|Numeral systems by culture|
|Positional systems by base|
|Non-standard positional numeral systems|
|List of numeral systems|
The system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000. Two sets of pronunciations for the numerals exist in Japanese: one is based on Sino-Japanese (on'yomi) readings of the Chinese characters and the other is based on the Japanese yamato kotoba (native words, kun'yomi readings).
Basic numbering in Japanese 
There are two ways of writing the numbers in Japanese, in Arabic numerals (1, 2, 3) or in Chinese numerals (一, 二, 三). The Arabic numerals are more often used in horizontal writing, and the Chinese numerals are more common in vertical writing.
Most numbers have two readings, one derived from Chinese used for cardinal numbers and a native Japanese reading used for ordinal numbers, though there are some exceptions (listed below) in which the Japanese version is preferred for both.
|Number||Character||Preferred reading||On reading||Kun reading|
|0||零 / 〇*||zero||rei / れい||zero / ぜろ|
|1||一||ichi||ichi / いち||hito(tsu) / ひと・つ|
|2||二||ni||ni, ji / に, じ||futa(tsu) / ふた・つ|
|3||三||san||san / さん||mi(ttsu) / み・っつ|
|4||四||yon||shi / し||yon, yo(ttsu) / よん、よ・っつ|
|5||五||go||go / ご||itsu(tsu) / いつ・つ|
|6||六||roku||roku / ろく||mu(ttsu) / む・っつ|
|7||七||nana||shichi / しち||nana(tsu) / なな・つ|
|8||八||hachi||hachi / はち||ya(ttsu) / や・っつ|
|9||九||kyū||kyū, ku / きゅう, く||kokono(tsu) / ここの・つ|
|10||十||jū||jū / じゅう||tō / とお|
|20||二十||ni-jū||ni-jū / にじゅう||hata(chi) / はた・ち|
|30||三十||san-jū||san-jū / さんじゅう||miso / みそ|
|100||百||hyaku||hyaku / ひゃく||(momo / もも)|
|1000||千||sen||sen / せん||(chi / ち)|
|10,000||万||man||man / まん||(yorozu / よろず)|
|100,000,000||億||oku||oku / おく||-|
|1,000,000,000,000||兆||chō||chō / ちょう||-|
|10,000,000,000,000,000||京||kei||kei / けい||-|
* The special reading maru (which means "round" or "circle") is also found. It may be optionally used when reading individual digits of a number one after another, instead of as a full number. A popular example is the famous 109 store in Shibuya, Tokyo which is read as ichi-maru-kyū. (It can also be read as 'ten-nine' - pronounced tō-kyū - which is a pun on the name of the Tokyu department store which owns the building.) This usage of maru for numerical 0 is similar to reading numeral 0 in English as oh. It literally means a circle. However, as a number, it is only written as 0 or rei (零).
Starting at 万, numbers begin with 一 (ichi) if no digit would otherwise precede. That is, 100 is just 百 hyaku, and 1000 is just 千 sen, but 10,000 is 一万 ichiman, not just *man. And, if 千 sen directly precedes the name of powers of myriad, 一 ichi is normally attached before 千 sen, which yields 一千 issen. That is, 10,000,000 is normally read as 一千万 issenman. But if 千 sen do not directly precede the name of powers of myriad or if numbers are lower than 2,000, attaching 一 ichi is optional. This is, 15,000,000 is read as 千五百万 sengohyakuman or 一千五百万 issengohyakuman, and 1,500 as 千五百 sengohyaku or 一千五百 issengohyaku.
The numbers 4 and 9 are considered unlucky in Japanese: 4, pronounced shi, is a homophone for death (死); 9, when pronounced ku, is a homophone for suffering (苦). See tetraphobia. The number 13 is sometimes considered unlucky, though this is a carryover from Western tradition.
In modern Japanese, cardinal numbers are given the on readings except 4 and 7, which are called yon and nana respectively. Alternate readings are used in month names, day-of-month names, and fixed phrases. For instance, the decimal fraction 4.79 is always read yon-ten nana kyū, though April, July, and September are called shi-gatsu (4th month), shichi-gatsu (7th month), and ku-gatsu (9th month) respectively. Intermediate numbers are made by combining these elements:
- Tens from 20 to 90 are "(digit)-jū".
- Hundreds from 200 to 900 are "(digit)-hyaku".
- Thousands from 2000 to 9000 are "(digit)-sen".
- Additionally, the tens from 30 to 90 in kun reading are formed by "(digit)-so", where the digit is also in kun reading: miso (30), yoso (40), iso (50), muso (60), nanaso (70), yaso (80), kokonoso (90). Variations include i for 50 and the suffix -ji for 20 through 90. However, for the most part, these are not in use in modern Japanese.
There are some phonetic modifications to larger numbers involving voicing or gemination of certain consonants, as typically occurs in Japanese (i.e. rendaku): e.g. roku "six" and hyaku "hundred" yield roppyaku "six hundred".
* This also applies to multiples of 10. Change ending -jū to -jutchō or -jukkei.
** This also applies to multiples of 100. Change ending -ku to -kkei.
In large numbers, elements are combined from largest to smallest, and zeros are implied.
|17||十七||jū nana, jū shichi|
|151||百五十一||hyaku go-jū ichi|
|469||四百六十九||yon-hyaku roku-jū kyū|
|2025||二千二十五||ni-sen ni-jū go|
Powers of 10 
Large numbers 
Following Chinese tradition, large numbers are created by grouping digits in myriads (every 10,000) rather than the Western thousands (1000):
|Rank||104||108||1012||1016||1020||1024||1028||1032||1036||1040||1044||1048||1052 or 1056||1056 or 1064||1060 or 1072||1064 or 1080||1068 or 1088|
Variation is due to Jinkōki, Japan's oldest mathematics text. The initial edition was published in 1627. It had many errors. Most of these were fixed in the 1631 edition. In 1634 there was yet another edition which again changed a few values. The above variation is due to inconsistencies in the latter two editions.
Examples: (spacing by groups of four digits is given only for clarity of explanation)
- 1 0000 : 一万 (ichi-man)
- 983 6703 : 九百八十三万 六千七百三 (kyū-hyaku hachi-jū san man, roku-sen nana-hyaku san)
- 20 3652 1801 : 二十億 三千六百五十二万 千八百一 (ni-jū oku, san-zen rop-pyaku go-jū ni-man, sen hap-pyaku ichi)
However, numbers written in Arabic numerals are separated by commas every three digits following English-speaking convention. If Arabic numbers and kanji are used in combination, Western orders of magnitude may be used for numbers smaller than 10,000 (e.g. 2,500万 for 25,000,000).
In Japanese, when long numbers are written out in kanji, zeros are omitted for all powers of ten. Hence 4002 is 四千二 (in contrast, Chinese requires the use of 零 wherever a zero appears, e.g. 四千零二 for 4002). However, in reading, the digit zero is sometimes pronounced as tobi (飛び) or tonde (飛んで) to indicate the lack of numbers, e.g. yon-sen tobi ni or yon-sen tonde ni can be used instead of the normal yon-sen ni.
Decimal fractions 
Japanese has two systems of numerals for decimal fractions. They are no longer in general use, but are still used in some instances such as batting and fielding averages of baseball players, winning percentages for sports teams, and in some idiomatic phrases (such as 五分五分の勝負 "fifty-fifty chance"), and when representing a rate or discount.
One system is as follows:
The other system of representing these decimal fractions of rate or discount uses a system "shifted down" with a bu becoming a "one hundredth" and so on, and the unit for "tenth" becoming wari:
This is often used with prices. For example:
- 一割五分引き (ichi-wari go-bu biki): 15% discount
- 打率三割八分九厘 (daritsu san-wari hachi-bu kyū-rin): batting average .389
With the exception of wari, these are rarely seen in modern usage. Decimal fractions are typically written with either kanji numerals (vertically) or Arabic numerals (horizontally), preceded by a decimal point, and are read as successive digits, as in Western convention. Note that, in written form, they can be combined with either the traditional system of expressing numerals (42.195 kilometers: 四十二・一九五 キロメートル), in which powers of ten are written, or with the place value system, which uses zero (50.04 percent: 五〇・〇四 パーセント.) In both cases, however, the reading follows the traditional system (yon-jū ni-ten ichi-kyū go kiromētoru for 42.195 kilometers; go ju-tten rei-yon pāsento for 50.04 percent.)
Formal numbers 
As with Chinese numerals, there exists in Japanese a separate set of kanji for numerals called daiji (大字) used in legal and financial documents to prevent unscrupulous individuals from adding a stroke or two, turning a one into a two or a three. The formal numbers are identical to the Chinese formal numbers except for minor stroke variations. Today, only the formal numbers for one, two, three, and ten are used in legal documents (for the reason that the numbers 4 to 9 as well as 100, 1000 and 10000 are written identically to the common ones, cf. table below). They are the ones whose common forms can be changed to a higher value by adding strokes (1 and 2 were explained above, while 3 can be changed to 5, and 10 to 1000). In some cases, the digit 1 is explicitly written like 壱百壱拾 for 110, as opposed to 百十 in common writing.
The four current banknotes of the Japanese yen, 1000-yen, 2000-yen, 5000-yen, and 10000-yen, have formal numbers 千, 弐千, 五千, and 壱万 respectively.
Old Japanese 
Old Japanese shares some vocabulary with later periods, but there are also some unique numbers which are not used any more.
- The transcription is based on the phoneme and is not phonetic. See Old Japanese language for further information.
- See Jōdai Tokushu Kanazukai for information on subscript notation.
|1||hi1to2||hi1to2hi1 (1 day), hi1to2to2se (1 year)|
|2||huta||hutayo1 (2 nights)|
|4||yo2||yo2so1 (40), yo2tari (4 people)|
|5||itu||ituto2se (5 years)|
|6||mu||mutuma (6 claws)|
|7||nana||nanase (many rapids)||Often used to mean many.|
|8||ya||yakumo1 (many clouds)||Often used to mean many.|
|9||ko2ko2no2||ko2ko2no2hashira (9 nobles / gods)|
|10||to2 / to2wo||to2woka (10 days)|
|10||so1||mi1so1 (30), yo2so1 (40), muso1 (60), yaso (80)||Found only in compound words; not used alone.|
|20||hata||hatati (20), hatatari (20 people), hatato2se (20 years)|
|50||i||ika (50 days)|
|100||ho||iho (500), ihoto2se (500 years), ihoyo2 (500 nights), yaho (800), mi1ho (300), muho (600), ko2ko2no2ho (900)||Used for multiple hundreds in compound numerals. Often used to mean many.|
|100||mo1mo1||mo1mo1ka (many days)||Used for non-multiple hundred and for the number "100" by itself. Often used to mean many.|
|1000||ti||tito2se (1000 years, many years)||Often used to mean many.|
Hand counting 
Japanese uses separate systems for counting for oneself and for displaying numbers to others, which both proceed up to ten. For counting, one begins with the palm open, then counts up to five by curling up (folding down) the fingers, starting from the thumb – thus one has just the thumb down (and others extended), while four has only the pinkie extended, and five has a fist. One then counts up to ten by proceeding in the reverse order, extending the fingers, starting at the pinkie – thus six is the same as four, seven the same as three, and so forth, with ten ending with the palm open. While this introduces ambiguity, it is not used to present to others, so this is generally not a problem. When displaying for others, one starts with the hand closed, and extends fingers, starting with the index, going to the pinkie, then ending with the thumb, as in the United States. For numbers above five, one uses an open hand (indicating five) and places the appropriate number of fingers from the other hand against the palm (palms facing each other) – so six has the index finger against the palm, and so forth. To display ten, one presents both hands open and palm outwards.
See also 
- 大正十一年大蔵省令第四十三号 (会計法規ニ基ク出納計算ノ数字及記載事項ノ訂正ニ関スル件) 第一条: 会計法規ニ基ク出納計算ニ関スル諸書類帳簿ニ記載スル金額其ノ他ノ数量ニシテ「一」、「二」、「三」、「十」、「廿」、「卅」ノ数字ハ「壱」、「弐」、「参」、「拾」、「弐拾」、「参拾」ノ字体ヲ用ユヘシ但横書ヲ為ストキハ「アラビア」数字ヲ用ユルコトヲ得
- 戸籍法施行規則 第三十一条 2: 年月日を記載するには、壱、弐、参、拾の文字を用いなければならない。
- 小切手振出等事務取扱規程 附則 (昭和四〇年四月一日大蔵省令第二〇号) 2: 小切手の券面金額は、当分の間、所定の金額記載欄に、漢数字により表示することができる。この場合においては、「一」、「二」、「三」及び「十」の字体は、それぞれ「壱」、「弐」、「参」及び「拾」の漢字を用い、かつ、所定の金額記載欄の上方余白に当該金額記載欄に記載の金額と同額をアラビア数字で副記しなければならない。
- 商業登記規則 第四十八条 2: 金銭その他の物の数量、年月日及び番号を記載するには、「壱、弐、参、拾」の文字を用いなければならない。ただし、横書きをするときは、アラビヤ数字を用いることができる。
- Counting on one's fingers, About.com, Japanese Language, Namiko Abe
- (Japanese) 大数の名前について
- Ancient Japanese number system
- English exercises for learning Japanese numerals
- Audio to learn the pronunciation for Japanese numbers
- Convert kanji numerals to arabic numerals (sci.lang.Japan FAQ page)
- Convert arabic numerals to kanji numerals (sci.lang.Japan FAQ page)