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How This Calculator Works
A Roman numeral is a number written using combinations of the letters I, V, X, L, C, D, and
M, each standing for a fixed value (1, 5, 10, 50, 100, 500, and 1,000). Enter a whole number to
see its Roman numeral spelling, or enter a Roman numeral to see the number it represents.
Roman numerals are built by combining symbols and adding their values together, largest to
smallest, left to right — for example, MCMXCIV is M (1,000) + CM (900) + XC (90) + IV (4) = 1,994.
The Romans themselves used a looser system over the centuries, but the version taught and used
today follows a consistent, standardized convention (the one this calculator uses).
The Formula
Number to Roman: starting from the largest value symbol (M = 1,000) down to the smallest
(I = 1), repeatedly subtract that symbol’s value from the number and append the symbol, as many
times as it fits, before moving to the next smaller symbol.
Roman to number: scan the letters and add each symbol’s value — except when a smaller-value
symbol appears immediately before a larger one, which means “subtract” instead (as in IV, IX,
XL, XC, CD, and CM).
Standard Roman numerals never repeat the same symbol more than three times in a row — a
four-in-a-row situation (like 4, or “IIII”) is instead written as a subtractive pair (“IV”)
using the next symbol up.
Worked Example
Converting the number 1,994:
1,994 contains one 1,000 → M
What’s left (994) contains one 900 (the subtractive pair for “one hundred less than a
thousand”) → CM
What’s left (94) contains one 90 → XC
What’s left (4) is the subtractive pair for “one less than five” → IV
Put it all together: MCMXCIV
Cómo funciona esta calculadora
Un numeral romano es un número escrito usando combinaciones de las letras I, V, X, L, C, D y
M, cada una con un valor fijo (1, 5, 10, 50, 100, 500 y 1,000). Ingresa un número entero para ver
su forma en numeral romano, o ingresa un numeral romano para ver el número que representa.
Los numerales romanos se construyen combinando símbolos y sumando sus valores, de mayor a menor,
de izquierda a derecha — por ejemplo, MCMXCIV es M (1,000) + CM (900) + XC (90) + IV (4) = 1,994.
Los propios romanos usaron un sistema más flexible a lo largo de los siglos, pero la versión que se
enseña y se usa hoy en día sigue una convención consistente y estandarizada (la que usa esta
calculadora).
La fórmula
Número a numeral romano: comenzando desde el símbolo de mayor valor (M = 1,000) hasta el
más pequeño (I = 1), resta repetidamente el valor de ese símbolo del número y añade el símbolo,
tantas veces como quepa, antes de pasar al siguiente símbolo más pequeño.
Numeral romano a número: recorre las letras y suma el valor de cada símbolo — excepto cuando
un símbolo de menor valor aparece inmediatamente antes de uno mayor, lo cual significa “restar”
en su lugar (como en IV, IX, XL, XC, CD y CM).
Los numerales romanos estándar nunca repiten el mismo símbolo más de tres veces seguidas — una
situación de cuatro seguidas (como el 4, o “IIII”) se escribe en su lugar como un par
sustractivo (“IV”) usando el siguiente símbolo superior.
Ejemplo resuelto
Convirtiendo el número 1,994:
1,994 contiene un 1,000 → M
Lo que queda (994) contiene un 900 (el par sustractivo para “cien menos que mil”) → CM
Lo que queda (94) contiene un 90 → XC
Lo que queda (4) es el par sustractivo para “uno menos que cinco” → IV
What is the largest number a Roman numeral can represent?
Standard Roman numerals go up to 3,999 (MMMCMXCIX). There is no standard symbol for zero or negative numbers, and repeating "M" a fourth time in a row isn't part of the standard system, which is why 4,000 has no standard representation.
Why do some numbers use a 'subtractive' pair like IV instead of IIII?
The standard convention avoids repeating any symbol more than three times in a row. Instead of IIII for 4, a smaller symbol is placed before a larger one to mean "subtract" — IV means "one less than five." The same pattern applies to IX (9), XL (40), XC (90), CD (400), and CM (900).
Why did my Roman numeral input show an error?
This calculator checks that whatever you typed is actually the standard, canonical way of writing that number — not just any combination of valid letters. For example, "IIII" and "VV" use real Roman letters but aren't how those numbers are properly written (they should be "IV" and "X").
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