---
title: "Z-Score Calculator — Standard Normal Distribution, Probability & Percentile"
description: "Calculate z-scores from a value, mean, and standard deviation. Find left-tail, right-tail, and two-tailed probabilities. Covers AP Statistics (US), A-Level (UK), IB Math, Japanese hensachi."
url: "https://worldcalculators.org/calculators/z-score/"
canonical: "https://worldcalculators.org/calculators/z-score/"
---

# Z-Score Calculator

Calculate z-scores from a value, mean, and standard deviation. Find left-tail, right-tail, and two-tailed probabilities. Covers AP Statistics (US), A-Level (UK), IB Math, Japanese hensachi.

## Quick answer

Hensachi is Japan's standardized score used for university entrance ranking: hensachi = 50 + 10z. A hensachi of 60 = z-score of +1 (top 16%). A score of 70 = z-score of +2 (top 2.3%). It's calculated from mock exam results, not actual university entrance scores. Most elite Japanese universities require hensachi above 65–70. This system is unique to Japan — the UK uses UCAS points, the US uses SAT/ACT percentiles, and Australia uses ATAR scores.

## Frequently Asked Questions

Hensachi is Japan's standardized score used for university entrance ranking: hensachi = 50 + 10z. A hensachi of 60 = z-score of +1 (top 16%). A score of 70 = z-score of +2 (top 2.3%). It's calculated from mock exam results, not actual university entrance scores. Most elite Japanese universities require hensachi above 65–70. This system is unique to Japan — the UK uses UCAS points, the US uses SAT/ACT percentiles, and Australia uses ATAR scores.
Both use the standard normal distribution, but the table format differs. US AP Statistics tables show cumulative probability from −∞ to z (left-tail: P(Z ≤ z)). UK A-Level tables use Φ(z) which also gives left-tail probability. Some UK resources use the right-tail complement. German Abitur tables may give right-tail probability 1 − Φ(z). Always check which convention your table uses before reading a probability.

Source: https://worldcalculators.org/calculators/z-score/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.