Mathematics ToolsStatistics

Z-Score & Normal Distribution Calculator

Compute standard scores (Z-scores) instantly for statistical analysis. Determine how many standard deviations a data point lies from the population or sample mean.

Calculated locally in browser.
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How to Use Z-Score & Normal Distribution Calculator

1

Enter Raw Score (X)

Type the individual observation or test score.

2

Enter Mean (μ) & Std Dev (σ)

Input the population or sample mean and standard deviation.

3

View Z-Score & Probability

Inspect the calculated Z-score, percentile, and normal curve placement.

About Z-Score & Normal Distribution Calculator

Calculates Z = (X - μ) / σ and estimates cumulative normal distribution probability via the error function erf(z / sqrt(2)).

Supported Formats

Numerical Values

Operational Limits

  • Assumes normal or near-normal distribution of the underlying dataset.

Key Features

  • Calculates Z = (X - μ) / σ
  • Computes cumulative probability P(Z < z) and two-tailed P
  • Displays percentile ranking (0% to 100%)
  • Visual standard normal distribution bell curve diagram
  • Clear step-by-step formula breakdown

Frequently Asked Questions

A negative Z-score indicates that the data point is below the mean, while a positive Z-score indicates it is above the mean.
Z-Score Calculator – Standard Score & Probability P(Z) | Toolxilla | Toolxilla