About this tool
The Z-Score Calculator is a free, in-browser tool that standardizes a raw value using z = (x − μ)/σ and translates the result into probabilities: the percentile (area to the left of the value on the standard normal curve), the probability of scoring above it, and the equivalent T-score used in many psychological and educational tests. A reverse mode converts a known z-score back into a raw value with x = μ + zσ.
Enter the value, the population mean and the standard deviation and every figure updates live. The normal CDF is computed with the Abramowitz–Stegun erf approximation (accurate to about 7 decimal places), entirely in your browser.
Frequently asked questions
What does a z-score tell me?
It expresses how many standard deviations a value lies above (positive) or below (negative) the mean, which lets you compare scores from different scales — e.g. 85 with mean 75 and sd 10 gives z = 1, the 84.13th percentile.
How is the percentile obtained from the z-score?
The percentile is the standard normal cumulative probability Φ(z) × 100 — the share of a normal population scoring at or below your value. The tile next to it shows 1 − Φ(z), the share scoring above.
What is the T-score shown in the results?
It is the linear rescaling T = 50 + 10z used in psychometrics, giving a scale with mean 50 and standard deviation 10 — unrelated to Student's t statistic.
Does this require the data to be normally distributed?
The z-score itself is just a rescaling and always valid, but the percentile and tail probability assume an approximately normal distribution; for clearly skewed data they will not match empirical ranks.