Z-Score Calculator
Convert a raw value into a z-score to see how far it sits from the mean in standard deviations.
Number of standard deviations the value lies from the mean.
15
1.5
Above the mean
Formula
About this calculator
A z-score, or standard score, tells you how many standard deviations a particular value lies above or below the mean of its distribution. A positive z-score means the value is above the mean; a negative one means it is below. A z-score of 0 indicates the value equals the mean exactly.
Standardizing data this way lets you compare values measured on different scales — for example, a test score and a height — by expressing each in common units of standard deviation. Z-scores are central to the normal distribution: about 68% of values fall within z = ±1, 95% within ±2, and 99.7% within ±3. The standard deviation must be greater than zero, otherwise the z-score is undefined.
Frequently asked questions
It tells you how far a value is from the mean, measured in standard deviations. A z-score of 2 means the value is two standard deviations above average.
Yes. A negative z-score simply means the value is below the mean. The sign indicates direction, and the magnitude indicates distance.
Values with z-scores beyond ±2 are often considered unusual, and beyond ±3 are rare, since roughly 99.7% of a normal distribution falls within three standard deviations of the mean.
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