Instantly find how far any value sits from the mean
Inputs
z = (x − μ) / σ
Result
Your value is at the 84.1th percentile
Between 1σ and 1.645σ — moderately typical
Common critical values
Click a critical value to set the input value so that z equals it exactly.
What is a Z-Score?
A z-score (standard score) measures how many standard deviations a data point lies above or below the population mean. Use this free z-score calculator to instantly compute z = (x − μ) / σ, see the cumulative percentile, and get a plain-English interpretation of where your value sits in any normal distribution — no formulas to memorise.
A z-score of 1.96 means the value is 1.96 standard deviations above the mean. In a normal distribution, 95% of all values fall within ±1.96σ of the mean, so z = 1.96 sits at the 97.5th percentile — the upper boundary of the common 95% confidence interval.
Yes. A negative z-score simply means the value is below the mean. For example, z = −1 means the value is one standard deviation below the mean, and about 15.9% of data in a normal distribution fall at or below that point.
Population standard deviation (σ) divides by N and is used when you have data for the entire group. Sample standard deviation (s) divides by N−1 and corrects for estimation bias. For z-score calculations, use whichever matches how your standard deviation was computed.
In most statistical contexts, a value with |z| > 2 is considered unusual (outside the middle 95% of a normal distribution), and |z| > 3 is treated as an extreme outlier, as only about 0.3% of data falls beyond three standard deviations from the mean.