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Statistical Precision Suite

Z-SCORE CALCULATOR

Standardize your data and explore the normal distribution. Compute z-scores from raw values and determine precise probabilities with our professional statistical toolset.

Raw Score to Z-Score

Standardize a specific data point relative to its population.

Enter parameters to see standardization

Z-Score & Probability Converter

Bidirectional conversion between z-scores and cumulative probabilities.

Fill any field to see statistical relationship

Probability Between Z-Scores

Find the area under the curve between any two z-points.

Enter bounds to visualize distribution area

What is a Z-Score?

A z-score, or standard score, is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean.

The Core Formula

z = (x - μ) / σ

Standard Score Calculation

  • x: The raw score (data point)
  • μ: The population mean
  • σ: The population standard deviation

Why Use Z-Scores?

Z-scores allow statisticians to compare scores from different distributions. For example, you can compare a score on an SAT test to a score on an ACT test by standardizing both to their respective normal distributions.

A z-score of 0 indicates the score is exactly the mean, while a z-score of 1.0 indicates the score is one standard deviation above the mean.

The 68-95-99.7 Rule

68.27%
Within ±1σ
95.45%
Within ±2σ
99.73%
Within ±3σ
In a standard normal distribution, nearly all data falls within 3 standard deviations of the mean. This is often referred to as the Empirical Rule.