The seven Roman numeral symbols and what each one is worth
Roman numerals are built from exactly seven letters: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500, and M is 1000. The values follow a simple ladder that alternates between one and five at each power of ten: 1, 5, 10, 50, 100, 500, 1000. Once you have that ladder memorised you already hold most of the system, because every numeral you will ever read is some arrangement of those seven letters.
The values are absolute rather than positional. In decimal notation the 2 in 20 means something different from the 2 in 2, because its column decides its weight. In Roman notation an X is 10 no matter where it appears in the string, so reading a numeral is a running total rather than a sum of column weights. That is also why the system needs no zero: there are no empty columns to hold open, so nothing has to stand in for a missing digit.
Repetition is limited. I, X, C, and M may repeat up to three times in a row, giving III for 3, XXX for 30, CCC for 300, and MMM for 3000. V, L, and D never repeat, because two of them always equal the next symbol up, and VV would simply be written X. The three M limit is what fixes the practical ceiling of the system at 3999, written MMMCMXCIX, since standard notation has no single symbol worth more than 1000.
Additive notation versus subtractive notation
The default rule is additive. When symbols are written in descending order of value you simply add them up. MMXXVI, the numeral this converter starts with, is 1000 plus 1000 plus 10 plus 10 plus 5 plus 1, which is 2026. VI is 5 plus 1, or 6. LXXVII is 50 plus 10 plus 10 plus 5 plus 1 plus 1, or 77. Nothing more complicated is happening in the long stretches of most numerals.
Subtractive notation is the exception, and it applies when a smaller symbol is placed immediately before a larger one. There are exactly six legal subtractive pairs: IV is 4, IX is 9, XL is 40, XC is 90, CD is 400, and CM is 900. The pattern behind that list is strict. Only the powers of ten (I, X, and C) may be used as the subtracting symbol, and each may only be subtracted from the next two values above it. I goes before V and X, X goes before L and C, C goes before D and M.
This is why combinations that look arithmetically reasonable are still invalid. IL would suggest 49 and IC would suggest 99, but I may only precede V and X, so the correct forms are XLIX (40 plus 9) and XCIX (90 plus 9). The restriction is not decoration. It is what guarantees that every number between 1 and 3999 has exactly one correct spelling, and that single correct spelling is what makes a converter able to check its own work.
Why 4 is IV but clock faces often show IIII
In the modern standard form, 4 is IV. The subtractive pair shortens what would otherwise be four repeated marks, and the same logic gives IX for 9 rather than VIIII. Applied consistently, subtractive notation is what keeps numerals compact: 1999 is MCMXCIX in nine characters instead of MDCCCCLXXXXVIIII in sixteen.
IIII is not a mistake so much as an older habit. Roman inscriptions and early manuscripts used additive forms freely, and subtractive notation was not applied consistently until well after the Roman period. The standard that schools teach today settled in the medieval and early modern era, so both spellings have genuine historical use behind them even though only one is now considered correct.
Clock and watch dials are the place where IIII survives in everyday life. The usual explanations are visual rather than mathematical: IIII sits opposite VIII on the dial and gives the two sides a similar weight of strokes, and the first four hours then read I, II, III, IIII as a run of pure tally marks. It is a convention rather than a rule, and plenty of famous dials ignore it, including the clock at the Palace of Westminster that houses Big Ben, which uses IV. This converter follows the modern standard, so it will produce IV for 4 and will reject IIII if you type it in.
Working through 1994 to MCMXCIV, and back again
Start by splitting the number by place value: 1994 is 1000 plus 900 plus 90 plus 4. Each of those parts has a single Roman spelling. 1000 is M, 900 is the subtractive pair CM, 90 is the subtractive pair XC, and 4 is the subtractive pair IV. Written in order, that gives M, CM, XC, IV, or MCMXCIV. Three of the four parts happen to be subtractive pairs, which is why 1994 looks so much less regular than a year like 2026.
The mechanical version of that process is the greedy method the converter uses internally. It walks a fixed list of thirteen values (1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1), and at each step it takes the largest value that still fits and subtracts it from the remainder. For 1994: take 1000 and write M, leaving 994; take 900 and write CM, leaving 94; take 90 and write XC, leaving 4; take 4 and write IV, leaving 0. The greedy walk always produces the one canonical spelling, which is why it can be trusted as the reference form.
Reading in the other direction is a left to right scan in which you compare each symbol with the one after it. In MCMXCIV, the opening M is followed by C, a smaller value, so M counts as a straight 1000. The next C is followed by M, a larger value, so C and M bind together as 900 and the total reaches 1900. Then X is followed by C, so XC binds as 90 and the total reaches 1990. Finally I is followed by V, so IV binds as 4 and the total closes at 1994. Apply the same scan to MMXXVI and you get 1000, 1000, 10, 10, 5, 1, which adds to 2026.
What this converter accepts and what it rejects
The page shows two linked fields, one for the Arabic number and one for the Roman numeral, and editing either one rewrites the other as you type. It opens on 2026 and MMXXVI. Anything you type into the numeral field is uppercased immediately, so mmxxvi and MMXXVI behave identically. Each field has its own copy button, and that button stays disabled while the value beside it is not a valid conversion.
Validation on the numeral side is stricter than a simple letter check. The input must consist only of M, D, C, L, X, V, and I, and then the parsed value has to convert back to exactly the string you typed. That round trip is what rejects non canonical spellings. IIII does parse to 4, but 4 renders as IV, so the strings differ and the input is refused. IC, VX, and MMMM fail the same test. When input is refused the number field is cleared and an invalid input message appears under the numeral, rather than the tool guessing at what you meant.
On the number side the field reads your text as an integer and only values from 1 to 3999 produce a numeral. Zero, negative numbers, and anything from 4000 upward clear the numeral field instead. Because the parse stops at the first character that is not a digit, a decimal is truncated at the point, so 12.5 yields XII rather than an error. There is no support for the vinculum, the overline that multiplies a symbol by 1000 in extended notation, so values above 3999 cannot be expressed here at all.
Where Roman numerals still turn up
Despite being replaced for arithmetic centuries ago, the system remains in steady decorative and ordinal use. Clock and watch dials, the front matter page numbers of printed books, act and chapter numbers, regnal numbers for monarchs and popes, building cornerstones, film and television copyright years, Super Bowl numbering, and the outer levels of formal outlines all still use it. In each case the numerals are labels or sequence markers rather than quantities to be calculated with.
Years are the conversion people ask for most often, and they show the full range of the notation. 2026 is MMXXVI and 2000 is MM, both short and purely additive. 1969 is MCMLXIX and 1999 is MCMXCIX, both long because they stack a 900 with a 90 or a 9. If a year looks unexpectedly long when you convert it, that stacking is almost always the reason.