the longest is 3888 = MMMDCCCLXXXVIII, 15 symbols, because every place holds an 8, the digit with the longest form.

You can even add Roman numerals: XXVII + XVI. Gather the symbols in order of size: XXX VV III. Two Vs make an X, so you get XXXX III. Four Xs in a row are not allowed and become XL, so the result is XLIII, or 43.

Why clocks show IIII instead of IV

Many clock faces with Roman numerals mark four as IIII. This is a long-standing clockmaking tradition, not a mistake. Visual balance is often given as the reason, since IIII on the right mirrors VIII on the left, but there is no single proven explanation.

In standard notation four is still IV. That is why the calculator answers "Invalid numeral" for the input IIII. The same goes for other non-standard shortcuts you sometimes see: IC for 99 (correctly XCIX), IM for 999 (correctly CMXCIX) and MIM for the year 1999 (correctly MCMXCIX).

Why there is no zero and why the limit is 3999

Roman numerals are not a positional system. A symbol's value does not depend on where it stands; X always means ten. So there is no need for a placeholder, which is the job zero does in our system. Calculations were done on a counting board and only the result was written down in numerals. Medieval tables sometimes used the word nulla for an empty value.

The 3999 limit follows from the repetition rule: M can appear at most three times in a row and there is no separate symbol for 4000. Larger numbers were written with a bar over a symbol that multiplies its value by a thousand, but that is not part of standard notation and cannot be typed as plain text.

Where you still see Roman numerals

Today Roman numerals appear most often in centuries (the XXI century in many European languages), in the names of monarchs (Peter I, Louis XIV), in book chapters and volumes, in film sequels and in the numbering of recurring events. In older documents and on gravestones the month is sometimes written as a Roman numeral too, for example 24.II.1918.