Z-Score & Percentile Calculator
Convert a value to a z-score and percentile from the mean and standard deviation — or a percentile back to a value — using the normal distribution.
How to use
- 1Enter the mean and standard deviation.
- 2Enter a value to get its z-score and percentile, or switch to find the value at a percentile.
How it's calculated
z = (x − μ) ÷ σ. Percentile = Φ(z), the standard normal CDF. Value at percentile p = μ + σ × Φ⁻¹(p).
Frequently asked questions
What does a z-score of 2 mean?
The value is 2 standard deviations above the mean — higher than about 97.7% of values in a normal distribution.
What's the 68-95-99.7 rule?
In a normal distribution about 68% of values fall within 1 SD of the mean, 95% within 2 and 99.7% within 3.
Does my data have to be normal?
Z-scores can always be calculated, but percentiles from Φ are only accurate if the data is roughly normally distributed.