Hensachi (Deviation Score) Calculator
＋More features: rank from hensachi, hensachi from rank
Both are approximations that treat the score distribution as close to a normal distribution.
What top % and rank does a hensachi correspond to?
Reverse-calculate hensachi from a rank
From a result such as “300th out of 1,200”, this estimates the hensachi (the number of examinees uses the field above).
Hensachi (偏差値) is Japan's standardized test score — results rescaled so that the mean is 50 and the standard deviation is 10 — used throughout Japanese school and entrance-exam rankings. Enter your score, the average score and the standard deviation to see your hensachi instantly. If you do not know the standard deviation, paste the whole class's scores and the tool calculates the average, the standard deviation and everyone's hensachi in one go. Useful for checking mock-exam results or processing grades.
How to use
- If your mock-exam score report shows the “average score” and the “standard deviation”, enter them in ①.
- If you know everyone's scores, such as for a class quiz, list the scores in ② to calculate everyone's hensachi at once.
How it is calculated
- Hensachi = 50 + 10 × (score − average) ÷ standard deviation
- The list calculation uses average = sum ÷ count, and the population standard deviation (the square root of the mean of the squared differences from the average).
- Example: scoring 80 on a test with average 60 and standard deviation 15 → 50 + 10 × (80 − 60) ÷ 15 = hensachi 63.3
Sources and assumptions
- Calculated by the standard statistical definition (hensachi = a score standardized to mean 50 and standard deviation 10).
Assumptions and notes
- The list calculation treats the entered scores as the whole population (population standard deviation). The result differs slightly from the sample standard deviation (dividing by n − 1).
- Hensachi for small groups (a single class, for example) fluctuates a lot — treat it only as a rough guide.
Frequently asked questions
How high (or low) can hensachi go?
There is no theoretical upper or lower limit. With an extremely high (or low) score within a group, hensachi above 80 or below 20 can occur (this happens on tests where many people score full marks, for example).
The standard deviation is not on my score report.
Hensachi cannot be calculated from the average score alone. If you know everyone's scores, use the list calculation in ②; for a mock exam, check the organizer's score statistics.
Is the hensachi of a 5-subject total the average of each subject's hensachi?
No. The hensachi of the total is calculated from the distribution of total scores, and in general it does not equal the average of the per-subject hensachi (though it is often close).