How Roman numerals work, and the rules for writing them
The seven Roman symbols, how addition and subtraction work in a numeral, how to write any number from 1 to 3,999, common mistakes such as IIII and IC, and where Roman numerals are still used today.
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In short
- There are seven symbols - I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1,000.
- Values normally run from largest to smallest and are added, so XVI is 10 + 5 + 1 = 16.
- A smaller symbol placed before a larger one is subtracted, in six pairs only - IV, IX, XL, XC, CD and CM.
- To write a number, split it by place value - 2026 is 2000 + 20 + 6, which is MM + XX + VI, or MMXXVI.
- The standard system stops at 3,999 and has no zero.
Roman numerals have outlived the empire that made them by about fifteen centuries. Students meet them in maths and in chapter numbers, readers see them on clock faces and in the names of kings, and film credits still use them for the year. Reading them takes a few minutes to learn, and writing them correctly needs only a handful of rules. This page sets those out with worked examples, and explains why some forms that seem to add up correctly are not valid numerals.
The seven symbols
| Symbol | Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1,000 |
Every Roman numeral is built from these. Notice the pattern: each step goes up by five times or two times in turn, 1, 5, 10, 50, 100, 500, 1,000.
How to read a numeral
Rule 1: add when values go down. Written left to right, large to small, symbols are added.
XVI = 10 + 5 + 1 = 16
MDCCL = 1,000 + 500 + 100 + 100 + 50 = 1,750
Rule 2: subtract when a smaller symbol comes first. A smaller symbol before a larger one is taken away from it.
IV = 5 − 1 = 4
IX = 10 − 1 = 9
XC = 100 − 10 = 90
Only six such pairs are allowed: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). Each one has a power of ten in front of the next one or two symbols up.
Rule 3: repeat at most three times. I, X, C and M may repeat up to three times in a row. So 3 is III, and 4 is IV rather than IIII. V, L and D are never repeated, because two Vs would simply be an X.
How to write a number
Split the number by place value, write each part, and join them.
For 2026: 2,000 is MM, 20 is XX and 6 is VI. Put them together and you have MMXXVI.
For 1994: 1,000 is M, 900 is CM, 90 is XC and 4 is IV. That gives MCMXCIV, which is a good one to practise, as it uses three subtractive pairs.
For 944: 900 is CM, 40 is XL and 4 is IV, which gives CMXLIV.
| Place | 1 | 4 | 5 | 9 |
|---|---|---|---|---|
| Units | I | IV | V | IX |
| Tens | X | XL | L | XC |
| Hundreds | C | CD | D | CM |
| Thousands | M |
The digits in between come from repeating or adding. A 2 or 3 repeats the symbol, so 20 is XX and 200 is CC. A 6, 7 or 8 starts from the 5 and adds, so 7 is VII, 60 is LX and 800 is DCCC.
With this pattern, you can write any number up to 3,999 by working through its digits. The calculator shows that same breakdown.
Common mistakes
IIII for 4. The standard form is IV. Many clock faces do use IIII, an old custom that has stayed in watchmaking, but it is not the standard form for writing numbers, and the calculator rejects it.
IC for 99. Subtraction is allowed only from the next one or two steps up. I can come before V and X, but not before C. So 99 is XCIX, which is 90 + 9.
VX, VL or LC. V, L and D are never subtracted, so these are not numerals. 5 is V and nothing needs VX.
XM for 990. X can come before L and C only. 990 is CMXC, 900 + 90.
MIM for 1999. This appears now and then in film credits, but the standard form is MCMXCIX.
The calculator checks a numeral by turning it into a number and back. If the result is not spelt the same, it is not standard and you will be told so, which catches all of the above.
Zero, big numbers and fractions
The Roman system has no symbol for zero. It was made for counting and recording, not for place value arithmetic, so a gap in a number simply had no symbol. That is why the standard system runs from 1.
The upper limit of 3,999 comes from rule 3, as four Ms in a row is not allowed. For bigger numbers, the Romans drew a line over a symbol to multiply it by 1,000, so a V with a bar meant 5,000. This vinculum form does not fit well into ordinary text, so it is not offered here.
The Romans did have a system of fractions, in twelfths, but that has fallen out of use.
Where they are used today
Clock and watch faces. Often with IIII for 4.
Book and document numbering. The front pages of a book may be numbered i, ii, iii, in small letters, to keep them apart from the main pages.
Names. Kings, queens and popes, such as Elizabeth II or Louis XIV, and family names such as Henry Ford III.
Years. Film and television credits and foundation stones often give the date in Roman numerals.
Events. Sporting events such as the Super Bowl and the Olympic Games use them for their sequence numbers.
Outlines and lists. Legal documents and exam papers use I, II, III or i, ii, iii for sections. Student exam questions in India often have parts marked this way.
Music and chemistry. Chord numbers in music theory and oxidation states in chemistry, such as iron(III), use them too.
To see a number spelt out in English or Hindi words instead, use the number to words converter. For other number systems, such as binary and hexadecimal, there is the binary, decimal and hex converter.
Reading a long numeral step by step
Long numerals look harder than they are. Go from left to right and compare each symbol with the next. If it is smaller, you have a subtractive pair, so read the two together. Otherwise, read it alone and add it to the total.
For MCMXLVII: M is 1,000. C comes before M, so CM is 900. X comes before L, so XL is 40. V, I and I come in falling order, so VII is 7. The total is 1,947.
For MDCCCLVII: M is 1,000, D is 500, CCC is 300, L is 50 and VII is 7, which makes 1,857.
| Number | Numeral |
|---|---|
| 1857 | MDCCCLVII |
| 1947 | MCMXLVII |
| 1950 | MCML |
| 2000 | MM |
| 2024 | MMXXIV |
| 2026 | MMXXVI |
| 3999 | MMMCMXCIX |
Writing a date in Roman numerals
People who want a date engraved on a ring or carved on a plaque usually convert each part on its own. So 15 August 1947 becomes XV.VIII.MCMXLVII. The order of the day and month follows local custom, so add a note if the date will be read abroad. It is worth running each part through the calculator before sending anything to an engraver, because a mistake cut into metal is hard to undo.
How the system came about
Roman numerals probably grew out of tally marks cut into sticks, which would explain why I, V and X look the way they do. They served well for recording amounts, but they are awkward for arithmetic, since there is no place value to line up in columns. The Indian numerals we use today, which reached Europe through Arabic mathematicians, made written calculation far easier, and over several centuries they replaced Roman numerals in commerce and science.
What this calculator assumes
- It accepts whole numbers from 1 to 3,999, and standard numerals only.
- Small letters are accepted and read as capitals, and commas in numbers are ignored.
- The numeral must be the standard way of writing its value. Forms such as IIII are rejected, even though the symbols add up.
- The bar notation for thousands is not used.
- The answer also shows the numeral in small letters, as used for page and section numbers.