Anzan Kentei: the mental arithmetic exam, level by level
The anzan kentei is Japan's written certification exam in mental arithmetic. This guide covers the published format of every Nishuren level, how the papers are scored, how Zenshuren's exam differs and where to start. Each level page adds a sample paper and a mock exam built to the published specification.
✓Checked against the official pages on 23 September 2026.
The levels
Each level page gives the official format, what changes from the level below, pacing and how Zenshuren differs, plus a printable sample paper with answers and a mock exam.
Anzan means calculation done in the head. In soroban (Japanese abacus) teaching it is a specific skill: working a problem on an imagined soroban, moving the beads in the mind instead of on the frame. The anzan kentei tests mental calculation on paper: printed problems, written answers, and all the working done in the head.
This guide covers the anzan exams of two federations, which use different formats. It follows the League of Japan Abacus Associations (Nishuren), which publishes a specification for every level, and notes where the League for Soroban Education of Japan (Zenshuren) differs. Anything read off a sample paper rather than a written rule is labelled as such.
A paper has up to three sections: mitori anzan (column addition and subtraction), kake anzan (multiplication) and wari anzan (division). On Nishuren's ladder the first paper is mitori only, and multiplication and division join at 6 kyu. On the official kyu samples, mitori is addition only until the ten-row problems at pre-1 and 1 kyu, where some problems include subtracted rows.
Who runs the exam
The League of Japan Abacus Associations (Nishuren) was founded in 1953 and began its anzan exam, together with an anzan dan exam, in 1974. Its kyu ladder runs from 10 kyu to 1 kyu with three pre-grades (pre-3, pre-2 and pre-1 kyu), and its separate dan exam has 13 ranks, from pre-shodan to 10th dan. Nishuren publishes the digit and row specification of every paper, and sittings are run locally by chambers of commerce and abacus leagues.
The League for Soroban Education of Japan (Zenshuren) was also founded in 1953, on 24 September. Its anzan exam is one ladder of 26 steps, from 10 kyu to 1 kyu and on through pre-shodan to 10th dan. Each section has its own three-minute clock and score, and no per-level question specification is published online. Its anzan exam at 3 kyu and above, including dan, has had the backing of Japan's education ministry (MEXT) since its 422nd exam on 21 July 2024. Nishuren's anzan kyu page names no backer.
The Nishuren kyu ladder
10 to 7 kyu share one paper of 50 mitori questions. From 6 kyu every paper has 80: mitori Nos. 1–20, kake Nos. 21–50 and wari Nos. 51–80. At pre-3 and pre-1 kyu each section is half the lower grade's specification and half the higher one, and on the official samples the lower grade's half comes first; at pre-2 kyu only the mitori specification is split, though the kake and wari samples change shape partway through. Shapes in brackets are what the official samples show, not rules.
Nishuren anzan kyu papers, from the first paper to 1 kyu
Level
Mitori anzan
Kake anzan
Wari anzan
Pass mark
10–7 kyu (one shared paper)
50 questions, 1-digit rows: 3 kuchi 3 ji (Nos. 1–15), 4 kuchi 4 ji (Nos. 16–30), 5 kuchi 5 ji (Nos. 31–50)
None
None
The score sets the grade: 250 or more for 10 kyu, 300 or more for 9 kyu, 350 or more for 8 kyu, 400 or more for 7 kyu
Hosho 5 keta (samples: 2-digit divisor with 3-digit quotient, and 3-digit divisor with 2-digit quotient)
400 of 500
Keta = digits, kuchi = rows, ji = total digits in the problem. Jitsuho counts the digits of both numbers in a multiplication; hosho counts the divisor and the quotient in a division, never the dividend. Specifications from Nishuren's anzan kentei page; shapes from its official sample papers.
How the kyu papers are scored
Nishuren's kyu exam is one paper on one clock: 12 minutes for the whole paper, in a single sitting. Candidates may calculate in any order, so no section has its own time.
From 6 kyu to 1 kyu, pre-grades included, the paper is out of 500. The official samples print section totals of mitori 200, kake 150 and wari 150, which works out to 10 points per mitori question and 5 per kake or wari question. The pass mark of 400 leaves 100 points to spare: ten mitori questions, twenty kake or wari questions, or a mix. Twelve minutes for 80 questions works out to 9 seconds a question, and with mitori worth double, the working order is worth planning.
The 10–7 kyu paper is 50 mitori questions at 10 points each, and the score decides the grade: 400 or more is 7 kyu, 350 or more 8 kyu, 300 or more 9 kyu and 250 or more 10 kyu. The official samples show addition only, and the clock works out to about 14 seconds a question.
Older practice material may not match: before April 2003 mitori had 15 questions, the paper was out of 450 and the pass mark was 360. The 10–7 kyu paper dates from fiscal 2003 and the pre-grades from fiscal 2014.
The Nishuren dan exam
Nishuren's anzan dan exam, in its current form since fiscal 2011, is one paper for all 13 ranks. Each section has its own clock: kake anzan, 60 questions in 3 minutes; wari anzan, 60 in 3 minutes; mitori anzan, 30 in 4 minutes. That works out to 3 seconds per kake or wari question and 8 per mitori question.
Each section climbs through three digit bands. Kake has 5 digits in total in Nos. 1–20 (2-digit × 3-digit or 3-digit × 2-digit), 6 in Nos. 21–40 (sixteen of them 3-digit × 3-digit) and 7 in Nos. 41–60 (3-digit × 4-digit or 4-digit × 3-digit), with no 4-digit × 4-digit question. Wari mirrors this, divisor and quotient together always 5, 6 or 7 digits. Mitori has ten rows of exactly 4, 6 and 8 digits in Nos. 1–10, 11–20 and 21–30.
All questions are bare numbers, and the official samples show no decimals but do show subtraction in mitori: on the 2018 sample, 48 of the 300 rows are subtracted and 3 of the 30 answers are negative, such as −2,800. The Hanno Chamber of Commerce and Industry, which administers the exam, states that dan answers need a comma every three digits.
Each section is ranked on its own against the table below, and the overall anzan rank is the lowest of the three. Nishuren's FAQ says every section must clear the rank, and the Hanno chamber states that the certificate is issued at the lowest section's rank. So kake at 180, wari at 160 and mitori at 100 is shodan, not 5th dan. A section's rank stays valid for the last five exams held, so sittings can be combined.
Nishuren's dan page does not state a maximum; the Kagoshima Chamber of Commerce and Industry, which also administers the exam, lists each section at 300 points. The dan mock exam follows that, with per-question points set by us rather than by Nishuren: 5 per kake or wari question, 10 per mitori question.
Nishuren anzan dan: the score needed in each section
Rank
Japanese name
Score in every section
Pre-shodan
jun-shodan
90
1st dan
shodan
100
Pre-2nd dan
jun-nidan
110
2nd dan
nidan
120
Pre-3rd dan
jun-sandan
130
3rd dan
sandan
140
4th dan
yodan
160
5th dan
godan
180
6th dan
rokudan
200
7th dan
nanadan
220
8th dan
hachidan
240
9th dan
kudan
260
10th dan
judan
290
Scores from Nishuren's dan page, applied to each section separately. The overall rank is the lowest section's rank.
Nishuren and Zenshuren compared
Both federations grade the same three skills with kyu and dan ranks, but the clock, the scoring and the lowest levels differ.
The two anzan exams side by side
Point
Nishuren
Zenshuren
Own English name
The League of Japan Abacus Associations
The League for Soroban Education of Japan, Inc.
Founded
1953
24 September 1953
Levels
10 kyu to 1 kyu plus pre-3, pre-2 and pre-1 kyu; a separate dan exam with 13 ranks
10 kyu to 1 kyu, then pre-shodan to 10th dan: 26 steps in all
Clock
Kyu: 12 minutes for the whole paper, any order. Dan: 3, 3 and 4 minutes by section
3 minutes per section at every level
Lowest levels
10–7 kyu: one shared paper of 50 mitori questions
8–10 kyu: mitori only (sections A and B). 7 kyu: multiplication and mitori, no division
Kyu scoring
One 500-point paper. From 6 kyu, pass at 400; on the 10–7 kyu paper the score sets the grade (250 or more for 10 kyu)
Each section out of 100; pass with 70 or more in every section
Dan scoring
Each section ranked from 90 (pre-shodan) to 290 (10th dan); overall rank = lowest section
Each section out of 200; 70 or more in all three is pre-shodan; 10th dan needs 190 or more
Decimals
None on the official dan samples
Only in dan
Published question specifications
Digits and rows for every level, plus sample papers
None per level online
Dates
Kyu: unified dates in June, October and February, plus anytime sittings at every kyu level. Dan: June, October and February
Kyu every month; dan six times a year
Education ministry (MEXT) backing
Not named on the anzan kyu page
3 kyu and above, including dan, since 21 July 2024
From each federation's own anzan pages, checked in September 2026.
Terms you will see
Kyu, dan and pre-grades
Kyu grades count down from 10 kyu to 1 kyu; dan ranks count up from shodan (1st dan) to 10th dan. A pre-grade (jun, as in jun-sankyu for pre-3 kyu) sits one step below the grade it names.
Keta
Digits. A 3-keta number has three digits.
Kuchi
One row of a mitori problem. 5 kuchi means five rows.
Ji
Total digits across all rows: 3 keta 10 kuchi 30 ji is ten 3-digit rows. With mixed widths, 1–2 keta 5 kuchi 6 ji means four 1-digit rows and one 2-digit row.
Jitsuho
Multiplicand and multiplier digits added together. Jitsuho 4 keta covers both 3-digit × 1-digit and 2-digit × 2-digit; on the official samples, 3 kyu uses only the first and 2 kyu only the second.
Hosho
Divisor and quotient digits added together; the dividend is not counted. 4,592 ÷ 82 = 56 is hosho 4 keta.
Mumeisu
A bare number with no unit, such as 200 or 3.5; a meisu carries one, such as 200 yen or 3 m 50 cm. Every dan question is a mumeisu.
Soroi
Every row the same width. The dan mitori problems are 4-, 6- and 8-digit soroi.
Negative answers
On the official dan samples, some mitori answers fall below zero: 3 of the 30 on the 2018 sample.
Where and when to sit, and what it costs
As of September 2026, Nishuren's kyu exam has unified dates in June, October and February, though the month can differ by local chamber of commerce or abacus league, and anytime (zuiji) sittings have existed at every kyu level since fiscal 2003. The anzan dan exam is also held in June, October and February.
Few chambers of commerce offer the anzan and dan exams, so check locally. Candidates can sit anywhere, not only at the nearest chamber.
Zenshuren holds kyu exams every month and dan exams six times a year, in January, March, May, July, September and November. These are the published patterns as of September 2026, not fixed dates.
Anzan exam fees
Level
Nishuren
Zenshuren
10–7 kyu
¥1,000
¥700
6–4 kyu
¥1,100
¥1,100
3–1 kyu
¥1,200
¥1,200
Pre-3, pre-2 and pre-1 kyu
¥1,200
No pre-kyu grades
Dan
¥1,500 for anzan only (soroban dan only ¥3,000; both ¥3,500)
¥1,900
Nishuren kyu fees include tax and apply from April 2024, repeated for fiscal 2026. Zenshuren fees include tax, from its fee page dated 30 June 2026. Checked in September 2026.
Flash anzan and yomiage anzan
Flash anzan is a separate exam
In flash anzan, numbers appear on a screen one at a time and the candidate gives the total; it is not part of either federation's written anzan kentei. Zenshuren's flash anzan exam runs from 20 kyu to 1 kyu and from shodan to 10th dan: 15 problems at 10 points each, with 100 or more to pass. In its joint 30-problem dan sitting, shodan starts at 100, each dan adds 20, and 10th dan needs 280 or more. Zenshuren publishes no digit counts or speeds. Flash Anzan is a trademark of its owner.
Published flash anzan speeds
The Japan Flash Anzan Kentei Association (Nihon Flash Anzan Kentei Kyokai) runs an online flash anzan kentei from 20 kyu to 20th dan, with MEXT backing since 1 February 2023, and publishes its speeds: 1 kyu is fifteen 2-digit numbers in 13 seconds, shodan the same in 10 seconds, 10th dan fifteen 3-digit numbers in 3 seconds and 20th dan in 1.5 seconds, with 7 of 10 correct to pass. Nishuren's flash exam has run with that association since 1 April 2026. The Guinness World Records time for fifteen 3-digit numbers is a record, not a grade standard: as of September 2026 it stands at 1.61 seconds, set on 18 February 2024, after earlier records of 1.64 seconds (2019) and 1.62 seconds (2023).
Yomiage anzan is not graded in the kentei
In yomiage anzan a caller reads numbers aloud. Neither federation's anzan kentei grades it; it is an event at national championships such as Zenshuren's Zen-Nihon Shuzan Senshuken Taikai and Nishuren's Soroban Grand Prix Japan. A separate body, the Zenkoku Shuzan Renmei (not to be confused with Zenshuren), runs a yomiage anzan dan exam from shodan to 10th dan: 10 problems of 10 numbers, from 3-digit numbers read in 20 seconds up to mixed 5- to 10-digit numbers in 38 seconds.
Nishuren's FAQ says a candidate may start at any level. From the first paper up, the ladder runs 10–7 kyu, 6, 5 and 4 kyu, pre-3 and 3 kyu, pre-2 and 2 kyu, pre-1 and 1 kyu, then dan.
To find a starting point, work the sample paper on the level page that looks about right, then run its mock exam on the official clock. On a kyu paper, a score of 400 or more suggests trying the next level; a score well short of it suggests the level below.
For a beginner, the 10–7 kyu paper is a natural first sitting, since one paper can place a candidate anywhere from 10 to 7 kyu. Multiplication and division join at 6 kyu.
Kani Math is a daily practice app for mental arithmetic and the soroban, not a kentei course or exam-preparation material.
Common questions
What is the difference between the anzan kentei and the soroban kentei?
The anzan kentei is mental calculation; the soroban kentei is worked on the abacus. Nishuren runs them as separate exams, and the two dan exams have been sat separately since June 2010.
Does a child have to start at 10 kyu?
No. Nishuren's FAQ says a candidate may start at any level. The 10–7 kyu paper suits a first sitting because its score covers four grades, but a child who can already work a higher level's sample paper, including its multiplication and division from 6 kyu up, can start there.
How long is the exam, and how much time is there per question?
At Nishuren, 12 minutes for the whole kyu paper, in any order: about 9 seconds a question from 6 kyu and about 14 on the 10–7 kyu paper. Its dan sections have their own clocks: 3 minutes for 60 kake questions, 3 for 60 wari and 4 for 30 mitori. Zenshuren gives 3 minutes per section at every level.
What score passes?
At Nishuren, 400 of 500 from 6 kyu to 1 kyu, pre-grades included. On the 10–7 kyu paper the score sets the grade, from 250 for 10 kyu to 400 for 7 kyu. Each dan section needs the rank's score, from 90 for pre-shodan to 290 for 10th dan, and the weakest section sets the overall rank. Zenshuren scores each kyu section out of 100 and passes 70 or more in every section.
Where can I find past papers?
Nishuren publishes official sample papers, linked under Sources. The papers and mock exams on these pages are written to the published specification and are not official or past papers.
Is Kani Math connected to the exam bodies?
No. Kani Math is not affiliated with any exam body, and a mock result is not a grade. The mock exam builds a fresh paper to the official specification, runs the official clock or none, allows any order, and scores and grades it the way the paper is scored, applying the lowest-section rule for dan.
Kani Math is not affiliated with, endorsed by or licensed by the League of Japan Abacus Associations (Nishuren), the League for Soroban Education of Japan (Zenshuren), the Japan Chamber of Commerce and Industry or any other exam body. The sample papers and mock exam on these pages are written to the published specification; they are not official papers, and a mock result is not a certification. Flash Anzan is a trademark of its owner. Exam details can change, so confirm them with whoever runs your sitting.