Z Score Calculator
Enter a value, mean, and standard deviation to instantly calculate the z-score and see where that value falls on the normal distribution.
Use the Z Score Calculator
Enter Values
The data point you want to evaluate.
The average of the population or sample.
Must be greater than zero.
Formula
x = observed value • μ = mean • σ = standard deviation
Fill in the fields on the left and click Calculate to see your z-score.
Z-Score
0.00
Percentile
—
of values fall below x
Deviation
—
from the mean
Interpretation
Step-by-Step Calculation
Summary
A z-score (standard score) measures how many standard deviations a data point is from the population mean. This calculator takes your value, mean, and standard deviation, computes the z-score using the formula z = (x - μ) / σ, and interprets the result in plain English. It also shows the corresponding percentile so you know what percentage of the population falls below that value.
How it works
- Enter the observed value (x) you want to evaluate.
- Enter the population mean (μ) for your data set.
- Enter the standard deviation (σ), which must be greater than zero.
- The calculator applies the formula z = (x - μ) / σ.
- The result shows the z-score, its interpretation, and the approximate percentile.
Use cases
- Determine how unusual a test score is compared to the class average.
- Compare measurements from different data sets with different units.
- Identify outliers in a data set (z-scores beyond ±2 or ±3).
- Convert raw scores to standardized scores for statistical analysis.
- Evaluate performance metrics against historical averages.
- Assess financial returns relative to market benchmarks.