Z-Score Calculator

A z-score tells you how many standard deviations a value is from the mean: z = (x − μ) / σ. A z-score of 1.5 means the value sits 1.5 standard deviations above the mean.

The percentile is the area under the standard normal curve to the left of z, times 100. This calculator computes it for you: a z-score of 1.5 is about the 93rd percentile.

The z critical value is the z-score that marks off a chosen area in the tails of the normal curve. For a 95% confidence level it is 1.96, and for 99% it is 2.576.

Use z when the population standard deviation is known or the sample is large (n ≥ 30). Otherwise the t-distribution accounts for the extra uncertainty of estimating the standard deviation from the sample.

Yes. A negative z-score simply means the value is below the mean — for example, z = −1 means one standard deviation below the mean, about the 16th percentile.