Z-Score Calculator

Calculate Z-ScoreFind Value from Z-Score

Value (x)

Mean (μ or x̄)

Standard Deviation (σ or s)

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What is a Z-Score?

A z-score (also called a standard score) tells you how many standard deviations a value is from the mean. It allows you to compare values from different distributions on a standardized scale.

Z-Score Formula

z = (x - μ) / σ

Where:

• z = z-score
• x = the value being standardized
• μ = the mean of the distribution
• σ = the standard deviation

To find the original value from a z-score:

x = (z × σ) + μ

Interpreting Z-Scores

Z-Score	Meaning
z = 0	Value equals the mean
z > 0	Value is above the mean
z < 0	Value is below the mean
z = 1	Value is 1 SD above mean
z = -2	Value is 2 SD below mean

Common Z-Score Benchmarks

• z = ±1.96 → 95% confidence interval bounds
• z = ±2.58 → 99% confidence interval bounds
• z = ±3 → Typical outlier threshold

Applications of Z-Scores

1. Comparing scores from different tests
2. Identifying outliers in datasets
3. Calculating percentiles in normal distributions
4. Quality control in manufacturing
5. Standardizing data for statistical analysis

Related Tools

• Standard Deviation Calculator - Calculate σ for your data
• T-Test Calculator - Compare means statistically
• Probability Calculator - Calculate probabilities