Z-Score Calculator
Calculate the z-score (standard score) showing how many standard deviations a value is from the mean. Find percentile rank and probability. Free.
Z-Score Calculator
toolznova.com • Free Calculator
How to Use
Calculate z-score in 3 steps.
Enter Value
Enter the data point value you want to evaluate.
Enter Mean & SD
Enter the population mean and standard deviation.
Get Z-Score
Click Calculate for z-score, percentile, and interpretation.
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Why Calculate Z-Score?
- Standardization: Compare values from different scales or distributions.
- Outlier Detection: Z-scores beyond ±3 are typically considered outliers.
- Normal Distribution: Find what percentage of data falls below a value.
- Exam Scoring: Convert raw scores to standardized scores for comparison.
- Finance: Compare investment performance across different asset classes.
- Quality Control: Identify products outside normal variation range.
Tips & Examples
- Z-score of 0 means the value equals the mean.
- Z = (x − μ) / σ — how many SDs the value is from the mean.
- |z| < 1: within 1 SD (68% of normal distribution data).
- |z| < 2: within 2 SDs (95% of normal distribution data).
- |z| > 3: outlier — only 0.3% of normal data falls here.
- Negative z-score means value is below the mean.
Free Z-Score Calculator Online
ToolzNova's free z-score calculator computes the standardized z-score, approximate percentile rank, and interpretation for any value given the mean and standard deviation.
Z-score (standard score) measures how many standard deviations a data point is from the mean. It's fundamental for comparing across different distributions and for finding percentile ranks in a normal distribution.
Z-Score Formula
Z = (x − μ) / σ. Where x is the value, μ is the mean, and σ is the standard deviation. A z-score of +2 means the value is 2 standard deviations above the mean, placing it at approximately the 97.7th percentile.