# Roman Numeral Translation Calculator

Welcome to our Roman Numeral Translation Calculator.

This calculator will convert from Roman numerals to the decimal (base-10) number system or from the decimal number system into Roman numerals.

Our converter will also show you detailed working out so you can create your own worked examples!

## Roman Numeral Translation Calculator

How To Use our Converter

## Roman Numeral Translation

How to convert from Roman to decimal

To convert a Roman number to the decimal (base-10) number system, we need to group the Roman numerals into their values and then add them together.

One thing to remember when doing Roman numeral translation is that the Roman numbers usually go from bigger to smaller.

However, if a smaller value Roman numeral (I, X or C) comes before a larger value then it is subtracted from the larger numeral.

This gives us two simple rules for roman numeral translation:

• When a smaller value numeral comes AFTER a larger value numeral it is ADDED
• But if a smaller value numeral comes BEFORE a larger value numeral it is SUBTRACTED!

There are 6 different possibilities for when then smaller numeral comes BEFORE the larger value, namely:

• IV = 4
• IX = 9
• XL = 40
• XC = 90
• CD = 400
• CM = 900

An example is that C has the value 100 and X has the value 10.

• CX is worth 100 + 10 = 110, BUT
• XC is worth 100 - 10 = 90 because the X comes before the C.

### Convert Roman numerals to Decimal Worked Examples

Example 1) What is XXIV as a number?

Step 1) Split up the Roman numerals into their values.

XXIV = X X IV

The IV has been written as one value because the I comes before the larger value V.

Step 2) Write down the values of each part.

X X IV = 10 + 10 + 4

10 + 10 + 4 = 24

So XXIV is equal to 24 as a number.

Example 2) Write CDLXXVI as a number.

Step 1) Split up the Roman numerals into their values.

CDLXXVI = CD L X X V I

The CD has been written as one value because C (100) comes before the larger value D (500).

Step 2) Write down the values of each part.

CD L X X V I = 400 + 50 + 10 + 10 + 5 + 1

400 + 50 + 10 + 10 + 5 + 1 = 476

So CDLXXVI is equal to 476 as a number.

Example 3) Write MCMXLVIII as a number.

Step 1) Split up the Roman numerals into their values.

MCMXLVIII = M CM XL V I I I

Step 2) Write down the values of each part.

M CM XL V I I I = 1000 + 900 + 40 + 5 + 1 + 1 + 1

1000 + 900 + 40 + 5 + 1 + 1 + 1 = 1948

So MCMXLVIII is equal to 1948 as a number.

## Convert Numbers to Roman Numerals

How to convert from numbers to Roman Numerals

To convert a decimal number (base-10) to the Roman number system, we need to change the decimal base-10 place value into Roman numerals representing their values.

The chart above can help to do this, or you can try your own worked examples below, on our Roman Numeral Translation calculator above.

### Convert Numbers to Roman Numerals Worked Examples

Example 1) Convert 64 into Roman numerals.

Step 1) Look at what place values we have.

64 = 60 + 4

Step 2) Write each place value as Roman numerals.

• 60 is LX
• 4 is IV

Step 3) Put the numerals together.

So 64 = LX + IV or LXIV

So 64 is equal to LXIV in Roman numerals.

Example 2) Convert 397 into Roman numerals.

Step 1) Look at what place values we have.

397 = 300 + 90 + 7

Step 2) Write each place value as Roman numerals.

• 300 is CCC
• 90 is XC
• 7 is VII

Step 3) Put the numerals together.

So 397 = CCC + XC + VII or CCCXCVII

So 397 is equal to CCCXCVII in Roman numerals.

Example 3) Convert 3489 into Roman numerals.

Step 1) Look at what place values we have.

3489 = 3000 + 400 + 80 + 9

Step 2) Write each place value as Roman numerals.

• 3000 is MMM
• 400 is CD
• 80 is LXXX
• 9 is IX

Step 3) Put the numerals together.

So 3489 = MMM + CD + LXXX + IX or MMMCDLXXXIX

So 3489 is equal to MMMCDLXXXIX in Roman numerals.

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