Z-Score Calculator

Find how many standard deviations a value is from the mean, and what percent of a normal distribution falls below it.

What Do You Want to Find?
Negative z-scores work.
–
Z-score
Below (percentile)
Above
Between −|z| and |z|
Value
Work

Saved Calculations

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How to Calculate a Z-Score

z = (x − μ) ÷ σ   x = μ + zσ

The percentile comes from the standard normal cumulative distribution Φ(z). Handy benchmarks: about 68% of values are within 1 standard deviation, 95% within 1.96, and 99.7% within 3.

Worked Example

Tips

Percentiles assume the data is roughly normal (bell-shaped). For a sample, use the sample mean and standard deviation. Probabilities are computed to better than 6 decimal places.