Roman Numeral Converter

Roman numerals use seven letters. Each has a fixed value, and a number is written by putting letters side by side, biggest first, and adding them up. To keep numbers short, a smaller letter placed just before a bigger one is taken away instead of added: IV is 5 − 1 = 4.

The rules

• Write the letters from biggest to smallest and add them: VIII = 5 + 1 + 1 + 1 = 8.
• I, X, C and M can repeat, but never more than three times in a row: III = 3, but 4 is IV, not IIII.
• V, L and D never repeat (VV would just be X) and are never taken away.
• Only I, X and C go in front of a bigger letter, and only before the next two: I before V and X, X before L and C, C before D and M. So 49 is XLIX, not IL, and 99 is XCIX, not IC.
• Only one letter can be taken away at a time: 8 is VIII, not IIX.
• That leaves six pairs: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400 and CM = 900.

The formula

Roman numeral = symbols for the thousands + symbols for the hundreds + symbols for the tens + symbols for the ones
for each digit d (with one, five and ten being I V X, X L C or C D M for that place):
d = 1 to 3 → one repeated d times · d = 4 → one + five · d = 5 → five · d = 6 to 8 → five + one repeated (d − 5) times · d = 9 → one + ten · d = 0 → nothing
4,000 and up: thousands written as a numeral with a line over it (× 1,000), then the rest

Worked example

2026. Split it into place values: 2026 = 2,000 + 0 hundreds + 20 + 6. Now swap each for its symbols: 2,000 is two thousands, MM. There are no hundreds, so nothing goes there. 20 is two tens, XX. 6 is five plus one, VI. Join them up, biggest to smallest: MMXXVI. To check, read it back letter by letter: M + M + X + X + V + I = 1,000 + 1,000 + 10 + 10 + 5 + 1 = 2,026.

One with every kind of pair: 1994 = 1,000 + 900 + 90 + 4 = M + CM + XC + IV = MCMXCIV. Going the other way, MCMXC splits into M, CM and XC: 1,000 + 900 + 90 = 1990.

When a numeral is not standard

If you type something that breaks a rule, the converter still reads it by adding up (taking away any letters in front of a bigger one), tells you which rule it breaks and shows the standard form. IIII is read as 4 and should be IV. VX is read as 5, but V is never taken away, so 5 is just V. IIX is read as 8 (an old way of writing it), but the standard is VIII. Many clock faces show 4 as IIII; that is a tradition, not the standard.

Numbers bigger than 3,999: the line over (vinculum)

The biggest normal numeral is MMMCMXCIX = 3,999, because M can only repeat three times. For bigger numbers, a line drawn over letters multiplies them by 1,000. The converter writes the thousands as a numeral with a line over it, then the rest as normal:

• 4,000 = IV (4 × 1,000) and 5,500 = VD (5,000 + 500).
• 10,000 = X, 100,000 = C and 1,000,000 = M.
• The biggest is 3,999,999 = MMMCMXCIXCMXCIX.

Some books write 4,000 as MV instead, and the Romans also used other marks (a frame round a numeral for × 100,000, and CIↃ for 1,000). The line-over style is the one most converters and textbooks use today. When you copy a result, the line is kept as a combining overline character, which shows up in most apps.

Dates

A date is three separate numerals: the day, the month and the year. 10 October 2026 is X.X.MMXXVI written day first, and the same in US order because the day and month are both 10. 25 December 2026 is XXV.XII.MMXXVI day first, or XII.XXV.MMXXVI month first. With a two-digit year, 2026 becomes XXVI. Years ending in 00 can’t be shortened, because there is no numeral for 0. If you are getting a tattoo, check the order (day or month first) twice before you book.

Roman sums

The Romans did sums on a counting board (an abacus), not with the letters themselves, so the converter changes each numeral to a number, does the sum and writes the answer back as a numeral. MMXXVI + XLII = 2,026 + 42 = 2,068 = MMLXVIII. Dividing gives a whole number and a remainder: MMXXVI ÷ XLII = 48 remainder 10, because 48 × 42 = 2,016 and 2,026 − 2,016 = 10, so XLVIII remainder X. An answer of 0 or below can’t be written.

Roman numerals are whole numbers from 1 upwards. There is no zero (medieval writers used N, for nulla) and no negative numbers. Fractions were counted in twelfths, with S for a half.