Z-Score Calculator
Calculate a z-score from a value, mean, and standard deviation — or find a value given a z-score. Returns left-tail, right-tail, and two-tailed probabilities.
| Curriculum / Country | Topic Name | Critical Value (5%) | Z-Table Format |
|---|---|---|---|
| 🇺🇸 AP Statistics (US) | Standard Normal Distribution | z* = 1.96 (two-tailed) | Cumulative left-tail |
| 🇬🇧 A-Level Maths (UK) | Normal Distribution / Hypothesis Testing | z = 1.6449 (one-tailed) | Φ(z) table — left-tail |
| 🌐 IB Math AA/AI | Normal Distribution — HL/SL | Varies by question | GDC (calculator) method |
| 🇩🇪 Germany (Abitur) | Normalverteilung | z₀.₀₅ = 1.645 | Φ table — right-tail convention |
| 🇯🇵 Japan (hensachi) | 偏差値 = 50 + 10z | N/A — rank-based | Transformed z for university ranking |
Frequently Asked Questions
What is Japanese hensachi (偏差値) and how does it relate to z-scores?
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.
How do UK and US z-tables differ?
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.