Hensachi is the score Japanese schools and cram schools use to rank students — a "hensachi 65 university," a kid with "hensachi 70 in math." Outside Japan it's an unfamiliar number, and even inside Japan few people can say exactly what it measures.
Here's the short version: hensachi is just a z-score, rescaled so the numbers land around 50 instead of 0. That makes it a clean way to see what standardization actually does to a score.
Start by dragging this graph.
// Hands-on Simulator
Drag the sliders freely, or pick a preset from the table on the right. Everything stays in sync.
| Hensachi | Top % | Rarity |
|---|---|---|
| 75 | 0.62% | 1-2 per grade |
| 70 | 2.28% | #1 in class of 40 |
| 65 | 6.68% | Top 2-3 in class |
| 60 | 15.87% | Top 1/6 |
| 55 | 30.85% | Slightly above avg |
| 50 | 50.00% | Dead average |
| 45 | 69.15% | Slightly below avg |
| 40 | 84.13% | Bottom ~16% |
// What Hensachi Really Is
The hensachi you just dragged around — its formula is this short:
That fraction in the middle is the z-score: how many standard deviations the score sits above or below the mean. Hensachi just stretches and shifts it — multiply by 10, add 50 — so the average lands on 50 and one standard deviation is worth 10 points.
So hensachi is "a position on any test, read off the same ruler" — exactly what standardizing a score gives you (drag the underlying z-score here).
// 3-Question Quiz — Check Your Understanding
Q1. Does a hensachi of 80 mean a raw score of 80 on the test?
Q2. Does a hensachi of 50 mean the average score?
Q3. A hensachi of 60 on two different exams — same ability level?
// The Pitfall: When Hensachi Misleads
Hensachi is computed as if scores follow a normal distribution.
Real exam results rarely form a clean bell curve, though.
Drag the skewness slider to the right and watch the "top %" drift away from what the same hensachi claims.
// KEY TAKEAWAY
- Hensachi is Japan's school-ranking score — not a mark, but a position within a group
- It's a z-score rescaled: mean → 50, one standard deviation → 10 points
- Hensachi 60 → top 16%. Hensachi 70 → top 2%. 10 points ≈ 5× the rarity
- When the real distribution is skewed, the "top %" hensachi implies can be off
// Frequently Asked Questions
Hensachi is the standard score Japanese schools and mock-exam companies use to express how a mark compares to the group. In statistical terms it's a z-score, rescaled: Hensachi = 50 + 10 × (Your Score − Mean) ÷ Std Dev. The average becomes 50; one standard deviation above the mean becomes 60.
Hensachi = 50 + 10 × (Your Score − Mean) ÷ Std Dev
First compute the mean and standard deviation from all scores, then plug a score in. At the mean you get 50; one standard deviation above the mean gives 60.
A hensachi of 50 means a score exactly at the group average. Whatever the raw mark, matching the mean gives a hensachi of 50.
A hensachi of 60 is roughly the top 15.87% (about 1 in 6). At 65 it's top 6.68%, at 70 it's top 2.28%. Each 10-point step makes the score markedly rarer.
No. Hensachi is a relative position computed as if scores were normal; rank is an absolute ordering taken straight from the data. When scores aren't normally distributed, the rank hensachi implies can differ noticeably from the real rank. The "Pitfall" section above shows this in action.
Mathematically, yes. A hensachi of 100 means "5 standard deviations above the mean" — extremely rare, but it can happen with small samples or outliers.
Generally, no. Hensachi measures position within the specific group that sat that exam. If the exam populations differ, a hensachi of 60 on one may represent a completely different ability level than 60 on another.
It works as a rough guide, but it's statistically loose. A hensachi of 60 in math and 55 in English come from different score distributions — each with its own standard deviation and shape. Strictly speaking they aren't on the same scale, so adding and dividing isn't really valid.
The practice is common in Japanese mock exams because the same students sit every subject, so the scales line up roughly. Just treat a "five-subject average hensachi" as a convenient shorthand for overall standing, not a rigorous composite statistic.
Underneath every hensachi is a normal curve.
Want to go deeper on the bell curve and the z-score it's built on?
StatPlay's interactive materials let you work through statistics by dragging.