Roman Numerals
Long before the digits we use today, the Romans wrote numbers with letters.
You still see them all over the place — on clock faces, at the end of films, and carved over
old doorways. Just a handful of symbols do all of the work:
\text{I}=1 \quad \text{V}=5 \quad \text{X}=10 \quad \text{L}=50 \quad \text{C}=100 \quad \text{D}=500 \quad \text{M}=1000
For everyday numbers you only need the first three or four:
\text{I} (one), \text{V} (five) and
\text{X} (ten). Memorise those and you can already read most of the
numbers you meet.
Our numbers use place
value: the same digit 3 means three, thirty or three
hundred depending on where it sits. Roman numerals don't work like that. A
\text{X} always means ten, wherever it is — you just write enough
symbols to add up to the number you want. And because you never need to say "this column is
empty", the Romans had no symbol for zero at all!
Building numbers by adding
To read a numeral you usually add the symbols from left to right, biggest first.
So \text{VII} is 5 + 1 + 1 = 7, and
\text{XVI} is 10 + 5 + 1 = 16. Here are a
few worked examples — notice how each one just stacks up the values:
- \text{VIII} = 5 + 1 + 1 + 1 = 8
- \text{XXVII} = 10 + 10 + 5 + 1 + 1 = 27
- \text{XXXVI} = 10 + 10 + 10 + 5 + 1 = 36
The subtraction trick
There is one neat twist. When a smaller symbol sits before a
larger one, you subtract it instead of adding. That is how four and nine are
written — it saves writing four symbols in a row:
\text{IV} = 5 - 1 = 4 \qquad \text{IX} = 10 - 1 = 9
So order matters: \text{VI} is six (five, then one more),
but \text{IV} is four (one less than five). The same trick
builds the tens: \text{XL} is
50 - 10 = 40, and \text{XIV} mixes both
ideas — 10 + (5 - 1) = 14.
The two traps everyone falls into the first time:
- \text{IV} is 4
(5 - 1), not 6. A smaller symbol
before a bigger one subtracts; a smaller symbol after a
bigger one adds (so \text{VI} really is six).
- You never write four of the same symbol in a row. Four is
\text{IV}, not \text{IIII}; forty is
\text{XL}, not \text{XXXX}. When you'd
reach a fourth, switch to the subtraction trick instead.
See it: build a number up
Step through a random number from 1 to 39,
one symbol at a time. Each symbol shows what it adds (or, for the subtraction trick, what it
works out to). Press Refresh for a fresh number.
Here is the same idea as an animation. Press play to turn a random number into its Roman
numeral, one symbol at a time. Replay it to get a different number each time.
Where you'll see them: clocks and dates
Roman numerals never really left us. A grand clock face counts the hours
\text{I} to \text{XII}, and films and
buildings often write their year in Roman numerals to look stately. To read a year, chop it
into thousands, hundreds, tens and ones and translate each piece.
Look closely at a fancy clock and you'll often spot \text{IIII}
for four o'clock, not the "correct" \text{IV}! Clockmakers have
done this for centuries — some say it balances the heavy \text{VIII}
on the opposite side, others that \text{IV} looked too much like the
start of a king's name. It's the one place the "never four in a row" rule is happily broken.
Old coins, cornerstones and the credits at the end of a film often stamp the year in Roman
numerals. To read \text{MMXXIV}, take it in chunks:
\text{MM} = 2000, \text{XX} = 20,
\text{IV} = 4 — together that's 2024.
Next time you spot a string of letters over a doorway, you can decode the year it was built.
Khan Academy introduces Roman numerals here: