How Roman Numerals Work

The ultimate guide to Roman Numerals. Learn how to write Roman Numerals quickly and easily.


Introduction

Roman numerals are an ancient system for writing numbers. The Roman numerals are: I, V, X, L, C, D, and M. These symbols represent 1, 5, 10, 50, 100, 500, and 1000, respectively. Romans combined these symbols to create a system for counting from 1 to 3,999.


Roman Numerals 1 to 10

I1
II2
III3
IV4
V5
VI6
VII7
VIII8
IX9
X10

Roman Numerals Chart

I1
V5
X10
L50
C100
D500
M1,000
Printable Roman Numeral Charts

Roman Numeral Rules

There are three rules for writing Roman numerals:

  1. Roman numerals are written largest to smallest from left to right. Add up the value of each symbol.
  2. Only I, X, C, and M can be repeated. Never repeat a symbol more than three consecutive times.
  3. When a smaller numeral is to the left of a bigger numeral, subtract it.

Romans and subsequent users were not as strict about how to write numbers. You may see cases where these rules were not strictly followed. However, today Roman numerals will almost always follow these rules.


Examples

Twenty-six is written with three symbols: X (10), V (5), and I (1). We use X twice to get twenty. Then add V and I once to get twenty-six. The final roman numeral for twenty-six is XXVI.

To write fifty-four we use L (50), V (5), and I (1). Because we cannot write I more than three time in a row, we must subtract 5 - 1 to get 4. Also, we must use L for 50 instead of using X (10) five times in row. The final roman numeral for fifty-four is LIV.

One-hundred forty-two uses C (100), L (50), X (10), and I (1). Start with C for 100. Next we use XL to get forty (50 - 10). Finally add II onto the end. The final Roman numeral for one-hundred forty-two is CXLII.

This is a tricky one. You have to do a lot of subtracting. For this Roman numeral we will use M (1000), C (100), X (10), V (5), and I (1).

Start with M for 1000. Followed by CM which is 900 (1000 - 100). For ninety we use C (100) minus X (10), which gives us XC. Finally, add seven to the end. Seven is 5 + 1 + 1 or VII. Putting it all together we get MCMXCVII. Phew!

Download Roman Numeral Reference Sheet

Knowing Roman numerals is a great skill to have. Although they are not widely used today you never know when it might come in handy.



Large Numbers in Roman Numerals

In Roman numerals you cannot repeat a symbol more than three consecutive times. As a result, there is a limit to how big of a number you can write. The largest Roman numeral is MMMCMXCIX which is 3,999.

To write larger numbers you can add a line over the symbol. A line over a Roman numeral indicates the number is multiplied by 1,000. For example, 4,000 would be written CD since 400 is written CD (500 - 100).

The system of adding a line above Roman numerals is called vinculum. The vinculum system is the most common way to write large Roman numerals today; however it is not the only way. The rules of Roman numerals change just as grammar and language change over time.


Zero, Negative Numbers, and Fractions

Roman numerals were invented to aid in record keeping. They were used on receipts to keep track of payments and deliveries. As a result, the Romans did not invent a symbol for zero or negative numbers.

Instead of zero, the Romans used the Latin work nulla, meaning "none." Eventually nulla was abbreviated with the letter N. Because of these limitations, Roman numerals were eventually replaced by the number system we use today.

Romans did use fractions. They would use a dot (•) to indicate 1/12th. The letter S was used as an abbreviation for Semis, meaning "half." For example, 3/12 (1/4) would be written as ∴ and 7/12th would be written S• (half + 1/12)

The Romans preferred to use twelfths instead of tenths as we more commonly use today. This is because twelve is dividable by more numbers than ten. The Roman's use of twelfths is also why there are 12 inches are in a foot.


History

Roman numerals were first used around 900 B.C (3,000 years ago). They were used widely throughout the Middle Ages. By around the 1500's, Roman numerals began to be replaced by the Arabic numeral system we use today.

The origin of Roman numerals is debated. Some scholars believe Roman numerals developed from a simpler form of tallying. Others contend Roman numerals were developed based on hand signals. I, II, III, and IIII look like fingers and V (5) looks like the thumb and pointer finger.

By the Middle Ages, Roman numerals had evolved into the system we know today. Roman numerals were not the first known counting system. But they are certainly the most common ancient counting system still used today.


Modern Uses

The use of Roman numerals has declined but has not completely gone away. Roman numerals are still used for:

  • Names of Kings, queens, and popes (e.g. Elizabeth II or Pope Benedict XVI
  • Superbowl numbers
  • Generation suffixes
  • Sequels in movies or video games
  • Chapters or volumes of books
  • Indicates the year of construction of buildings, bridges, etc.
  • And many more

Roman numerals are commonly used on clock faces. One interesting note is that clocks often use IIII for four rather than IV.

Roman numeral clock

Roman numerals written on the Admiralty Arch in London indicate when the building was constructed. The Latin phrase on the building translates to In the tenth year of King Edward VII, to Queen Victoria, from most grateful citizens, 1910. Interestingly, the year 1910 is written in Roman numerals as MDCCCCX. A keen observer will notice that C is repeated four times. The more common way to write 1910 in Roman numerals is MCMX.

Admiralty Arch

Resources

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