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

\(\overline{V}\)

5000

XXXI

10 + 10 + 10 + 1 = 31

\(\overline{X}\)

10000

XXXII

10 + 10 + 10 + 1 + 1 = 32

\(\overline{L}\)

50000

XXXIII

10 + 10 + 10 + 1 + 1 + 1 = 33

\(\overline{C}\)

100000

XXXIV

10 + 10 + 10 – 1 + 5 = 34

\(\overline{D}\)

500000

XXXV

10 + 10 + 10 + 5 = 35

\(\overline{M}\)

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.

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 = \(\overline{IX}\)

100 = C

40 = XL

3 = III

Therefore,

9143 = \(\overline{IX}\) CXLIII

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