Z-Score Calculator
Calculate standard score and percentile rank from mean and standard deviation
Values
Data Value (x)
x
Population Mean (μ)
μ
Standard Deviation (σ)
σ
Formula
z = (x − μ) / σ
z > 0 → above average
z < 0 → below average
z = 0 → exactly average
Z-Score
—
—
% Below this value—
% Above this value—
95% Confidence Interval—
What Is a Z-Score?
A z-score (standard score) tells you how many standard deviations a value is from the mean. A z-score of +2.0 means the value is 2 standard deviations above the mean; −1.5 means 1.5 SDs below the mean.
Z-scores are used to compare values from different distributions, find percentile ranks in a normal distribution, identify outliers (|z| > 3 is unusual), and calculate confidence intervals in hypothesis testing.
lightbulb The 68-95-99.7 Rule
1z = ±1: 68.3% of data falls within
2z = ±2: 95.4% of data falls within
3z = ±3: 99.7% of data falls within
✓ Values with |z| > 3 are statistical outliers