Percentile Calculator (Z-score)
A percentile shows how a value compares to the rest of a dataset — for example a test score, height, or any other trait that is approximately normally distributed. Enter your own value along with the mean and standard deviation of the reference group, and this calculator instantly works out your z-score and matching percentile.
結果
76.2
Percentile
- Z-score
- 0.714
How this was calculated
- 1Calculate the z-score: (value − mean) ÷ standard deviation(180 − 175) ÷ 7 = 0.714
- 2Convert the z-score to a percentile
公式
Z = (value − mean) ÷ standard deviation, then percentile via the normal distribution
The z-score expresses how many standard deviations a value lies from the mean. A z-score of 0 is exactly average (50th percentile), +1 is well above average (roughly the 84th percentile), and −1 well below (roughly the 16th percentile). This calculator converts the z-score to a percentile using the cumulative normal distribution (the Abramowitz-Stegun approximation).
ステップ解説
- 1Enter your own value, such as a test score or height.
- 2Enter the mean and standard deviation of the reference group.
- 3Read off the z-score and the matching percentile.
計算例
Value 180, mean 175, standard deviation 7
→ Z ≈ 0.71 → roughly the 76th percentile.
Value exactly equal to the mean
→ Z = 0 → exactly the 50th percentile.
Value two standard deviations above the mean
→ Z = 2 → roughly the 97.7th percentile.
Reference table
| Z-score | Percentile | Meaning |
|---|---|---|
| −2 | 2.3rd | Well below average |
| −1 | 15.9th | Below average |
| 0 | 50th | Exactly average |
| +1 | 84.1st | Above average |
| +2 | 97.7th | Well above average |
Rules of thumb for a normal distribution; use the calculator above for your own value.
よくある間違い
- Using a mean and standard deviation that don't match the right reference group (for example applying a national average to a very specific subgroup).
- Thinking a percentile is the same as a percentage of the maximum, when it actually indicates what percentage of the group you outperform.
- Treating the result as absolute truth when the assumption of a normal distribution doesn't always hold.
Important to know
- This calculator has no built-in population statistics. Look up a reliable mean and standard deviation from an official source, such as your national statistics office.
Limitations
- This calculation assumes a normal distribution. Not every trait is normally distributed, which affects how accurate the percentile is.
活用シーン
- Comparing a test score against the rest of the class or country.
- Interpreting growth charts or medical measurements relative to a reference group.
- Putting job application or assessment results in perspective relative to other candidates.
よくある質問
Where do I find the mean and standard deviation of a group?
National statistics offices publish this for things like height, income and weight. For test scores, the school or exam body often provides class or national norms.
What does a negative z-score mean?
A negative z-score means your value is below the mean. The more negative it is, the lower your percentile; a z-score of −2, for example, corresponds to roughly the 2.3rd percentile.
Can the percentile be higher than 100 or lower than 0?
No, a percentile by definition always lies between 0 and 100. This calculator explicitly caps the result to that range, even for extreme z-scores.
What is the difference between a percentile and a quartile?
Quartiles divide a dataset into four equal parts (25%, 50%, 75%), while percentiles divide the same dataset into a hundred equal parts. Each quartile therefore corresponds to a specific percentile.
Was this calculator helpful?