Knowledge

Deutsche Version

11/23/2006
 Online Converter for Decimal/Roman Numerals

This web page allows you to convert a decimal numeral into a Roman numeral and vice versa.

Contents

  1. Rule of Addition
  2. Rule of Sorting
  3. Rule of Shortest Notation
  4. Rule of Subtraction
  5. Converter for Decimal/Roman Numerals
  6. See Also

Rule of Addition

The system of Roman numerals is a so-called additive system. Thus, the values of the used numeric symbols just have to be added in order to get the number represented. The Roman numeral system uses this basic set of symbols:

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

For example, to find out the value of the Roman numeral CCLXVII, you just have to calculate:

  C +   C +  L +  X + V + I + I = CCLXVII
100 + 100 + 50 + 10 + 5 + 1 + 1 = 267

Rule of Sorting

The rule of addition is complemented by the rule of sorting: The symbols within a Roman numeral have to be sorted from left to right in descending order: Symbols with the highest values are on the left; to the right the values decrease more and more. Thus, the Roman numeral CCLXVII cannot alternatively be written as, for instance, IIVXLCC.

Rule of Shortest Notation

Another rule is that you should use the shortest notation if a value can be represented with different combinations of Roman symbols. For example, the value 55 could theoretically be written as:

10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1 = 55
 X    X    X    X    X   I   I   I   I   I = XXXXXIIIII

Instead, you should prefer the shorter notation...

50 + 5 = 55
 L   V = LV

Rule of Subtraction

A common addition to the aforementioned rules is the rule of subtraction: If a Roman symbol with a smaller value stands on the left of a symbol with a higher value, then the smaller value is not added, but has to be subtracted. The rule of sorting makes it possible to write some numbers in a shorter notation. For example, according to the rule of addition the value 44 is written as:

10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 = 44
 X    X    X    X   I   I   I   I = XXXXIIII

The rule of subtraction makes it possible to write:

(-10) + 50 + (-1) + 5 = 44
   X     L     I    V = XLIV

Unfortunately, the rule of subtraction is not always interpreted in the same way. The prevailing interpretation allows only to shorten (V)IIII, (L)XXXX and (D)CCCC. Therefore, only the following combinations are allowed according to this "strict" rule of subtraction:

Roman Decimal
IV 4
IX 9
XL 40
XC 90
CD 400
CM 900

For instance, the value 99 is to be written according to the strict rule of subtraction:

(-10) + 100 + (-1) + 10 = 99
   X      C     I     X = XCIX

A less common, "wider" interpretation of the rule of subtraction allows instead:

(-1) + 100 = 99
  I      C = IC

Converter for Decimal/Roman Numerals

The following tool allows you to convert decimal numerals not greater than 9999 and Roman numerals with not more than 21 characters:

  • The conversion of a decimal numeral into a Roman numeral is done according to the rule of addition, the rule of sorting, the rule of the shortest notation and the strict rule of subtraction.
  • The conversion of a Roman numeral into a decimal numeral is done according to the rule of addition, the rule of sorting, and both rules of subtraction. (This makes is possible to convert most uncommon notations.)
decimal:   Roman:
 
 

Note: The converter is released under the GNU General Public License (GPL) and requires JavaScript to be enabled in your browser.

See Also

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