Updated Number System

Roman Numeral Converter

Convert numbers to Roman numerals and Roman numerals back to numbers, validate numerals, perform arithmetic with Roman numerals, and see a step-by-step breakdown of how each numeral is built.

Number → Roman Roman → Number Validator Arithmetic & Rules

All-in-One Roman Numeral Suite

Switch between number to Roman conversion, Roman to number conversion, validation, arithmetic operations and a detailed rules-based breakdown.

Convert an integer between 1 and 3999 into a standard Roman numeral.

Convert a Roman numeral to an integer. Standard symbols I, V, X, L, C, D and M are supported.

Case-insensitive. Spaces are ignored.

Check whether a Roman numeral is valid and whether it is written in a standard canonical form.

Perform basic arithmetic on two Roman numerals. Results are given in both number and Roman form when possible.

Division uses integer division with a quotient and remainder. Roman results are only shown if the value is between 1 and 3999.

See how a Roman numeral is constructed from its symbols, including subtractive pairs and the running total.

Roman Numeral Converter – Number To Roman, Roman To Number And Rules

This Roman Numeral Converter lets you work with Roman numerals in several ways. You can convert an integer to a Roman numeral, convert a Roman numeral back to a standard number, check whether a numeral is written correctly, perform arithmetic and see a step-by-step breakdown. It is designed for students, teachers and anyone curious about number systems.

Roman Numerals – Basic Symbols

Roman numerals use a small set of symbols with fixed values:

I = 1 V = 5 X = 10 L = 50
C = 100 D = 500 M = 1000

Numbers are built by combining these symbols. Most of the time you add the values. Sometimes, when a smaller symbol appears before a larger one, it is subtracted. For example, VI = 5 + 1 = 6, while IV = 5 − 1 = 4.

Number To Roman – Standard Range 1 To 3999

The number to Roman tab in this converter accepts integers from 1 to 3999. The standard form is built from groups such as:

1 = I 4 = IV 5 = V 9 = IX
10 = X 40 = XL 50 = L 90 = XC
100 = C 400 = CD 500 = D 900 = CM
1000 = M

The converter decomposes the number into thousands, hundreds, tens and ones and writes each part using standard Roman patterns. This produces a consistent representation, such as 944 → CMXLIV.

Roman To Number – Reading From Left To Right

To convert a Roman numeral back to a number, you read from left to right and compare each symbol with the next one. If a symbol is followed by a larger value, you subtract it. Otherwise, you add it. For example, MCMXCIV is processed as:

M (1000) + CM (900) + XC (90) + IV (4) = 1994

The Roman to number tab applies this rule and also produces the canonical version of the numeral, which is the standard way the same value would normally be written.

Validator – Canonical vs Non-Canonical Forms

Not every combination of symbols that adds to a value is considered a good Roman numeral. For example, IIII can be interpreted as 4, but IV is the preferred canonical form. The validator tab:

  • Checks that only valid symbols are used
  • Applies subtractive rules such as IV, IX, XL, XC, CD and CM
  • Computes the value and compares it with the canonical form

You will see whether a numeral is valid and whether it is canonical or a non-standard variant. This is helpful when checking exercises or historic inscriptions.

Roman Numeral Arithmetic

The arithmetic tab allows you to add, subtract, multiply and divide two Roman numerals. Internally the tool:

1. Converts each Roman numeral to an integer
2. Applies the chosen operation (+, −, × or ÷)
3. Shows the numerical result, and if it is between 1 and 3999, the Roman result

For division, the result is given as an integer quotient and a remainder. If the final number is outside the standard range, the converter still shows the numeric result but cannot express it as a standard Roman numeral.

Rules And Breakdown – Understanding Each Step

The breakdown tab shows how a Roman numeral is evaluated step by step. Each row displays the symbol or pair of symbols, the value they contribute, the operation and the running total. This makes it easy to see why a numeral has a particular value and how subtractive pairs such as IV and CM change the total.

Key Rules For Roman Numerals

  • Symbols are usually written from largest to smallest from left to right.
  • Only powers of ten (I, X, C) are used in subtractive pairs.
  • Subtractive pairs are limited to IV, IX, XL, XC, CD and CM.
  • I, X and C are not typically repeated more than three times in a row.
  • There is no zero in traditional Roman numerals.

Roman Numeral Converter

Frequently Asked Questions

Helpful answers about supported number ranges, lowercase input, canonical forms, teaching use-cases, and how arithmetic is handled.

The standard number-to-Roman converter supports whole numbers from 1 to 3999, which is the traditional textbook range for Roman numerals. The arithmetic tab may compute results outside this range, but some values cannot be expressed as valid Roman numerals using the classical system.

Yes. Input is case-insensitive and spaces are ignored. The converter automatically normalizes everything to uppercase before processing, so “xvii” and “XVII” are treated the same.

Historically, some numerals used additive patterns such as “VIIII” for 9. While valid, the preferred modern canonical form is subtractive, such as “IX.” The validator identifies these cases, explains the difference, and shows the recommended form.

Yes. The breakdown and validator tabs are ideal for classrooms and study sessions. They show how each numeral is constructed step-by-step rather than simply displaying the final answer.

Division uses integer division. The tool returns both the quotient and remainder in numeric form. If the quotient is between 1 and 3999, the converter also provides its Roman numeral representation, and when possible, the same for the remainder.