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Mathematics

Z-Score Calculator

📊Z-score Calculator

What is Z-Score Calculator?

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A z-score (standard score) expresses a value's distance from the population mean in standard deviation units. z = (x − μ) / σ. Positive z = above average; negative z = below average.

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How to Z-Score Calculator

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  1. 1z = (x − μ) / σ
  2. 2Percentile from z-score: use standard normal CDF
  3. 3z=1.96 → 97.5th percentile
  4. 4Enables comparison across different measurement scales

Worked Examples

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Example 1
Given:Score 85 · Mean 70 · SD 15
Result:z = 1.0 → 84th percentile

(85-70)/15=1.0; P(Z<1)=84.1%

Common z-score percentiles

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z-scorePercentile
-2.02.3%
-1.015.9%
050%
1.084.1%
1.9697.5%
2.5899.5%
3.099.9%
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Reviewed October 2026
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