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Roman Numerals Calculator

Convert between decimal numbers and Roman numerals

Examples

1
I
4
IV
9
IX
27
XXVII
48
XLVIII
2023
MMXXIII

Roman Numerals Converter Guide

A Roman numerals converter changes integers to Roman numerals and back. It supports standard symbols and subtractive notation (IV, IX, XL, XC, CD, CM) for values up to 3,999.

What is Roman Numerals Converter?

The Roman numerals converter implements the canonical mapping and parsing rules, handling additive (e.g., VIII) and subtractive (e.g., IX) forms and validating input to avoid illegal sequences.

How to Use the Roman Numerals Converter

  1. Enter a number (1-3999) or a Roman numeral string.
  2. Convert to see the equivalent in the other system.
  3. Validate: the tool flags invalid repetitions or orderings.
  4. Copy the result for dates, clocks, outlines, or typography.
  5. Switch case as needed (upper/lower).

Formulas & Methods

  • Symbol values: I=1, V=5, X=10, L=50, C=100, D=500, M=1000.
  • Rules:
    • Max three repeats (e.g., III, XXX, CCC, MMM).
    • Subtractive pairs: IV, IX, XL, XC, CD, CM.
    • V, L, D do not repeat.
  • Algorithm (to Roman): greedy subtract largest symbol not exceeding the number.
  • Algorithm (from Roman): scan left to right; subtract if next is larger, else add.

Assumptions & limitations

  • Classical range up to 3999 without overbars; extended systems vary and are not standardized.
  • Input sanitation avoids illegal forms like IC for 99 (should be XCIX).

Examples

Example A — To Roman
1984 -> MCMLXXXIV.

Example B — From Roman
MMXXV -> 2025.

| Decimal | Roman | |---:|---| | 4 | IV | | 49 | XLIX | | 944 | CMXLIV | | 2024 | MMXXIV |

Pro Tips & Best Practices

  • Use standard subtractive pairs to avoid invalid forms.
  • For years, prefer uppercase for readability.
  • Avoid using Roman numerals for computations; convert to decimals first.
  • Validate user input to catch illegal repeats/order.

Related Calculators

FAQ

Q: What are the basic Roman numerals?

A: I=1, V=5, X=10, L=50, C=100, D=500, M=1000.

Q: How does subtractive notation work?

A: Place a smaller numeral before a larger one to subtract: IV=4, IX=9, XL=40, XC=90, CD=400, CM=900.

Q: What range can I convert?

A: Commonly 1 to 3,999 using standard symbols. Larger numbers sometimes use bars for thousands, but conventions vary.

Q: Are there zeros or negative numbers?

A: Roman numerals have no symbol for zero and do not represent negatives in the classic system.

Q: How do I format years and outlines?

A: Years often appear as Roman numerals (MMXXV). Outlines use uppercase with periods (I., II., III.).

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