Roman numerals are a
numeral system of
ancient Rome based on letters of the alphabet,
which are combined to signify the sum (or in some cases, the
difference) of their values. The first ten Roman numerals are:
 \mathrm{I,\;II,\;III,\;IV,\;V,\;VI,\;VII,\;VIII,\;IX,\;X}
The Roman numeral system is decimal but not directly
positional and does not include a
zero. It is a cousin of the
Etruscan numerals, and the letters derive
from earlier nonalphabetical symbols; over time the Romans came to
identify the symbols with letters of the
Latin alphabet. The system was modified
slightly during the
Middle Ages to
produce the system used today.
Roman numerals are commonly used in numbered lists (such as the
outline format of an article), clock faces, pages preceding the
main body of a book, chord triads in music analysis, dated notices
of copyright, months of the year, successive political leaders or
children with identical names, and the numbering of annual events.
See
modern usage below.
For arithmetic involving Roman numerals, see
Roman arithmetic and
Roman abacus.
Symbols
Roman numerals are based on seven symbols: a stroke (identified
with the letter I) for a unit, a chevron (identified with the
letter V) for a five, a crossstroke (identified with the letter X)
for a ten, a C (identified as an abbreviation of
Centum)
for a hundred,
etc.:
Symbols are iterated to produce multiples of the decimal (1, 10,
100, 1000) values, with V, L, D substituted for a multiple of five,
and the iteration continuing: I "1", II "2", III "3", V "5", VI
"6", VII "7", etc., and the same for other bases: X "10", XX "20",
XXX "30", L "50", LXXX "80"; CC "200", DCC "700",
etc. At
the fourth iteration, a
subtractive principle may be
employed, with the base placed
before the higher base:
IIII or IV "4", VIIII or IX "9", XXXX or XL "40", LXXXX or XC "90",
CCCC or CD "400", DCCCC or CM "900".
The Romans only used what is called capital (upper case) letters in
modern usage. In the Middle Ages,
minuscule (lower case) letters were developed,
and these are commonly used for Roman numerals: i, ii, iii, iv,
etc. Also in medieval use was the substitution of
j for a final
i to end numbers, such as
iij for 3 or
vij for 7. This was not a separate
letter, but merely a
swash
variant of
i. It is used today, especially in
medical prescriptions, to prevent
tampering with the numbers after they are written.
For large numbers (4000 and above), a bar can be placed above a
base numeral, or parentheses placed around it, to indicate
multiplication by 1000, although the Romans
themselves often just wrote out the "M"s:
The parentheses are more versatile; (II) is synonymous with MM, but
is not found.
The basic multiples of Roman numerals thus follow a pattern:

×1 
×2 
×3 
×4 
×5 
×6 
×7 
×8 
×9 
Ones 
I 
II 
III 
IV 
V 
VI 
VII 
VIII 
IX 
Tens 
X 
XX 
XXX 
XL 
L 
LX 
LXX 
LXXX 
XC 
Hundreds 
C 
CC 
CCC 
CD 
D 
DC 
DCC 
DCCC 
CM 
Thousands 
M 
MM 
MMM 






Ten thousands 









Hundred thousands 









A practical way to write a Roman number is to consider the modern
Arabic numeral system, and separately
convert the thousands, hundreds, tens, and ones as given in the
chart above. So, for instance, 1234 may be thought of as "one
thousand and two hundreds and three tens and four", obtaining M
(one thousand) + CC (two hundreds) + XXX (thirty) + IV (four), for
MCCXXXIV. Thus eleven is XI (ten and one), 32 is XXXII (thirty and
two) and 2009 is MMIX (two thousand and nine). Note that the
subtractive principle is not extended beyond the chart, and IL is
not used for 49, which can only be forty (XL) and nine
(IX), or XLIX.
Origins
Although the Roman numerals are now written with letters of the
Roman alphabet, they were originally independent symbols.
The
Etruscans, for example, used I Λ X 8 ⊕ for I V X L C M, of
which only I and X happened to be letters in their alphabet.
One
folk etymology has it that the V
represented a hand, and that the X was made by placing two Vs on
top of each other, one inverted.
However, the EtruscoRoman numerals
actually appear to derive from notches on tally sticks, which continued to be used by
Italian and Dalmatian shepherds
into the 19th century.
Thus, I descends not from the letter I but from a notch scored
across the stick. Every fifth notch was double cut (i.e. , , , ,
etc.), and every tenth was cross cut (X),
IIIIΛIIIIXIIIIΛIIIIXII…, much like European
tally marks today. This produced a positional
system:
Eight on a counting stick was eight tallies,
IIIIΛIII, or the eighth of a longer series of tallies; either way,
it could be abbreviated ΛIII (or VIII), as the existence of a Λ
implies four prior notches. By extension,
eighteen was the
eighth tally after the first ten, which could be abbreviated X, and
so was XΛIII. Likewise, number
four on the stick was the
Inotch that could be felt just before the cut of the Λ (V), so it
could be written as either IIII or IΛ (IV). Thus the system was
neither additive nor subtractive in its conception, but
ordinal. When
the tallies were transferred to writing, the marks were easily
identified with the existing Roman letters I, V, X
The tenth V or X along the stick received an extra stroke. Thus 50
was written variously as N, И, K, Ψ, ,
etc., but perhaps
most often as a chickentrack shape like a superimposed V and I  .
This had flattened to (an inverted T) by the time of
Augustus, and soon thereafter became
identified with the graphically similar letter L. Likewise, 100 was
variously Ж, , , H, or as any of the symbols for 50 above plus an
extra stroke. The form Ж (that is, a superimposed X and I) came to
predominate. It was written variously as >I or , was then
abbreviated to or C, with C variant finally winning out because, as
a letter, it stood for , Latin for "hundred".
The hundredth V or X was marked with a box or circle. Thus 500 was
like a superimposed on a or — that is, like a Þ with a cross bar,—
becoming
D or Ð by the time of Augustus, under the graphic
influence of the letter D. It was later identified
as the
letter D, perhaps as an abbreviation of "halfthousand"; this at
least was the folk etymology given to it later on.
Meanwhile, 1000 was a circled or boxed X: , , ⊕, and by Augustinian
times was partially identified with the Greek letter Φ
phi. In different traditions it then evolved along several
different routes. Some variants, such as Ψ and ↀ, were historical
dead ends, although folk etymology later identified D for 500 as
graphically half of Φ for 1000 because of the CD variant. A third
line, , survives to this day in two variants:
 One, , led to the convention of using parentheses to indicate
multiplication by a thousand: the original CIƆ = (I) 1000, then
(III) for 3000, (V) 5000, (IX) 9000, (X) 10 000, (L)
50 000, (C) 100 000, (D) 500 000, (M) 1000 000,
etc. This was later extended to double parentheses, as in
, , etc. See alternate
forms below.
 In the other, became and , eventually changing to M under the
influence of the Latin word "thousand".
Zero
In general, the number
zero did not have
its own Roman numeral, but a primitive form (
nulla) was
known by medieval
computists (responsible
for calculating the date of
Easter). They
included zero (via the
Latin word meaning
"none") as one of nineteen
epacts, or the age
of the moon on March 22. The first three epacts were
nulla, xi, and xxii (written in
minuscule or lower case). The first known
computist to use zero was
Dionysius
Exiguus in 525. Only one instance of a Roman numeral for zero
is known. About 725,
Bede or one of his
colleagues used the letter
N, the initial of
nulla, in a table of epacts, all written in Roman
numerals.
Fractions
A coin (1/3 or 4/12 of an ).
Note the four dots •••• indicating its value.
Though the Romans used a
decimal system for
whole numbers, reflecting how they
counted in Latin, they used a
duodecimal
system for
fraction, because the
divisibility of twelve makes it easier
to handle the common
fraction
of 1/3 and 1/4 than does a system based on ten . On
coins, many of which had values that were duodecimal
fractions of the unit , they used a tallylike notational system
based on twelfths and halves. A dot • indicated an "twelfth", the
source of the English words
inch and
ounce; dots
were repeated for fractions up to five twelfths. Six twelfths (one
half) was abbreviated as the letter
S for "half".
Uncia dots were added to S for fractions from seven to
eleven twelfths, just as tallies were added to V for whole numbers
from six to nine.
Each of these fractions had a name, which was also the name of the
corresponding coin:
Fraction 
Roman Numeral 
Name (nominative and genitive) 
Meaning 
1/12 
• 

"ounce" 
2/12 = 1/6 
•• or : 

"sixth" 
3/12 = 1/4 
••• or ∴ 

"quarter" 
4/12 = 1/3 
•••• or :: 

"third" 
5/12 
••••• or :•: 

"fiveounce" (quinque unciae → quincunx) 
6/12 = 1/2 
S 

"half" 
7/12 
S• 

"sevenounce" (septem unciae → septunx) 
8/12 = 2/3 
S•• or S: 

"twice" (as in "twice a third") 
9/12 = 3/4 
S••• or S:• 
or

"less a quarter" (dequadrans →
dodrans)
or "ninth ounce" (nona uncia →
nonuncium)

10/12 = 5/6 
S•••• or S:: 
or

"less a sixth" (desextans → dextans)
or "ten ounces" (decem unciae →
decunx)

11/12 
S••••• or S:•: 

"less an ounce" (deuncia → deunx) 
12/12 = 1 
I 

"unit" 
The arrangement of the dots was variable and not necessarily
linear. Five dots arranged like :·: (as on the face of a
die) are known as a
quincunx
from the name of the Roman fraction/coin. The Latin words
sextans and
quadrans are the source of the
English words
sextant and
quadrant.
Other Roman fractions include:
 1/8 (from sesqui +
uncia, i.e. 1½ uncias), represented by a sequence of the
symbols for the semuncia and the uncia.
 1/24 (from semi +
uncia, i.e. ½ uncia), represented by several variant
glyphs deriving from the shape of Greek letter sigma , one variant resembling the pound sign without
the horizontal line(s) and another resembling Cyrillic letter
.
 1/36 ("two sextulas") or , represented by ƧƧ, a sequence of two
reversed S.
 1/48 , represented by Ɔ, a reversed C.
 1/72 (1/6 of an uncia), represented by Ƨ, a reversed S.
 1/144 ("half a sextula"), represented by ƻ, a reversed S
crossed by a horizontal line.
 1/288 (a scruple), represented by the
symbol .
 1/1728 , represented by a symbol resembling closing guillemets
».
IIII vs IV
The notation of Roman numerals has varied through the centuries.
Originally, it was common to use IIII to represent
four,
because IV represented the
Roman god
Jupiter, whose Latin name,
IVPPITER, begins with IV. The
subtractive notation (which uses IV
instead of IIII) has become the standard notation only in modern
times. For example,
Forme of Cury, a
manuscript from 1390, uses IX for
nine, but IIII for
four. Another document in the same manuscript, from 1381,
uses IV and IX. A third document in the same manuscript uses IIII,
IV, and IX. Constructions such as IIIII for
five, IIX for
eight or VV for
10 have also been discovered.
Subtractive notation arose from
regular Latin usage: the number 18 was or “two from twenty”; the
number 19 was or "one from twenty". The use of subtractive notation
increased the complexity of performing
Roman arithmetic, without conveying the
benefits of a full
positional
notation system.
Likewise,
on some buildings it is possible to see MDCCCCX, for example,
representing 1910 instead of MCMX – notably Admiralty Arch in London.
The Leader
Building in Cleveland,
Ohio, at the corner of Superior Avenue and E.6th Street,
is marked MDCCCCXII, representing 1912 instead of MCMXII.
Another
notable example is on Harvard Medical School's Gordon Hall, which reads MDCCCCIIII for 1904
instead of MCMIV. In Dubrovnik, Croatia, a
commemorative inscription marking the 1000th anniversary of
King Tomislav’s coronation
(Croatia’s first King), appears as DCCCCXXV  MDCCCCXXV (925
1925).
Calendars and clocks
Clock faces that are labeled using Roman numerals conventionally
show IIII for four o'clock and IX for nine o'clock, using the
subtractive principle in one case and not the other. There are many
suggested explanations for this, several of which may be
true:
 Louis XIV, king of France,
who preferred IIII over IV, ordered his clockmakers to produce
clocks with IIII and not IV, and thus it has remained.
 Using the standard numerals, two sets of figures would be
similar and therefore confusable by children and others unused to
reading clockfaces: IV and the VI; and IX and XI. Since the first
pair are additionally upside down on the face, an added level of
confusion would be introduced. It is used to make greater character
distinction between them by using IIII and VI
 The fourcharacter form IIII creates a visual symmetry with the
VIII on the other side, which the twocharacter IV would not.
 With IIII, the number of symbols on the clock totals twenty
I's, four V's, and four X's, so clock makers need only a single
mold with a V, five I's, and an X in order to make the correct
number of numerals for their clocks: VIIIIIX. This is cast four
times for each clock and the twelve required numerals are
separated:
 V IIII IX
 VI II IIX
 VII III X
 VIII I IX
 The IIX and one of the IX’s are rotated 180° to form XI and
XII. The alternative with IV uses seventeen I's, five V's, and four
X's, requiring the clock maker to have several different
molds.
 Only the I symbol would be seen in the first four hours of the
clock, the V symbol would only appear in the next four hours, and
the X symbol only in the last four hours. This would add to the
clock's radial symmetry.
 Many clocks use IIII because that was the tradition established
by the earliest surviving clock, the Wells Cathedral clock built between
1386 and 1392. It used IIII because that was the typical method
used to denote 4 in contemporary manuscripts (as iiij or iiii).
That clock had an asymmetrical 24hour dial and used Arabic
numerals for a minute dial and a moon dial, so theories depending
on a symmetrical 12hour clock face do not apply.
Subtractive principle
Generally, Roman numerals are written in descending order from left
to right, and are added sequentially, for example MMVI (2006) is
interpreted as 1000 + 1000 + 5 + 1.
Certain combinations employ a subtractive principle, which
specifies that where a symbol of smaller value precedes a symbol of
larger value, the smaller value is subtracted from the larger
value, and the result is added to the total. For example, in
MCMXLIV (1944), the symbols C, X and I each precede a symbol of
higher value, and the result is interpreted as 1000 plus (1000
minus 100) plus (50 minus 10) plus (5 minus 1).
A numeral for 10
^{n} (I, X, or C) may not
precede a numeral larger than 10
^{n+1}, where
n is an
integer. That is, I may
precede V and X, but not L or C; X may precede L or C, but not D or
M. The numerals 5×10
^{n} (V, L, or D) may not be
followed by a numeral of greater or equal value. Any symbol that
appears more than once consecutively may not be followed by a
symbol of larger value.
Modern usage
Roman
numerals remained in common use until about the 14th century, when
they were replaced by HinduArabic
numerals (thought to have been introduced to Europe from
alAndalus, by way of Arab traders and
arithmetic treatises, around the 11th century). The Roman
number system is generally regarded as obsolete in modern usage,
but is still seen occasionally. Classical numbering is often used
to suggest importance or timelessness, or in other cases where an
alternate numbering system is useful for clarity. Examples of their
current use include:
 Names of monarchs and Popes, e.g. Elizabeth II, Benedict XVI. These are ordinal numbers; e.g. "II" is pronounced "the
second".
 The year of production of television shows and films.
 Hour marks on some clockfaces and timepieces.
 The year of construction on some building faces and cornerstones.
 Publication dates of books (particularly older ones); page
numbering of preliminary pages; volume numbers on spines and
chapter numbers.
 Film series and sequels of novels and video games (such as Final Fantasy), typically emulating use in
older books.
 Outline use I, II, III and i,
ii, iii as part of their organizational structure.
 A recurring grand event, such as the Olympic Games, Super
Bowl, WrestleMania, or the Sprint AllStar Race.
 Historic events, such as World War
II
 Names of Army Corps.
 Crossword puzzle clues, particularly
cryptic crosswords.
 Names of cranial nerves.
 Guitar chord diagrams.
 Parts of laws, such as Titles (e.g. Civil Rights Act of 1964) or
Schedules (e.g. Controlled
Substances Act).
 Sports teams, indicating the number of players in the squad. In
rugby union, the 1st XV of a particular
club would be the 1st and best team the club has, likewise for the
XIII in rugby league, and XI for
football , field hockey and cricket.
 Some countries use Roman numerals to number centuries (instead
of "18th century", "XVIII century" is used). This
is uncommon in the Englishspeaking world.
 Call signs of some
American television stations (usually based on the station's
channel number; such as WXII, KXII, WXIX, WPVI, etc.)
 RAF squadrons have two names, there's the
standard number name (which is most commonly used) and the Roman
numeral name (e.g. No. 15 Squadron RAF or No. XV
Squadron RAF).
Sometimes the numerals are written using lowercase letters (thus:
i, ii, iii, iv, etc.), particularly if numbering paragraphs or
sections within chapters, or for the pagination of the front matter
of a book.
Undergraduate degrees at British universities are generally graded
using I, IIi, IIii, III for first, upper second (often pronounced
"two one"), lower second (often pronounced "two two") and third
class respectively.
In
chemistry, Roman numerals were formerly
used to denote the
group in the
periodic table of the
elements. But there was not international agreement as to
whether the group of metals which dissolve in water should be
called Group IA or IB, for example, so although references may use
them, the international norm has recently switched to Arabic
numerals. However, Roman numerals are still used in the
IUPAC nomenclature of
inorganic chemistry, for the
oxidation number of
cations which can take on several different positive
charges. For example, FeO is iron(II) oxide and
Fe
_{2}O
_{3} is iron(III) oxide. In contrast, Arabic
numerals are used to denote the formal
oxidation state (which is not always the
same as the oxidation number) of positively or negatively charged
atoms. They are also used for naming
phases of
polymorphic crystals, such as
ice.
In
astronomy, the
natural satellites or "moons" of the
planets are traditionally designated by
capital Roman numerals, at first by order from the center of the
planet, as the four
Galilean
satellite of
Jupiter are numbered, and
later by order of discovery; e.g.,
Callisto was "Jupiter IV" or "J IV".
Notably, the notation IV was mostly disused by the Romans for its
similarity to the first two letters of Jupiter. With recent
discoveries—Jupiter currently has 63 known satellites—as well as
computerization, this is somewhat disparaged for the minor worlds,
at least in computerized listings.
Science fiction, and not astronomy
per se, has adopted the use for numbering the planets
around a star; e.g., Planet Earth is called "
Sol
III".
In
photography, Roman numerals (with
zero) are used to denote varying levels of brightness when using
the
Zone system.
In
earthquake seismology, Roman numerals are used to designate
degrees of the
Mercalli
intensity scale.
Music theory
In
music theory, while
scale degrees are typically represented with
Arabic numerals, often modified with a
caret
or
circumflex, the
triad that have these degrees as their roots
are often identified by Roman numerals (as in
chord symbols). See also
diatonic functions. Uppercase Roman
numerals indicate major triads while lowercase Roman numerals
indicate minor triads, as the following chart illustrates.
Lowercase Roman numerals with a
degree
symbol indicate
diminished
triads. For example, in the
major mode
the triad on the seventh scale degree, the leading tone triad is
diminished.
Also in music theory, individual strings of stringed instruments,
such as the
violin, are often denoted by
Roman numerals, with higher numbers denoting lower strings. For
example I signifies the E string on the violin and the A string on
the
viola and
cello,
these being the highest strings, respectively, on each instrument.
They are also sometimes used to signify
position. In this case, the number in Roman
numerals corresponds with the position number. For example, III
means third position and V means fifth.
Modern nonEnglishspeaking usage
The above uses are customary for Englishspeaking countries.
Although many of them are also maintained in other countries, those
countries have additional uses for Roman numerals that are not
normally employed in Englishspeaking regions.
The
French,
Hungarian,
Italian,
Portuguese,
Polish,
Romanian,
Russian,
Spanish and
Catalan languages use capital Roman
numerals to denote
centuries. For example,
XVIII refers to the eighteenth century, so as to avoid
confusion between the
18th century and the
1800s.
(The Italians also take the opposite approach, basing names of
centuries on the digits of the years; for example is a common
Italian name for , the fifteenth century.) Some scholars in
Englishspeaking countries have adopted the former method.
In
Italy, Poland, Russia, Central Europe, and in Portuguese, Romanian and Serbian languages, mixed Roman and Arabic
numerals are used to record dates (usually on
tombstones, but also elsewhere, such as in formal letters and
official documents). Just as an old clock recorded the hour
by Roman numerals while the minutes were measured in
Arabic numerals, the month is written in
Roman numerals while the day is in Arabic numerals: 14.VI 1789 is
14 June 1789.
This is how dates are inscribed on the walls of
the Kremlin, for example. This method has the advantage
that days and months are not confused in rapid notetaking, and
that any range of days or months can be expressed without
confusion. For instance, VVIII is May to August, while 1.V 
31.VIII is 1 May to 31 August.
In
Eastern Europe, especially the
Baltic nations,
Roman numerals are used to represent the days of the week in
hoursofoperation signs displayed in windows or on doors of
businesses. Monday is represented by
I, which is
the initial day of the
week. Sunday is
represented by
VII, which is the final day of the week.
The hours of operation signs are tables composed of two columns
where the left column is the day of the week in Roman numerals and
the right column is a range of hours of operation from starting
time to closing time. The following example hoursofoperation
table would be for a business whose hours of operation are 9:30 AM
to 5:30 PM on Mondays, Wednesdays, and Thursdays; 9:30 AM to 7:00
PM on Tuesdays and Fridays; and 9:30 AM to 1:00 PM on Saturdays;
and which is closed on Sundays.
I 
9:30–17:30 
II 
9:30–19:00 
III 
9:30–17:30 
IV 
9:30–17:30 
V 
9:30–19:00 
VI 
9:30–13:00 
VII 
— 
A five–watt resistor as per GOST 2.728–74.
In
CIS countries,
capital Roman numerals I, II and V still are sometimes used
according to the regional standard
GOST
2.728–74 (2002), to specify rated
resistor
power (in watts) in schematic symbols by inscribing the numeral
along inside the symbol rectangle.
Since the French use capital Roman numerals to refer to the
quarters of the year (
III is the third quarter), and this
has become the norm in some European standards organisation, the
mixed Roman–Arabic method of recording the date has switched to
lowercase Roman numerals in many circles, as
4viii1961.
(
ISO
has since specified that dates should be given in all Arabic
numerals, in
ISO 8601 formats.)
In
geometry, Roman numerals are often used
to show lines of equal length.
In
Poland, Romania, Serbia and other
European countries to lesser extent, Roman numerals are used for
floor numbering. Likewise apartments
in central Amsterdam are indicated as 138III, with both an
Arabic numeral (number of the block or house) and a Roman numeral
(floor number). The apartment on the ground floor is
indicated as ' '.
In
Poland, Roman
numerals are used for ordinals in names of some
institutions. In particular high schools (" " 
5th High
School in Kraków), tax offices (" " 
2nd Office of
Treasury in Gdańsk) and courts (" " 
District Court, 1st
Civil Division)  use Roman numerals. Institutions that use "
" notation always use Arabic numerals. These include elementary ("
") and middle schools (" ").
Roman numerals are rarely used in
Asia.
The
motion picture rating
system in Hong
Kong uses categories I, IIA, IIB, and III based on Roman
numerals.
Alternate forms
In the Middle Ages, Latin writers used a horizontal line above a
particular numeral to represent one thousand times that numeral,
and additional vertical lines on both sides of the numeral to
denote one hundred times the number, as in these examples:
The same overline was also used with a different meaning, to
clarify that the characters were numerals. Sometimes both underline
and overline were used, e. g. , and in certain (
serif)
typefaces, particularly
Times New Roman, the capital letters
when used without spaces simulates the appearance of the under/over
bar, e.g.
MCMLXVII.
Sometimes 500, usually D, was written as followed by an
apostrophus or
apostrophic C (which resembles a
backwards C, i.e. ), while 1,000, usually M, was written as . This
is believed to be a system of encasing numbers to denote thousands
(imagine the Cs as parentheses). This system has its origins from
Etruscan numeral usage. The D and M symbols to represent 500 and
1,000 were most likely derived from and , respectively.
An extra denoted 500, and multiple extra s are used to denote
5,000, 50,000, etc. For example:
Base number 

CIƆ = 1,000 
CCIƆƆ = 10,000 
CCCIƆƆƆ = 100,000 
1 extra Ɔ 
IƆ = 500 
CIƆƆ = 1,500 
CCIƆƆƆ = 10,500 
CCCIƆƆƆƆ = 100,500 
2 extra Ɔs 
IƆƆ = 5,000 

CCIƆƆƆƆ = 15,000 
CCCIƆƆƆƆƆ = 105,000 
3 extra Ɔs 
IƆƆƆ = 50,000 


CCCIƆƆƆƆƆƆ = 150,000 
Sometimes was reduced to a
lemniscate
symbol ( ) for denoting 1,000.
John
Wallis is often credited for introducing this symbol to
represent infinity ( ), and one conjecture is that he based it on
this usage, since 1,000 was
hyperbolically
used to represent very large numbers. Similarly, 5,000 ( ) was
reduced to ; and 10,000 ( ) was reduced to .
In medieval times, before the letter
j emerged as a
distinct letter, a series of letters
i in Roman numerals
was commonly ended with a flourish; hence they actually looked like
ij,
iij,
iiij, etc. This proved useful
in preventing fraud, as it was impossible, for example, to add
another
i to
vij to get
viij. This
practice is now merely an
antiquarian's
note; it is never used.
Medieval Roman numerals
Most uniquely, during the Middle Ages there came about a unique,
more comprehensive shorthand for writing Roman numerals, called
today the "medieval Roman numerals." This system used almost every
other letter of the Roman alphabet to stand as abbreviations for
more longhand numbers (usually those that consisted of repetitions
of the same symbol). They are still listed today in most
dictionaries, although through disfavor are primarily out of
use.
Modern
number

Medieval
abbreviation

Notes 
5 
A 
Resembles an upsidedown V. Also said to equal 500. 
6 
ↅ 
Either a ligature of VI, or the Greek letter stigma (Ϛ), having the same numerical
value. 
7 
S, Z 
Presumed abbreviation of septem, Latin for 7. 
11 
O 
Presumed abbreviation of (e.g.) onze, French for
11. 
40 
F 
Presumed abbreviation of English forty. 
70 
S 
Also could stand for 7, and has same etymology. 
80 
R 

90 
N 
Presumed abbreviation of nonaginta, Latin for 90. 
150 
Y 
Possibly derived from the lowercase y's shape. 
151 
K 
This unusual abbreviation's origin is unknown; it has also been
said to stand for 250. 
160 
T 
Possibly derived from Greek tetra, as 4 x 40 =
160. 
200 
H 

250 
E 

300 
B 

400 
P, G 

500 
Q 
Redundant with D, abbreviation for quingenti, Latin
for 500. 
800 
W 
More properly, the Greek ω, as W was a
fairly new creation. Carried over from Gothic. 
900 
ĵ, ↑ 
Resembled a crooked up arrow. Carried over from Gothic. 
2000 
Z 

Modern Roman numerals
Some "modern" Roman numerals, post
Victorian era, are shown below:
Standard 
Arabic 
Notes 
none 
0 
N for nulla was used at least once (by Bede about 725). 
I 
1 

II 
2 

III 
3 

IV 
4 
IIII is still used on clock and Tarot card faces. See Calendars and clocks above. 
V 
5 
IIIII was used rarely in the Middle Ages. 
VI 
6 

VII 
7 

VIII 
8 
IIX was used rarely in the Middle Ages. 
IX 
9 

X 
10 
VV was used rarely in the Middle Ages. 
XI 
11 

XII 
12 

XIII 
13 

XIV 
14 

XV 
15 

XVI 
16 

XVII 
17 

XVIII 
18 

XIX 
19 

XX 
20 

XXI 
21 

XXV 
25 

XXX 
30 

XXXV 
35 

XL 
40 

XLV 
45 

XLIX 
49 
Per rule above, IL would
not be generally accepted. 
L 
50 

LX 
60 

LXIX 
69 

LXX 
70 
The abbreviation for the Septuagint 
LXXVI 
76 

LXXX 
80 

XC 
90 

XCIX 
99 
As opposed to the "shortcut" way IC seen above. 
C 
100 
This is the origin of using the slang term "Cbill" or "Cnote"
for "$100 bill". 
CL 
150 

CC 
200 

CCC 
300 

CD 
400 

CDXCIX 
499 
Per rule above, ID would
not be generally accepted. 
D 
500 

DC 
600 

DCLXVI 
666 
Using every symbol except M in descending order gives the
beast number. 
DCC 
700 

DCCC 
800 

CM 
900 

CMXCIX 
999 
Per rule above, IM would
not be generally accepted. 
M 
1,000 

MCDXLIV 
1,444 
Smallest pandigital number
(each symbol is used) 
MDCLXVI 
1,666 
Largest efficient pandigital number (each symbol occurs exactly
once) 
MCMXC 
1,990 
Shortcuts like XMM and MXM disagree with the rule stated
above 
MCMXCVII 
1,997 
MCMXCIX 
1,999 
Shortcuts like IMM and MIM disagree with the rule stated
above 
MM 
2,000 

MMI 
2,001 

MMIX 
2,009 

MMD 
2,500 

MMM 
3,000 

MMMDCCCLXXXVIII 
3,888 
Longest number (most symbols, without overlines or without
extra symbols containing overlines). 
MMMCMXCIX 
3,999 
Largest number without an overline at any symbol. 

4,000 
sometimes MMMM or M 

5,000 

MDCLXVI 
6,666 
This number uses every symbol up to once. 

10,000 


50,000 


100,000 


500,000 


1,000,000 


1,444,000 
Smallest pandigital number
(each symbol is used with one line above every symbol) 


1,666,000 
Largest efficient pandigital number (each symbol is used with
one line above every symbol) 


2,000,000 


3,888,000 
Longest number (most symbols, each symbol is used with one line
above every symbol) 

An accurate way to write large numbers in Roman numerals is to
handle first the thousands, then hundreds, then tens, then
units.
Example: the number 1988.
One thousand is M, nine hundred is CM, eighty is LXXX, eight is
VIII.
Put it together: MCMLXXXVIII.
Unicode
Unicode has a number of characters
specifically designated as Roman numerals, as part of the
Number Forms range from U+2160 to U+2188. This range
includes both upper and lowercase numerals, as well as
precombined
glyphs for numbers up to 12 ( or
XII), mainly intended for the clock faces for
compatibility with large EastAsian character
sets such as
JIS X 0213 that provide
these characters. The precombined glyphs should only be used to
represent the individual numbers where the use of individual glyphs
is not wanted, and not to replace compounded numbers. Additionally,
glyphs exist for archaic forms of 1000, 5000, 10,000, large
reversed C ( ), late 6 ( , similar to Greek
Stigma: ), early 50 ( , similar to down
arrow ), 50,000, and 100,000. Note that the small reversed c, is
not intended to be used in roman numerals, but as
lower case Claudian
letter ,
Table of Roman numerals in Unicode
Code 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
A 
B 
C 
D 
E 
F 
Value 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
50 
100 
500 
1,000 
U+2160 
Ⅰ 
Ⅱ 
Ⅲ 
Ⅳ 
Ⅴ 
Ⅵ 
Ⅶ 
Ⅷ 
Ⅸ 
Ⅹ 
Ⅺ 
Ⅻ 
Ⅼ 
Ⅽ 
Ⅾ 
Ⅿ 
U+2170 
ⅰ 
ⅱ 
ⅲ 
ⅳ 
ⅴ 
ⅵ 
ⅶ 
ⅷ 
ⅸ 
ⅹ 
ⅺ 
ⅻ 
ⅼ 
ⅽ 
ⅾ 
ⅿ 
Value 
1000 
5000 
10,000 
– 
– 
6 
50 
50,000 
100,000 

U+2180 
ↀ 
ↁ 
ↂ 
Ↄ 
ↄ 
ↅ 
ↆ 
ↇ 
ↈ 

The characters in the range U+2160–217F are present only for
compatibility with
other character set standards which provide these characters. For
ordinary uses, the standard Latin letters are preferred. Displaying
these characters requires a program that can handle Unicode and a
font that contains appropriate glyphs for
them.
Games
After the
Renaissance, the Roman system
could also be used to write
chronograms.
It was common to put in the first page of a book some phrase, so
that when adding the I, V, X, L, C, D, M present in the phrase, the
reader would obtain a number, usually the year of publication. The
phrase was often (but not always) in Latin, as chronograms can be
rendered in any language that utilises the Roman alphabet.
See also
References
 Or more precisely, "a decimal system in which the number 5 is
an auxiliary base" (Ifrah 200:193)
 Roman numerals: How they work: Larger
numbers
 Georges Ifrah, The Universal History of Numbers: From
Prehistory to the Invention of the Computer. Translated by
David Bellos, E. F. Harding, Sophie Wood, Ian Monk. John Wiley
& Sons, 2000.
 W.I. Milham, Time & Timekeepers (New York:
Macmillan, 1947) p. 196
 Paul Lewis, Clocking the fours: A new theory about IIII
 Capelli, A. Dictionary of Latin Abbreviations.
1912.
 Perry, David J. Proposal to Add Additional Ancient Roman Characters to
UCS.
 Unicode Number Forms
 For the first two rows
External links