# Conversion of Roman Numerals to Numbers – Rules, Examples | How to Convert Roman Numerals to Numbers?

Find a way for converting Roman Numerals to Numbers. You can learn about the basic details such as Roman Number Definition, Procedure for Converting Roman Numerals to Numbers. You can also check the solved Examples on how to change Roman Numerals to Numbers by going through this article completely.

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## Roman Numerals – Definition

Romans used some roman alphabets to specify numbers. These are called Roman Numerals. Roman Numerals are nothing but English alphabets except j, u, and w. There are seven Roman numerals. Roman Numerals are I, V, X, C, L, D, and M. Bar on the Roman letters means its value is multiplied by 1000 times. The values of Roman Numerals are as follows

Commonly Used Roman Numeral Symbols and their Equivalent Numbers
I=1 V=5
X=10 C=100
L=50 D=500
M=1000

### How to Convert Roman Numerals to Numerals?

For a given roman numeral r

• Find the largest roman numeral(n) with the large decimal value(v) taken from the  roman numeral r:
Roman Numeral(n) Decimal Value(v)
I 1
v 5
IX 9
X 10
XL 40
L 50
XC 90
C 100
CD 400
D 500
M 1000
• If the largest numeral appears first then count how many times it appears. It appears a Maximum of three times. Multiply its value by the number of times it appeared. The value V of the roman number is added to the decimal number x.
• If the largest numeral appears second then subtract the value of the numeral before it from its value. The value v of the Roman Numeral is added to the decimal number X.

X=X + V

• Repeat steps 1 to 3 until you find Roman Numerals of r.

### Roman Numerals to Numbers Conversion Examples

1. Convert the roman numeral XXXVII to Number?

Solution:

In this example, Highest Roman Numeral is X. Roman Numeral X appeared three times. The value of X multiplied by three times. So the decimal number (X) has 30. The Second highest decimal number is V and its value is 5 and it is added to the decimal number. I is appearing two times and its value is 1 and it is added to a decimal number(X). Therefore, the given roman number XXXVII converted to numbers is 37.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I X 10 10
2 X 10 20
3 X 10 30
4 V 5 35
5 I 1 36
6 I 1 37

2. Convert Roman Numeral MMXXI to Number?

Solution:

In this example, Highest Roman Numeral is M. Roman Numeral M appeared two times. The value of M multiplied by two times.so the decimal number X has 2000. Second, the highest decimal number is X and its value is 10 and it appeared two times. Its value is added to the decimal number. Now decimal number(X) has 2020. I appear one-time. Its value is 1 and it is added to the decimal number. Thus given number MMXXI converted to Numbers is 2021.

Iteration Highest Roman Numeral(n) Highest Decimal Value(v) Decimal Number(X)
I M 1000 1000
2 M 1000 2000
3 X 10 2010
4 X 10 2020
5 I 1 2021

3. Convert Roman Numeral CDLII to Number?

Solution:

In this example, Highest Roman Numeral is D. It appeared second of the Roman Numeral, so subtract the value of the Roman Numeral before its value.  so the decimal number( X) has 400. Roman Numeral L has the decimal value 50 and it is added to a decimal number(X). The value of I is 1 and it is added to a decimal number. The given number is 451.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I D 500 500
2 c 100 400
3 L 50 450
4 I 1 451
5 I 1 452

4. Convert Roman Numeral CCCL to Number?

Solution:

In this example, Highest Roman Numeral is c. Roman Numeral C appeared three times. The value of X multiplied by three times. So the decimal number X has 300.second highest decimal number is L. Its value is 50 and it is added to a decimal number(X). The given number CCCL is 350.

Iteration Highest Roman Numeral(n) Highest Decimal value(v) Decimal Number(X)
I C 100 100
2 C 100 200
3 C 100 300
4 L 50 350

### FAQ’s on Conversion of Roman Numerals to Numbers

1. What is the value of XLVI?

Here the largest value of the Roman Numeral is L. since it is placed second the value of the L numeral is subtracted from first. So the total is 40. The values of V and I are added to the total. The value of XLVI is 46.

2. What is the value of L in Roman Numerals?

The value of L in Roman Numerals is 50.

3. Why bar is placed on the Roman Numeral?

when a bar is placed on the roman numeral its value is increased by 1000 times.

4. What is the value of M?

The value of M is 1000.