Formula
The z-score divides the distance from the mean by the standard deviation:
Z = (value − mean) / standard deviation
A confidence interval uses a z multiplier. This page finds the z of one value.
Assumptions
- The standard deviation is greater than zero.
- The mean and the value use the same unit.
Worked example
A value of 130, with mean 100 and standard deviation 15, has a z-score of 2.
Input definitions
- Value
- The observation being located.
- Standard deviation
- The spread of the distribution. It must be greater than zero.
Limitations
Results are rounded for display. This is a classroom calculation, not a measurement from a lab or a financial filing.
Questions
What does a negative z-score mean?
The value is below the mean.
Is this a percentile?
No. It is the number of standard deviations, not a percent of the population.