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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.

  • 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
\(\begin{array}{l}\overline{V}\end{array} \)
5000
XXXI 10 + 10 + 10 + 1 = 31
\(\begin{array}{l}\overline{X}\end{array} \)
10000
XXXII 10 + 10 + 10 + 1 + 1 = 32
\(\begin{array}{l}\overline{L}\end{array} \)
50000
XXXIII 10 + 10 + 10 + 1 + 1 + 1 = 33
\(\begin{array}{l}\overline{C}\end{array} \)
100000
XXXIV 10 + 10 + 10 – 1 + 5 = 34
\(\begin{array}{l}\overline{D}\end{array} \)
500000
XXXV 10 + 10 + 10 + 5 = 35
\(\begin{array}{l}\overline{M}\end{array} \)
1000000

Date In Roman Numerals Conversion

We can represent the date of the day using roman numerals. Let us take the format to represent the date as MM-DD-YYYY (Month-Day-Year). For example, 12-20-2019 is written as XII-XX-MMXIX.

We can easily write the years of the 21st century as shown below.

2001 = MMI

2002 = MMII

2003 = MMIII

2004 = MMIV

2005 = MMV

2006 = MMVI

2007 = MMVII

2008 = MMVIII

2009 = MMIX

2010 = MMX and so on

Numbers To Roman Numerals Conversion

To convert numbers into roman numerals, we first need to split the given number based on the numerical value or place value of the digits in the number. It is very easy to convert any numbers into a roman form and conversely, any roman form into a number. The below example helps in better understanding of the above conversion.

Video Lesson on Roman Numerals

Roman Numerals Solved Examples

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 =

\(\begin{array}{l}\overline{IX}\end{array} \)

100 = C

40 = XL

3 = III

Therefore,

9143 =

\(\begin{array}{l}\overline{IX}\end{array} \)
CXLIII

Test your knowledge on Roman Numerals Conversion

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