Z-Score Calculator

Subtract the mean from your value and divide by the standard deviation: z = (x − μ) / σ. The z-score tells you how many standard deviations the value is above (positive) or below (negative) the mean.

It standardizes a value so you can compare it across different distributions. A z-score of 0 is exactly average, +1 is one standard deviation above the mean, and −2 is two standard deviations below. Most values in a normal distribution fall between −3 and +3.

Find the area to the left of the z-score under the standard normal curve — that area, times 100, is the percentile. For example, z = 0 is the 50th percentile, and z = 1.0 is about the 84th percentile.

There is no universally good or bad z-score; it depends on context. In quality control, a z-score beyond ±3 often flags an outlier. On a test, a higher positive z-score means you scored further above average.

Yes. A negative z-score simply means the value is below the mean. The sign indicates direction and the magnitude indicates distance in standard deviations.