Z-score Calculator
Enter a raw value, mean, and standard deviation to compute the standardized z-score and percentile for normal distributions.
Z-score: 1.8000
Percentile: 96.41%
How to Use This Calculator
- Enter the raw score you wish to standardize.
- Provide the distribution mean and standard deviation.
- Review the computed z-score to understand relative position.
- Use the percentile to gauge how the score compares to the population.
Formula
z = (x − μ) / σ
Percentile = Φ(z), where Φ is the standard normal CDF
Full Description
Z-scores standardize observations by subtracting the mean and dividing by the standard deviation, allowing comparisons across different scales. They indicate how many standard deviations a value lies from the mean.
Percentiles translate z-scores into cumulative probabilities, showing the proportion of the distribution below the raw score.
Frequently Asked Questions
Can z-scores be negative?
Yes. Negative z-scores indicate values below the mean.
What if σ = 0?
Z-scores are undefined when the standard deviation is zero because there is no variability.
Do z-scores assume normality?
They are most meaningful under approximate normality, though standardization itself is a simple transformation.
How do I convert percentiles back to raw scores?
Find the z-score corresponding to the percentile, then compute x = μ + zσ.