Z-Score Calculator
Calculate z-score (standard score) to find how many standard deviations a value is from the mean
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Calculate Z-Score and Percentile
Z-score tells you exactly where a value falls in a normal distribution. Our calculator converts raw values to z-scores, finds percentiles, and calculates probabilities. Essential for standardized testing, statistics, and data analysis.
What is a Z-Score?
A z-score (or standard score) measures how many standard deviations a data point is from the mean. A z-score of 0 means the value equals the mean. Positive z-scores are above the mean, negative below. In a normal distribution, about 68% of values have z-scores between -1 and +1, and 95% between -2 and +2.
Z-Score Formula
z = (x - μ) / σHow to Use This Calculator
Z-Score Applications
Test Scores
Compare performance across different tests and scales.
Quality Control
Identify measurements that are out of specification.
Research
Standardize variables for statistical analysis.
Finance
Measure how unusual market returns are.
Frequently Asked Questions
A z-score of 1.96 means the value is 1.96 standard deviations above the mean. In a normal distribution, about 97.5% of values fall below this point, making it the 97.5th percentile. This is why ±1.96 defines the 95% confidence interval.