Z-Score Calculator
Calculate the z-score (standard score) of a value given the mean and standard deviation.
The standard deviation must be greater than zero.
Z-Score
Calculation Steps
What a Z-Score Measures
A z-score, or standard score, tells you how many standard deviations a raw value lies above or below the mean of its distribution. A positive z-score means the value is above the mean, a negative z-score means it is below the mean, and a z-score of zero means it is exactly equal to the mean.
The Z-Score Formula
The z-score is found by subtracting the mean from the value and dividing by the standard deviation.
- Formula: z = (x − μ) / σ
- x: the raw value
- μ: the mean of the distribution
- σ: the standard deviation
Why Z-Scores Are Useful
Because z-scores express every value on the same standardized scale, they let you compare observations from different distributions and look up probabilities from the standard normal distribution. The standard deviation must be greater than zero, otherwise the z-score is undefined.