Roman Numerals

What are Roman numerals?

Long ago, the Romans wrote numbers using letters instead of the digits 0–9 that we use today. This way of writing numbers is called Roman numerals, and you can still spot them all around you — on clocks, on old buildings, in the names of kings, and at the end of films.

Roman numerals use just seven symbols. Once you learn these seven, you can read and write almost any number.

Symbol	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

A handy way to remember the order is the sentence: I Value Xylophones Like Cats Do Mice.

The two big rules: add and subtract

Roman numerals are read from left to right, looking at the size of each symbol next to its neighbour.

Rule 1 — Adding. If a symbol is the same as or smaller than the one before it, you add the values.

• VI = 5 + 1 = 6
• XV = 10 + 5 = 15
• LXX = 50 + 10 + 10 = 70

Rule 2 — Subtracting. If a smaller symbol comes before a larger one, you subtract the small value from the large value.

• IV = 5 − 1 = 4
• IX = 10 − 1 = 9
• XL = 50 − 10 = 40
• CM = 1000 − 100 = 900

Why do we subtract at all?

Here is the why. The Romans had a rule that a symbol could only be repeated three times in a row. So you could write 3 as III, but you could not write 4 as IIII — that would be four in a row. To get around this, they put a smaller symbol in front to mean "one less". So IV means "one less than five" = 4, and IX means "one less than ten" = 9. This keeps the numbers short and tidy.

Only these subtractions are allowed:

Subtraction	Means	Value
IV	5 − 1	4
IX	10 − 1	9
XL	50 − 10	40
XC	100 − 10	90
CD	500 − 100	400
CM	1000 − 100	900

Building a number step by step

The trick to writing any number is to break it into thousands, hundreds, tens, and ones, then write each part.

Example 1 — Write 27.

1. 27 = 20 + 7.
2. 20 = XX (two tens).
3. 7 = VII (5 + 1 + 1).
4. Put them together, largest first: XXVII.

Example 2 — Write 49.

1. 49 = 40 + 9.
2. 40 = XL (subtraction rule).
3. 9 = IX (subtraction rule).
4. Together: XLIX.

Example 3 — Write 2024.

1. 2024 = 2000 + 0 + 20 + 4.
2. 2000 = MM.
3. 20 = XX.
4. 4 = IV.
5. Together: MMXXIV.

Reading Roman numerals back into numbers

To read a Roman numeral, scan left to right and ask at each step: "is the next symbol bigger?" If yes, subtract; if no, add.

Example 4 — Read MCMXCIX.

1. M = 1000.
2. CM = 900 (C before M).
3. XC = 90 (X before C).
4. IX = 9 (I before X).
5. Total: 1000 + 900 + 90 + 9 = 1999.

Roman numerals on a clock

Look at a clock with Roman numerals. The hours read I, II, III, IIII, V, VI, VII, VIII, IX, X, XI, XII. Notice that many clocks use IIII for 4 instead of IV — this is an old tradition used by clockmakers to make the face look balanced, even though IV is the "correct" maths way.

A practice activity

Try this with a partner or on your own:

1. Write your age in Roman numerals.
2. Write the current year. (Hint: start with the thousands.)
3. Decode these: XIV, XXIX, XL, LXVI, XCIV.
4. Encode these: 8, 19, 44, 90, 100.

Answers — Decode: 14, 29, 40, 66, 94. Encode: VIII, XIX, XLIV, XC, C.

Where this leads

Roman numerals are a great way to see that there is more than one way to write numbers. They also strengthen your sense of place value and adding and subtracting in your head. To compare them with the system we use every day, take a look at Place Value: Tens and Ones and Addition and Subtraction. Keep an eye out for Roman numerals in the world — once you can read them, you will see them everywhere!