Roman Numeral Conversion : Definition, Conversion Rules

Roman Numerals Conversion

A number in Roman Numerals is a collection of the symbols (or letters/characters) C, D, I, L, M, V, X has written in a specific order (e.g. M’sM’s first, followed by D’sD’s, C’sC’s etc.). Generally, a subtractive notation is used in some cases to avoid four characters being replicated in sequences, such as IIII or XXXX, as shown below.

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• If “I” is placed before V or X, it represents one less, then four is IV (one less than 5), and 9 is IX (one less than 10)
• If “X” is placed before L or C, it represents ten less, then 40 is XL (10 less than 50), and 90 is XC (10 less than 100)
• If “C” is placed before D or M, it represents a hundred less, then 400 is CD (100 less than 500), and 900 is CM (100 less than 1000)

Roman Numerals Calculation

The below table shows the calculations to get the number for a given roman numeral.

Roman Numeral	Calculation to get the number	Roman Numeral	Calculation to get the number
I	1 = 1	XXXVI	10 + 10 + 10 + 5 + 1 = 36
II	1 + 1 = 2	XXXVII	10 + 10 + 10 + 5 + 1 + 1 = 37
III	1 + 1 + 1 = 3	XXXVIII	10 + 10 + 10 + 5 + 1 + 1 + 1 = 38
IV	5 – 1 = 4	XXXIX	10 + 10 + 10 – 1 + 10 = 39
V	5	XL	-10 + 50 = 40
VI	5 + 1 = 6	XLI	-10 + 50 + 1 = 41
VII	5 + 1 + 1 = 7	XLII	-10 + 50 + 1 + 1 = 42
VIII	5 + 1 + 1 + 1 = 8	XLIII	-10 + 50 + 1 + 1 + 1 = 43
IX	10 – 1 = 9	XLIV	-10 + 50 – 1 + 5 = 44
X	10	XLV	-10 + 50 + 5 = 45
XI	10 + 1 = 11	XLVI	-10 + 50 + 5 + 1 = 46
XII	10 + 1 + 1 = 12	XLVII	-10 + 50 + 5 + 5 + 1 = 47
XIII	10 + 1 + 1 + 1 = 13	XLVIII	-10 + 50 + 5 + 1 + 1 + 1 = 48
XIV	10 – 1 + 5 = 14	XLIX	-10 + 50 – 1 + 10 = 49
XV	10 + 5 = 15	L	50
XVI	10 + 5 + 1 = 16	LX	50 + 10 = 60
XVII	10 + 5 + 1 + 1 = 17	LXX	50 + 10 + 10 = 70
XVIII	10 + 5 + 1 + 1 + 1 = 18	LXXX	50 + 10 + 10 + 10 = 80
XIX	10 – 1 + 10 = 19	XC	-10 + 100 = 90
XX	10 + 10 = 20	C	100
XXI	10 + 10 + 1 = 21	CC	100 + 100 = 200
XXII	10 + 10 + 1 + 1 = 22	CCC	100 + 100 + 100 = 300
XXIII	10 + 10 + 1 + 1 + 1 = 23	CD	-100 + 500 = 400
XXIV	10 + 10 – 1 + 5 = 24	D	500
XXV	10 + 10 + 5 = 25	DC	500 + 100 = 600
XXVI	10 + 10 + 5 + 1 = 26	DCC	500 + 100 + 100 = 700
XXVII	10 + 10 + 5 + 1 + 1 = 27	DCCC	500 + 100 + 100 + 100 = 800
XXVIII	10 + 10 + 5 + 1 + 1 + 1 = 28	CM	-100 + 1000 = 900
XXIX	10 + 10 – 1 + 10 = 29	M	1000
XXX	10 + 10 + 10 = 30	¯¯¯¯VV¯	5000
XXXI	10 + 10 + 10 + 1 = 31	¯¯¯¯¯XX¯	10000
XXXII	10 + 10 + 10 + 1 + 1 = 32	¯¯¯¯LL¯	50000
XXXIII	10 + 10 + 10 + 1 + 1 + 1 = 33	¯¯¯¯CC¯	100000
XXXIV	10 + 10 + 10 – 1 + 5 = 34	¯¯¯¯¯DD¯	500000
XXXV	10 + 10 + 10 + 5 = 35	¯¯¯¯¯¯MM¯	1000000

Converting a Date to Roman Numerals

2001 = MMI

2002 = MMII

2003 = MMIII

2004 = MMIV

2005 = MMV

2006 = MMVI

2007 = MMVII

2008 = MMVIII

2009 = MMIX

2010 = MMX and so on

 

Converting Numbers to Roman Numerals

To convert numbers to roman numerals, we must first divide the provided number into two groups based on the numerical value or place value of the digits. Any number can be converted to a roman form, and any roman form can be converted to a number. The example below will help you comprehend the aforementioned conversion.

 

Roman Numerals Example

Example 1:

Convert the number 1786 into the form of a roman numeral.

Solution:

First we need to split 1786 into thousands, hundreds, tens and units.

1786 = 1000 + 700 + 80 + 6

1000 = M

700 = DCC

80 = LXXX

6 = VI

Therefore, 1786 = MDCCLXXXVI
 

Example 2:

Convert the number 9143 into the roman numeral.

Solution:

Let us split 9143 into thousands, hundreds, tens and units.

9143 = 9000 + 100 + 40 + 3

9000 = ¯¯¯¯¯¯¯IX

100 = C

40 = XL

3 = III

Therefore,

9143 = ¯¯¯¯¯¯¯IX CXLIII