Z-Score Calculator
Standardize an observed value or convert a known z-score back to the measurement scale. Normal probability areas show the left-tail percentile, right tail and symmetric two-sided tail without implying that your actual data follow a normal distribution.
Your result
How the calculation works
z=(value−mean)/population SD. Value=mean+z×SD. Left area=Φ(z); right area=1−Φ(z); two-sided tail=2×min(left,right).
Worked example
A value of 85 with mean 70 and SD 10 has z=1.5. Under a standard normal model, the left area is approximately 0.93319, or the 93.319th percentile.
Assumptions and limitations
Population SD must be positive. Probabilities use a normal model and floating-point CDF; extreme tails can underflow. These are model-based areas, not empirical percentile ranks.
Check distribution assumptions before interpreting percentiles. A high z-score does not establish causation, importance or a diagnosis. Use sample-specific methods when population parameters are estimated.
Sources and editorial responsibility
Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.
Method reviewed 2026-10-13. Calculation standards · Report an issue