Z-Score Calculator

Calculate z = (x − μ) / σ

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About Z-Score Calculator

A z-score calculator that converts raw values to standard scores: z = (x − μ) / σ. Shows percentile rank, probability from z-table, and how many standard deviations a value is from the mean. Includes reverse lookup (z to raw value). All calculations are client-side. Essential for statistics, quality control, and data analysis.

Z-Score Calculator Features

  • Z-score
  • Percentile
  • Probability
  • Reverse lookup
  • Distribution
A z-score measures how many standard deviations a data point is from the mean: z = (x − μ) / σ. A z of 0 = at the mean, z of 1 = one SD above, z of −2 = two SDs below. The 68-95-99.7 rule: 68% of data falls within ±1σ, 95% within ±2σ, 99.7% within ±3σ.

How to Use

Enter value and distribution:

  • Value (x): The data point
  • Mean (μ): Population mean
  • Std Dev (σ): Standard deviation

Interpretation

  • |z| < 1: Within normal range
  • |z| = 1.96: 95th percentile boundary
  • |z| = 2.58: 99th percentile boundary
  • |z| > 3: Outlier territory

Applications

  • Quality control: Six Sigma (z = 6)
  • Grading: curve scores
  • Finance: stock volatility
  • Medicine: growth charts

Step-by-Step Instructions

  1. 1Enter the raw value.
  2. 2Enter the mean.
  3. 3Enter the standard deviation.
  4. 4View the z-score.
  5. 5Check the percentile rank.

Z-Score Calculator — Frequently Asked Questions

What does a z-score of 1.96 mean?+

97.5% of values in a normal distribution fall below z = 1.96. This is why ±1.96 defines the 95% confidence interval (2.5% in each tail).

Can z-scores be negative?+

Yes! Negative z means the value is below the mean. z = −1 means one standard deviation below average.

What's the difference between z-score and percentile?+

Z-score measures distance from mean in SDs. Percentile tells what percentage of values fall below. z = 0 corresponds to 50th percentile, z = 1 to ~84th percentile.

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