Roman Numerals

Roman Numerals

Roman Numerals ﹣ Calculator

Here you will find all the information about the Roman Numerals. In addition to the calculator for converting Roman numerals, you will find below all the rules for Roman numerals as they are taught in mathematics lessons today, as well as other historical rules and descriptions. Examples for converting Roman numerals round off the topic.

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Contents on the topic 'Roman Numerals'

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Introduction to Roman Numerals

Roman Numerals Roman numerals – often called Latin numerals – originated in Roman antiquity. The script, composed of individual numerals, is still used today for numbers, a specific date, on clock faces, and for other special purposes. In the form used today, the Latin letters I (1), V (5), X (10), L (50), C (100), D (500) and M (1000) are included as numerals.

Unlike the usual decimal system, the value of Roman numerals is based on the addition of the individual number signs or symbols. This is why it is also called an additive number system. The value of the individual Arabic numerals of a number in the decimal system, on the other hand, depends on the respective digit position, so that from right to left, ones, tens, hundreds, etc. are added up. It is therefore called the place value system.

Pupils learn about Roman numerals as early as primary school. In secondary schools, Roman numerals are then studied in greater depth in mathematics lessons.

Display a date in Roman numerals

If you would like to convert any date into a Roman numeral, we recommend our subject area Roman Date. There, you can easily do the conversion with the help of our other smart calculator.

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Input 'Help' on the Calculator for the Conversion of Roman Numerals

With the calculator for converting Roman numerals, you can calculate in both directions. You can easily convert decimal numbers, i.e., ‘normal’ numbers, into Roman numerals and vice versa (Roman numerals into decimal numbers).

Roman or decimal number

Calculator: Roman or decimal number Please enter either a decimal number or a Roman numeral, i.e., a character string consisting of the upper- or lower-case letters M, D, C, L, X, V or I. The calculator automatically recognises which number format you have entered and converts a decimal number into a Roman numeral accordingly or, conversely, converts a Roman numeral into a decimal number.

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Rules for Roman Numerals

Roman numerals are made up of individual numerals or symbols whose individual values are added together (addition number writing). The following rules define Roman numerals as they are taught today, e.g., in school lessons.

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Basic

Each symbol in a Roman numeral has a specific value. The symbols in a Roman numeral are basically arranged in order of size, from large to small.

MDCLXVI
1000500100501051
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1. Addition Rule

A smaller symbol after a larger symbol is added.

Example: XIII = 13

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2. Subtraction Rule

With the help of the subtraction rule, only three consecutive identical symbols are necessary in a Roman numeral, e.g., IX instead of VIIII for the decimal number 9.

A smaller symbol in front of a larger symbol is subtracted.

Example: IX = 9

The following should be noted for the subtraction rule:

  • Only one character may be prefixed for subtraction at a time.
  • V, L and D, i.e., the intermediate digits for 5, 50, and 500, may not be prefixed.
  • I, X and C may only be prefixed to one of their next two larger symbols.

Only IV and IX, XL and XC, or CD and CM are valid.

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3. Maximum number of consecutive identical symbols

I, X and C may be used no more than three times in succession when applying the subtraction rule.

V, L and D may only be used once in succession.

Example: VV = 10 is not possible because X = 10.

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Historical Deviations from Rules

The above rules for the definition and correct syntax of Roman numerals are taught in school lessons, for example, and are still valid today. However, other rules for Roman numerals were also used in historical documents and drawings. The following deviations are accepted by our calculator for converting Roman numerals, whereby this is indicated in the result window in the derivation with a *). The corresponding info text explains the deviation from today's rules.

Deviation 1

With the subtraction rule, two preceding characters are allowed for subtraction instead of just one.

Example: Not only IX = 9, but also IIX = 8 is allowed. According to the school rules, IIX would not be allowed, but VIII should be used instead.

Deviation 2

I and X may not precede only one of the next two larger symbols, but each larger symbol..

Example: Not only IV = 4 and IX = 9, but also IC = 99 is allowed. According to the school rules, IC would not be allowed. XCIX should be used instead.

Deviation 3

A combination of deviation 1 and deviation 2 is also encountered. Thus, two characters for subtraction may be preceded by a symbol other than the next two largest.

Example: IIC = 98. Based on the school rules, IIC would not be allowed. XCVIII should be used instead.

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Example of the Conversion of a Decimal Number into a Roman Numeral

Mr Marmor is a stonemason and wants to carve the year 2024 in Roman numerals. To convert the decimal number 2024 into the desired Roman numeral, he proceeds step by step as follows:

1. Convert thousands

First, the highest digit of 2024, i.e., the two thousands, is converted into a Roman numeral. The addition rule described above states, "A smaller symbol after a larger symbol is added." This is similar to all leading M.

2 thousands become MM

2. Convert hundreds

The second digit of 2024 to be converted is zero. Roman numerals, however, do not have and do not need a separate symbol for zero, which is why it is converted to an "empty character".

0 hundreds become ''

3. Convert tens

The third digit of 2024 to be converted is 2. This is calculated again according to the addition rule.

2 tens become XX

4. Convert one

The fourth digit of 2024 to be converted is 4. 4 could be represented as a Roman numeral using IIII. But since, according to today's rules, four identical symbols in a row should be avoided, the 4 is now represented using the subtraction rule described above: "A smaller symbol in front of a larger symbol is subtracted." Instead of IIII, we write IV, i.e., 5 minus 1.

4 units become IV

5. Stringing together Roman characters

Finally, the individual results of the four previous steps only have to be strung together to obtain the desired Roman numeral:MM, XX and IV finally result in MMXXIV.

2024 = MMXXIV

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Example of the conversion of a Roman Numeral into a Decimal Number

In Petra's school lessons, Roman numerals are currently being discussed. Petra now has to convert the Roman numeral MCCXXXIV into a decimal number. She proceeds as follows: Petra goes through the Roman numeral from left to right to convert each symbol into its decimal number.

What does the Roman numeral M mean?

M = 1000

What does the Roman numeral CC mean?

Since two Cs occur in succession in MCCXXXIV, one can convert the value of both Cs in succession as follows:

CC = 100 + 100 = 200

What does the Roman numeral XXX mean?

Since three Xs occur in a row in MCCXXXIV, one can convert the value of all three Xs in a row as follows:

XXX = 10 + 10 + 10 = 30

What does the Roman numeral IV mean?

For the last numeral IV in MCCXXXIV, the subtraction rule comes into play, because here the I is a smaller symbol in front of the larger V. The I is thus subtracted from the V:

IV = 5 -1 = 4

5. Add up individual results

The individual results of the four previous steps must finally only be added to obtain the desired decimal number, i.e., 1000 + 200 + 30 + 4 = 1234.

MCCXXXIV = 1234

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Questions and Answers

In the following, we present some questions about the Roman numerals together with the corresponding answers.

Is there a Roman zero?

No, the ancient Romans did not yet have a zero in their number system. An additive number notation, such as the Roman one, does not need a zero, so there is no sign for the zero in Roman numerals. Not only because of the missing zero, but also because performing complicated calculations with Roman numerals is only possible to a limited extent.

How many Roman numerals may be next to each other?

According to the rules taught in school, only three Roman numerals are allowed in a row, e.g., III, XXX or CCC. Thus, for example, to represent the number 4, one can avoid the four characters IIII by writing IV instead, i.e., 5 minus 1.

The Roman symbols of the bundle of five, i.e., V, L and D for 5, 50 and 500, on the other hand, may only be used once in succession, as, for example, VV is to be replaced by X or LL by C.

This is because, from 4,000 onwards, four Ms in a row would have to be used. This was avoided either by defining additional characters for 5,000 (ↁ), 10,000 (ↂ), etc., or by a multiplier for the number of Ms, for example, X-M for 10×M=10,000.

How to add Roman numerals?

Roman numerals were and are used to represent numbers. While multiplying, dividing or subtracting Roman numerals in writing is hardly possible because of the missing zero, it is possible to add two Roman numerals by adding the individual characters step by step. For example: 26 + 15 = XXVI + XV = XXXVVI = XXXXI = XLI = 41.

However, this only works to a limited extent as soon as the numbers to be added contain, for example, a 4, for whose conversion into a Roman numeral the subtraction method ("A smaller symbol is subtracted from a larger symbol") is used. Then it becomes difficult to add, e.g., 26 and 14: 26 + 14 = XXVI + XIV = XXXVIIV = ?

How many Roman numerals are there?

As described above, there are seven Roman numerals: I (1), V (5), X (10), L (50), C (100), D (500) and M (1000). Occasionally, there are other signs for larger Roman numerals, such as ↁ for 5,000, ↂ for 10,000, etc.

The seven characters are often subdivided into characters with ten bundles (I, X, C and M) and characters with five bundles (V, L and D). The four characters with ten bundles form the basic digits, and the three characters with five bundles are the intermediate digits.

Source information

As source for the information in the 'Roman Numerals' category, we have used in particular:

Last update on November 15, 2022

The last changes in the 'Roman Numerals' category were implemented by Michael Mühl on November 15, 2022. The main changes were:

  • 15.11.2022: Publication of the topic Roman Numerals together with the corresponding texts.
  • Editorial revision of all texts in this category