Large Roman Numerals

The rules in how Roman numerals work allow each symbol at most three times in a row and give every place its own letters: I–V–X for units, X–L–C for tens, C–D–M for hundreds. The thousands place only has M, so it can go up to MMM and no further. Put the largest form of every place together and you get MMM + CM + XC + IX = 3,999.

Writing 4,000 as MMMM breaks the repeat rule, which is why the converter on this site stops at 3,999.

A line over a numeral means "this many thousands". Florian Cajori, in A History of Mathematical Notations (1928, § 51), describes the thousand-fold value of a number being indicated "by a horizontal line placed above it".

The part under the bar is read like any other numeral and then multiplied by 1,000. Whatever follows without a bar is added in the normal way: in the last row, M̄ is 1,000,000 and CM is 900.

There is more than one way to write numbers between 4,000 and 9,999. The tables on this site put the whole thousands part under the bar and leave the rest without it:

• 4,000 = IV (IV thousands), not MMMM or MV̄;
• 13,000 = XIII (XIII thousands);
• 2,026,000 would be MMXXVI with a bar: 2,026 thousands.

The advantage is that you read the barred part as a normal numeral, so the four rules still apply inside it.

Split the numeral where the bar ends. Read the barred part as an ordinary numeral and multiply it by 1,000, then read the rest and add it.

• XLVXXVI: the barred part is XLV = 45, so 45,000; the rest is XXVI = 26. Total: 45,026.
• CCL: CCL = 250 under the bar, nothing after it. Total: 250,000.
• MCM: M under the bar is 1,000 × 1,000 = 1,000,000; CM = 900. Total: 1,000,900.

With this convention the largest number you can write is 3,999 thousands plus 3,999: MMMCMXCIXCMXCIX = 3,999,999.

Three mistakes come up again and again:

1. A bar over only the first letter. In IV both I and V are under the bar. A bar over the I alone would mean 1,000 + 5.
2. Mixing in MMMM. 4,000 is not MMMM: the repeat rule still applies.
3. Barring the whole numeral. In 45,026 the XXVI stays without a bar; barring it would turn 26 into 26,000.

Cajori (§ 51) also records strokes placed on the top and on the sides of a numeral to indicate hundreds of thousands, with the example |X|CLXXXDC for 1,180,600. The older sign for 1,000 itself was CIƆ, an I between a C and a reversed C (§ 53).

These forms belong to the history of the system. They are useful for reading old sources, not for writing a modern date or title.

On a computer the bar is a combining character, U+0305 COMBINING OVERLINE (Unicode data). You type the letter and then the overline, which attaches itself to the letter before it: V + U+0305 = V̅. For I̅V̅ you need it twice, once after each letter.

• In running text, write the number in digits. A reader who sees X̅ may not know the convention.
• In dates, you never need it: years go up to 3,999 without a bar.
• In a tattoo or engraving, ask the artist to draw the bar as a line, and check the numeral first with the converter.

Convert a numberGet the Roman numeral for any number from 1 to 3,999, with the breakdown.Open the tool