Z-Score Calculator
Calculate the z-score (standard score) for any value in a normal distribution. Find the percentile ranking and probability associated with your data point.
Inputs
Results
Z-Score
-1
Percentile Rank15.87%
Cumulative Probability0.1587
Probability Above84.13%
InterpretationValue is 1.00 standard deviations below the mean
How to Use This Calculator
- Enter the individual data value (X), the population mean (μ), and the population standard deviation (σ).
- The z-score is computed as z = (X − μ) / σ, measuring how many standard deviations X is from the mean.
- A z-score of 0 means X equals the mean; ±1 covers ~68% of data; ±2 covers ~95%; ±3 covers ~99.7%.
- Percentile Rank shows the percentage of values in a standard normal distribution that fall below X.
- The probability output (area under the curve) is useful for hypothesis testing and quality control (Six Sigma).
- σ must be greater than 0; negative z-scores simply indicate values below the mean.
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Formula
z = (x - μ) / σRelated Calculators
Standard Deviation Calculator
Calculate the mean, median, standard deviation, and variance for a set of numbers. Supports both population and sample calculations.
Confidence Interval Calculator
Calculate the confidence interval for a population mean. Determine the margin of error and range where the true population parameter likely falls.
Probability Calculator
Calculate probability of single events, combined events (AND/OR), permutations, and combinations.
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