Calculate z-score (standard score) to find how many standard deviations a value is from the mean
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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.
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
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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.
Use the normal distribution's cumulative function. Our calculator does this automatically. Common values: z=0 → 50th percentile, z=1 → 84th, z=2 → 98th, z=-1 → 16th, z=-2 → 2nd.
Yes, but it's rare in normal distributions—only 0.3% of values have z > 3 or z < -3. Values beyond this range are often considered outliers. In some fields, z-scores can be much higher (like finance).
A negative z-score simply means the value is below the mean; a positive one means it's above. The sign shows direction and the magnitude shows how many standard deviations away it is — so z = -1.5 is 1.5 standard deviations below average.