Z-Score Calculator

Calculate z-score, percentile, and probability from any raw score in a normal distribution.

Z-Score

1

Percentile (below)

84.13%

Above percentile

15.87%

z = (75 − 65) / 10 = 1

Z-Score Calculator Formula & How It Works

z = (X − μ) / σ | Percentile ≈ Φ(z) × 100%
  • X = observed value
  • μ = population mean
  • σ = population standard deviation
  • Φ(z) = cumulative distribution function of standard normal

A z-score measures how many standard deviations a value is from the mean. z=0 is the mean; z=+1 is one SD above; z=−1 is one SD below. Z-scores allow comparison across different scales — converting test scores with different means and SDs to a common scale. The standard normal table (Φ) converts z to percentile.

Z-Score Calculator FAQs

What is a z-score?

A z-score indicates how many standard deviations a data point is above or below the mean. z = (X − μ) / σ. A score of 75 on a test where μ=65 and σ=10 has z = (75−65)/10 = 1.0 — one standard deviation above the mean (84th percentile).

How do I interpret a z-score?

z=0: at the mean. z=+1: 84th percentile. z=+2: 97.7th percentile. z=+3: 99.9th percentile. Negative z-scores are below the mean. Most 'normal' values fall between z=−2 and z=+2 (95% of the distribution).

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