# Roman Numeral Converter

Convert numbers, dates, and fractions from and to Roman numerals. Read the explanation below to see how the Converter works.

## How does the Converter work?

Enter a number into the panel on the left. If you enter an Arabic numeral (for example 22) and you want to convert it to a Roman numeral, you need to click the “Convert to Roman” button. If you enter a Roman numeral (for example XIX) click the “Convert to Arabic” button to convert it to an Arabic numeral.

If you are unsure how the Converter works and want to see some examples, you can click the buttons below to populate the left panel with one of our three examples. There are both Arabic and Roman numerals in each example, so you can test them in both directions to see how the relevant parts are converted. We also encourage you to keep reading this page to learn more about how the conversion works.

## How do Roman numerals work?

### Basic Roman numbers

Roman numerals are made using a few capital Latin letters, namely I, V, X, L, C, D, and M. Each letter has a corresponding value which can be summarized in the table below.

I | 1 |

V | 5 |

X | 10 |

L | 50 |

C | 100 |

D | 500 |

M | 1000 |

To make a Roman numeral you need to put together these letters so that their values add up to the desired number. For example, if you need a Roman numeral for 56, you should use L (for 50), V (for 5), and I (for 1) so that your number is LVI (you can check that indeed 50 + 5 + 1 = 56). Sometimes, you need to repeat a certain letter. For example, 23 is XXIII because each X stands for 10 and each I stands for 1 and we need two of the former and three of the latter (XXIII = X + X + I + I + I = 10 + 10 + 1 + 1 + 1 = 23). But you should not repeat a letter more than three times. Instead of repeating a letter four times, you should place it in front of a higher-value letter – this way they are subtracted rather than added. For example, 934 is CMXXXIV: C in front of M means that we subtract 100 from 1000 to get 900, XXX is 3 × 10, and I in front of V means that we subtract 1 from 5 to get 4, therefore getting 900 + 30 + 4 = 934. You need to be careful, because you can only subtract certain numbers: you can put I in front of V or X, X in front of L or C and C in front of D or M. You cannot subtract, say, V from C to get 95 – VC is not a correct Roman numeral. The correct way of writing 95 is XCV. Finally, except for the subtractions described above, symbols are always written from the one with the largest value on the left to the smallest on the right. So, for 551 it is not correct to write LID because the letters are in a wrong order – the correct order is DLI (because D > L > I, that is, 500 > 50 > 1). Below you can find a table with examples of basic Roman numbers.

I | 1 |

II | 2 |

III | 3 |

IV | 4 |

V | 5 |

VI | 6 |

VII | 7 |

VIII | 8 |

IX | 9 |

X | 10 |

XI | 11 |

XII | 12 |

XIII | 13 |

XIV | 14 |

XV | 15 |

XVI | 16 |

XVII | 17 |

XVIII | 18 |

XIX | 19 |

XX | 20 |

XI | 21 |

XII | 22 |

XIII | 23 |

XIV | 24 |

XV | 25 |

XVI | 26 |

XVII | 27 |

XVIII | 28 |

XIX | 29 |

XXX | 30 |

XL | 40 |

L | 50 |

LX | 60 |

LXX | 70 |

LXXX | 80 |

XC | 90 |

C | 100 |

CXXI | 121 |

CXLIV | 144 |

CLXIX | 169 |

CXCVI | 196 |

CCXXV | 225 |

CCLVI | 256 |

CDLXXVI | 476 |

DCXXII | 622 |

MCDXCII | 1492 |

MDCCLXXXIX | 1789 |

MCMXXXIX | 1939 |

MCMXCI | 1991 |

MMXIX | 2019 |

Sometimes four identical letters are used consecutively. For example, you may find IIII written instead of IV on some old clocks to represent 4. Or you may find 40 written somewhere as XXXX instead of XL. Although some authors do this, this way of writing numbers is less popular and although understood by our Converter, it is not recommended.

Sometimes you may also find Roman numerals written using small letters, for example 6 as vi or 13 as xiii. Unfortunately, the Converter does not understand small letters and they have to be changed to capital letters before such numbers can be converted.

### Roman numbers greater than 1000

There are many ways of writing Roman numerals – their use was changing over time both in Ancient Rome and in medieval Europe where they continued to be widely used even after the fall of the Roman Empire. This applies also to writing very large numbers – there are a few known ways of writing them. Probably the most popular way of doing it was to add a horizontal bar above a letter to multiply its value by 1000. Therefore, since VI is 6, the value of VI is 6,000. This can be done with any whole number, for example, CMXXXIV is 934,000. You can also mix the letters with and the letters without a bar: for example, LXVDXXXVI is 65,536. And although numbers below 4,000 are traditionally written using M for thousands, it is not wrong to write IIXIX for 2019 (however, MMXIX is preferred). Below you can see a few examples of how to write large numbers using Roman numerals. If you want to enter such numbers into the Converter, instead of an overline, you need to enclose the relevant letters with square brackets – the last column indicates how to do it.

Arabic numeral | Roman numeral | Converter input or output |
---|---|---|

24,901 | XXIVCMI | [XXIV]CMI |

40,075 | XLLXXV | [XL]LXXV |

238,900 | CCXXXVIIICM | [CCXXXVIII]CM |

299,792 | CCXCIXDCCXCII | [CCXCIX]DCCXCII |

384,400 | CCCLXXXVICD | [CCCLXXXVI]CD |

1,048,576 | MXLVIIIDLXXVI | [MXLVIII]DLXXVI |

4,999,999 | MMMMCMXCIXCMXCIX | [MMMMCMXCIX]CMXCIX |

The maximum number that can be written in this way is MMMMCMXCIXCMXCIX, that is 4,999,999. It is not possible to write a larger number given the rules presented above.

### Roman fractions

Roman fractions work in a similar way to whole numbers: to create a fraction you need to arrange symbols in the order of descending value in such a way so that they sum up to the number you want to represent. There are 14 symbols that can be used to create fractions. They are listed in the table below.

Latin name | Meaning | Rational fraction | Approximate decimal value | Actual characters | Visual approximations | Keyboard friendly |
---|---|---|---|---|---|---|

semis |
half | 1/2 | 0.50000 | S | S | S |

quincunx |
five ounces | 5/12 | 0.41667 | 𐆐𐆐𐆑 | ⁙ | ..... |

triens |
third | 4/12 = 1/3 | 0.33333 | 𐆐𐆐 | ∷ | .... |

quadrans |
fourth | 3/12 = 1/4 | 0.25000 | 𐆐𐆑 | ∴ | ... |

sextans |
sixth | 2/12 = 1/6 | 0.16667 | 𐆐 | : | .. |

sescuncia |
1.5 ounces | 1/8 | 0.12500 | 𐆒𐆑 | Є· | E. |

uncia |
ounce | 1/12 | 0.08333 | 𐆑 | · | . |

semuncia |
half of an ounce | 1/24 | 0.04167 | 𐆒 | Є | E |

binae sextulae |
two sextulas | 1/36 = 1/72 + 1/72 | 0.02778 | 𐆓𐆓 | ƧƧ | ZZ |

sicilicus |
sicle-shaped | 1/48 | 0.02083 | 𐅀 | Ɔ | O |

sextula |
sixth of an ounce | 1/72 = 1/6 × 1/12 | 0.01389 | 𐆓 | Ƨ | Z |

dimidia sextula |
half of sextula | 1/144 = 1/2 × 1/72 | 0.00694 | 𐆔 | ₴ | A |

scripulum |
tiny stone | 1/288 | 0.00347 | ℈ | Э | P |

siliqua |
grain | 1/1728 | 0.00058 | 𐆕 | » | Q |

Only the *uncia* and the *siliqua* symbols can be repeated, both up to 5 times. Other symbols cannot be repeated, unless they are already repeated in the table above (like *sextula* is to form *binae sextulae*).

As you can see, the highest precision you can get using Roman fractions is 1/1728. Moreover, the fractions are based on the number 12, which makes it impossible to accurately write down many fractions that can be easily expressed using modern decimal system. For example, 0.1 (or 1/10) will be written as *uncia* + *sextula* + 5 × *siliqua* which is 1/12 + 1/72 + 5 × 1/1728 = 173/1728 ≈ 0.10012. Most of the time, finding an appropriate Roman fraction results in an approximation rather than exact value of the number you are trying to represent. You can see a table with several examples below. The last column shows the calculation of the Roman numeral’s exact value, written in the decimal system so that you can compare it to the original number (in columns one and two).

Rational fraction | Decimal approximation | Roman numeral (visual approximations) | Calculation |
---|---|---|---|

1/2 | 0.5 | S | 1/2 = 0.5 |

1/3 | 0.33333 | ∷ | 1/3 ≈ 0.33333 |

1/4 | 0.25 | ∴ | 1/4 = 0.25 |

1/10 | 0.1 | ·Ƨ»»»»» | 1/12 + 1/72 + 5/1728 = 173/1728 ≈ 0.10012 |

1/5 | 0.2 | :ƧƧЭ»»»» | 1/6 + 1/36 + 1/228 + 4/1728 = 173/864 ≈ 0.20023 |

3/10 | 0.3 | ∴Є₴»» | 1/4 + 1/24 + 1/144 + 2/1728 = 259/864 ≈ 0.29977 |

1/7 | 0.14286 | Є·ƧЭ» | 1/8 + 1/72 + 1/228 + 1/1728 = 247/1728 ≈ 0.14294 |

12345/100000 | 0.12345 | ·ƧƧ₴Э»»» | 1/12 + 1/36 + 1/144 + 1/228 + 3/1728 = 71/576 ≈ 0.12326 |

99/100 | 0.99 | S⁙ЄƧƧЭ» | 1/2 + 5/12 + 1/24 + 1/36 + 1/228 + 1/1728 = 1711/1728 ≈ 0.99016 |

999/1000 | 0.999 | S⁙ЄƧƧ₴Э»»»» | 1/2 + 5/12 + 1/24 + 1/36 + 1/144 + 1/228 + 4/1728 = 863/864 ≈ 0.99884 |

9999/10000 | 0.9999 | I | 1 |

314/100 | 3.14 | IIIЄ·Ƨ»» | 3 + 1/8 + 1/72 + 2/1728 = 3 121/864 ≈ 3.14005 |

31415/10000 | 3.1415 | IIIЄ·Ƨ»»»»» | 3 + 1/8 + 1/72 + 5/1728 = 3 245/1728 ≈ 3.14178 |

The Converter reads and writes Roman fractions using three sets of symbols. “Actual characters” are the symbols described in a document written by David J. Perry about characters for classical Latin in Unicode (Unicode is a standard for displaying characters on computers and other electronic devices). These symbols can be considered to be the proper characters, that is characters that have the meaning associated with appropriate Roman fractions and were designed based on the symbols historically used for Roman fractions. Unfortunately, due to their relative obscurity, some of these characters may be unavailable, even on modern computers. Therefore, if you use “Actual characters” you may see blank squares or other placeholder images instead of the appropriate graphical symbols. In this case, we suggest using the “Visual approximations” character set, which includes symbols that are available on most modern systems and which are visually similar to the Roman characters although their intended meaning may be different (for example, the hryvnia symbol for *dimidia sextula*). Neither “Actual characters” nor “Visual approximations” has symbols that can be easily typed with a keyboard. Therefore, the third options is also available: “Keyboard friendly” characters are easy to use if you are entering Roman fractions into the Converter using your keyboard (as long as you can type Latin letters).

You can combine fractions with whole numbers. To do that, write the fraction immediately after the whole number. For example, 3.14 can be written as IIIЄ·Ƨ»» using the “Visual approximations” setting.

### Roman Zero

There isn’t much evidence that Ancient Romans used zero. In the Middle Ages scholars started to describe 0 in various ways. One of them was letter N. This way of denoting 0 was also adopted in the Converter.

## Arabic numerals

Arabic numbers must satisfy a few of conditions to be understood by the Converter:

- You cannot separate thousands using a comma. The digits must be kept together and nothing should separate them. For example, for three thousand you should write 3000 and not 3,000.
- The Converter attempts to get the decimal separator (most likely a dot) from your system settings, but you can change it to something else if you wish. Make sure that the decimal separator in the settings is the same as the one in the numbers you are trying to convert.
- If you use a decimal fraction lower than 1, your number must start with 0. That is, 0.25 will be understood as a fraction (a quarter) but .25 will be understood as a dot followed by the integer 25.
- You can also use rational fractions. To do that type a whole number and use space to separate it from a fraction. Fraction must be written as a numerator followed by a the “/” character followed by the denominator. For example, 3 7/50 will be understood by the Converter as 3.14. You can skip the whole number. Then, for example, 1/4 will be understood as 0.25.

You can disable fractions for Arabic numerals. By default, rational fractions are used (because they are more accurate), so if both types of fractions are enabled, the Converter will generate rational fractions. If you prefer decimal fractions, you have to disable rational fractions, which will force the Converter to generate decimal fractions. If you disable both types of fractions, the Converter will treat fractions as separate whole numbers, which can be desirable, for example, when you want to convert dates (see below).

## Converter functions and features

### Notes

The Converter displays its calculations in the form of notes. It also shows approximate values of rational fractions in decimal form so that you can easily compare how far apart are the corresponding Roman and Arabic fractions after conversion. Finally, the notes will provide you with information about any problems the Converter has encountered. In case a number cannot be converted, it is left in the output field in its initial form, and the explanation is provided in the Notes field.

### Converting dates

You should disallow rational fractions if you want to translate dates written with slashes. For example, with rational fractions on, when converting 12/6/10 from Arabic to Roman numerals, the 12/6 part will be treated as the first fractional number, and 10 will be treated as a separate whole number, so the result will be II/X. If you disallow rational fraction, the result will be XII/VI/X.

Similarly, using decimal separator in dates can yield unexpected results. For example, if you set a dot as your decimal separator and try to convert 2019.03.11 from Arabic to Roman numerals with decimal fractions enabled, the 2019.03 part will be treated as the first number and 11 will be treated as the second number, separated by a dot. As a result, you will get MMXIXƧƧ»»»».XI (if “Visual approximations” is selected). Disabling decimal fractions will ensure that the result is the desired MMXIX.III.XI.

### Converting multiple numbers

In general, you can type any text you like into the input field. The Converter will search the text for numbers and try to substitute them while leaving the rest of the text unchanged. This way you can easily convert many numbers at a time, for example by entering each number in a new line.

However, sometimes you may get unexpected results, especially if you convert Roman numerals to Arabic. This can happen if your text uses the symbols used for Roman numerals for other purposes. For example, every single capital letter I may get changed into a 1. If you use “Keyboard friendly” setting, dots may get converted to fractions. And so on.

### Options

The Converter has some settings that can be used to customize the conversion process. Most of them have already been described above. To display the available options, click the “Show options” button just below the Input and Output fields at the beginning of the page. Click the button again to hide options.

The group titled “Roman numeral fractions” lets you decide what characters the Converter should use while reading and writing Roman numeral fractions. You can find detailed explanation of how such fractions work as well as what are the available symbols in the “Roman fractions” section above.

The group titled “Arabic numeral fractions” allows you to decide three things: whether you want the Converter to read and write fractions written in a rational format, whether you allow fractions written using a decimal separator, and what is the decimal separator character. You can find more details about these options in the “Arabic numerals” section above.

### Feedback

Please write to us if you spot a bug or know a way to improve our Converter. Click the “Leave Feedback” button do display the Feedback form. The button can be found at the beginning of the page, just below the Input and Output fields. You can click this button again to hide the Feedback form.

Feedback form allows you to attach current input and output of the Converter. If you spot a bug in the output, use this option to make sure that the authors fully understand what the problem is. Describe what you think went wrong in the “Your feedback” field, tick the “Attach Converter data” button, and click the “Submit” button. Thank you for your cooperation! Julius Ceasar would have been proud.