Z-Score Calculator
Find
Result
z = 2.6
78 is 2.6 standard deviations above the mean, at the 99.53rd percentile of a normal distribution.
- P(X < 78)
- 0.9953
- P(X > 78)
- 0.0047
- Two-tailed P(|Z| ≥ 2.6)
- 0.0093
Standard normal curve
z = (x − μ) ÷ σ. About 68% of a normal distribution lies within 1 standard deviation of the mean, 95% within 1.96 and 99.7% within 3. Percentiles assume the data are roughly normal; for skewed data, rank the actual values instead.
Standardize a value against a normal distribution: its z-score, the percentile it falls at and its one- and two-tailed probabilities. The calculator also finds the probability between two values and the value at any percentile.
Formula
Worked Example
78 sits (78 − 65) ÷ 5 = 2.6 standard deviations above the mean. Φ(2.6) = 0.9953, so 99.53% of a normal distribution lies below it and fewer than 1 in 200 values are higher.
Frequently Asked Questions
What z-score is considered unusual?
In many contexts, absolute z-scores above 2 are uncommon and above 3 are rare under normal assumptions.
Can z-score be negative?
Yes. Negative values indicate observations below the mean.