How it works
Compute the z-score of a value relative to a normal distribution and its percentile.
Enter a raw value, the mean, and the standard deviation. The calculator returns the standardized score z = (x − μ) ÷ σ and the cumulative percentile Φ(z).
Formula
z = (x − μ) ÷ σ; percentile = Φ(z) × 100.
x- Raw value
μ- Mean
σ- Standard deviation
z- Z-score
Examples
- 85 in a distribution with μ=70, σ=10Value 85 · mean 70 · σ 10z = 1.5 · ≈ 93.3rd percentile
Frequently asked questions
What does the z-score tell me?
How many standard deviations a value is above (positive) or below (negative) the mean.
What is the percentile?
The proportion of a normal distribution that falls at or below the value (Φ(z)).
How to read the result
A z-score of 0 is the mean; each unit of z is one standard deviation.
Limitations
Assumes a normal distribution; standard deviation must be positive.
Source: Standard score (z = (x − μ) / σ) and the standard normal CDF.