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
Here is our Roman numeral translation calculator which will help you to convert roman numerals to decimal and decimal to roman numerals.
Our roman numeral translation calculator will also show you the formula and working out you need to convert between the two systems.
This convert will convert numbers up to six digits into Roman numerals.
Roman numeral translation calculator: How It Works...
Step 1) Choose which calculator you want - roman to decimal or decimal to roman
Step 2) Type in the number you want to convert.
Step 3) Click the Convert button and the answer will be displayed.
Roman Numeral Values
There are just 7 Roman numerals: I, V, X, L, C, D and M.
Unlike most other number systems, the numerals can only be used in particular sequences.
Another rule is that apart from M, you can only have a maximum of 3 of any given numeral in a row.
Here is a quick overview of the 7 Roman numerals and what each is worth.
| Roman Numerals | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
We can also use an overline with each Roman numeral which has the effect of multiplying the value by 1000, so:
| Roman Numerals | Value |
|---|---|
| V | 5,000 |
| X | 10,000 |
| L | 50,000 |
| C | 100,000 |
| D | 500,000 |
| M | 1,000,000 |
So XLMM would represent 42,000.
Different representations
Numbers over 4,000 can be written in different ways in Roman numerals:
The number 4,000 can be written:
- MV
- MMMM
- IV
Our translator uses the format of the first example, so 4000 is represented by MV
Roman Numeral Translation Quick Table
This quick conversion table shows you some common roman number to decimal number conversions.
| Number | Roman Numerals |
|---|---|
| 1 | I |
| 2 | II |
| 3 | III |
| 4 | IV |
| 5 | V |
| 6 | VI |
| 7 | VII |
| 8 | VIII |
| 9 | IX |
| 10 | X |
| 11 | XI |
| 12 | XII |
| 13 | XIII |
| 14 | XIV |
| 15 | XV |
| 16 | XVI |
| 17 | XVII |
| 18 | XVIII |
| 19 | XIX |
| 20 | XX |
| Number | Roman Numerals |
|---|---|
| 10 | X |
| 20 | XX |
| 30 | XXX |
| 40 | XL |
| 50 | L |
| 60 | LX |
| 70 | LXX |
| 80 | LXXX |
| 90 | XC |
| 100 | C |
| 200 | CC |
| 300 | CCC |
| 400 | CD |
| 500 | D |
| 600 | DC |
| 700 | DCC |
| 800 | DCCC |
| 900 | CM |
| 1000 | M |
| 2000 | MM |
We have some more detailed Roman Numeral Lists, including printable sets below.
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
Step 3) Add them up.
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
Step 3) Add them up.
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
Step 3) Add them up.
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.
More Roman Numerals Resources
Roman Numerals List
Our Roman Numeral lists can help you to quickly convert different numbers from Roman numerals to numbers.
The lists can also help you to spot patterns and understand how Roman numerals work.
We have a wide range of lists to help you with your Roman numeral conversion.
Roman Numerals Worksheets
We also have a collection of Roman numerals worksheets for helping to learn how to convert from Roman numerals to numbers.
Our worksheets cater for a range of abilites and have differing levels of support.
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The calculator will also show you your number as a product of primes.
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